From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- macros/latex/contrib/mandi/README | 10 + macros/latex/contrib/mandi/mandi.dtx | 12180 +++++++++++++++++++++++++++++++++ macros/latex/contrib/mandi/mandi.ins | 81 + macros/latex/contrib/mandi/mandi.pdf | Bin 0 -> 1343851 bytes 4 files changed, 12271 insertions(+) create mode 100644 macros/latex/contrib/mandi/README create mode 100644 macros/latex/contrib/mandi/mandi.dtx create mode 100644 macros/latex/contrib/mandi/mandi.ins create mode 100644 macros/latex/contrib/mandi/mandi.pdf (limited to 'macros/latex/contrib/mandi') diff --git a/macros/latex/contrib/mandi/README b/macros/latex/contrib/mandi/README new file mode 100644 index 0000000000..cc3680da78 --- /dev/null +++ b/macros/latex/contrib/mandi/README @@ -0,0 +1,10 @@ +The mandi package provides commands for typesetting symbols, expressions, and +quantities used in introductory physics and astronomy. Many of the commands are +inspired by Matter & Interactions by Ruth Chabay and Bruce Sherwood. Many of +the astronomical commands were inspired by my own classroom needs. This package +does not do computations. It only provides commands for typesetting. + +Run mandi.ins through pdfLaTeX to generate files mandi.sty and vdemo.py. Run +mandi.dtx through pdfLaTeX to generate mandi.pdf (documentation). I assume a +TeX Live 2011 or later distribution is installed. + diff --git a/macros/latex/contrib/mandi/mandi.dtx b/macros/latex/contrib/mandi/mandi.dtx new file mode 100644 index 0000000000..7c2653c695 --- /dev/null +++ b/macros/latex/contrib/mandi/mandi.dtx @@ -0,0 +1,12180 @@ +% \iffalse meta-comment +% !TEX TS-program = dtxmk +% +% Copyright (C) 2018 by Paul J. Heafner +% --------------------------------------------------------------------------- +% This work may be distributed and/or modified under the conditions of the +% LaTeX Project Public License, either version 1.3 of this license or (at +% your option) any later version. The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.3 or later is part of all distributions of LaTeX version +% 2005/12/01 or later. +% +% This work has the LPPL maintenance status `maintained'. +% +% The Current Maintainer of this work is Paul J. Heafner. +% +% This work consists of the files mandi.dtx +% mandi.ins +% mandi.pdf +% README +% +% and includes the derived files mandi.sty +% vdemo.py. +% --------------------------------------------------------------------------- +% +% \fi +% +% \iffalse +% +%<*internal> +\iffalse +% +% +%<*package> +%%\ProvidesPackage{mandi}[2019/01/12 2.7.5 Macros for physics and astronomy] +\NeedsTeXFormat{LaTeX2e}[1999/12/01] +% +% +%<*vdemo> +# +from vpython import * + +G = 6.7e-11 + +# create objects +giant = sphere(pos=vector(-1e11,0,0),radius=2e10,mass=2e30,color=color.red) +giant.p = vector(0,0,-1e4) * giant.mass +dwarf = sphere(pos=vector(1.5e11,0,0),radius=1e10,mass=1e30,color=color.yellow) +dwarf.p = -giant.p + +for a in [giant,dwarf]: + a.orbit = curve(color=a.color,radius=2e9) + +dt = 86400 +while 1: + rate(100) + dist = dwarf.pos - giant.pos + force = G * giant.mass * dwarf.mass * dist / mag(dist)**3 + giant.p = giant.p + force*dt + dwarf.p = dwarf.p - force*dt + for a in [giant,dwarf]: + a.pos = a.pos + a.p/a.mass * dt + a.orbit.append(pos=a.pos) +% +% +%<*internal> +\fi +\def\nameofplainTeX{plain} +\ifx\fmtname\nameofplainTeX\else + \expandafter\begingroup +\fi +% +% +%<*internal> +\ifx\fmtname\nameofplainTeX + \expandafter\endbatchfile +\else + \expandafter\endgroup +\fi +% +% +%<*driver> +\ProvidesFile{mandi.dtx} +% +% +%<*driver> +\documentclass[10pt]{ltxdoc} +\setlength{\marginparwidth}{0.50in} % placement of todonotes +\usepackage{\jobname} % load mandi +\usepackage{parskip} % no indents/space btwn paras +\usepackage[textwidth=1.0cm]{todonotes} % allow for todonotes +\usepackage[left=0.75in,right=1.00in]{geometry} % main documentation +\usepackage{array,rotating,microtype} % accessory packages +\usepackage[listings,documentation]{tcolorbox} % workhorse package +\usepackage{anyfontsize} +\usepackage{float} +\usepackage{changepage} %%%%%%%%%% +\usepackage{nameref} +\hypersetup{colorlinks, linktoc=all} +\tcbset{index german settings} +\tcbset{color hyperlink=blue} +\tcbset{doc head command={interior style={fill,left color=red!15!white}}} +\tcbset{color command=red} +\tcbset{doc head environment={interior style={fill,left color=red!15!white}}} +\tcbset{color environment=red} +\tcbset{lefthand ratio=0.70} +\newcommandx{\ntodo}[2][1,usedefault]{% + \ifthenelse{\equal{#1}{}} + {\todo[size=\footnotesize,fancyline,caption={#2},color=yellow!40] + {\begin{sideways}#2\end{sideways}}} + {\todo[size=\footnotesize,fancyline,caption={#1},color=yellow!40] + {\begin{sideways}#2\end{sideways}}}} +\DisableCrossrefs % index descriptions only +\PageIndex % index contains page numbers +\CodelineNumbered % number source lines +\RecordChanges % record changes +\begin{document} % main document + \DocInput{\jobname.dtx} + \newgeometry{left=1.00in,right=1.00in,top=1.00in,bottom=1.00in} + \PrintIndex + \restoregeometry +\end{document} % end main document +% +% \fi +% +% \newcommand*{\pkgname}[1]{\texttt{#1}} +% \newcommand*{\mandi}{\pkgname{mandi}} +% \newcommand*{\mi}{\textit{Matter \& Interactions}} +% \hyphenation{Matter Interactions} +% \newcommand*{\opt}[1]{\textsf{\textbf{#1}}} +% \newcommand*{\baseunits}{\emph{baseunits}} +% \newcommand*{\drvdunits}{\emph{drvdunits}} +% \newcommand*{\altnunits}{\emph{altnunits}} +% +% \IndexPrologue{\section{Index}Page numbers refer to page where the +% corresponding entry is described. Not every command defined in the +% package is indexed. There may be commands similar to indexed commands +% described in relevant parts of the documentation.} +% +% \CheckSum{6558} +% +% \CharacterTable +% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +% Digits \0\1\2\3\4\5\6\7\8\9 +% Exclamation \! Double quote \" Hash (number) \# +% Dollar \$ Percent \% Ampersand \& +% Acute accent \' Left paren \( Right paren \) +% Asterisk \* Plus \+ Comma \, +% Minus \- Point \. Solidus \/ +% Colon \: Semicolon \; Less than \< +% Equals \= Greater than \> Question mark \? +% Commercial at \@ Left bracket \[ Backslash \\ +% Right bracket \] Circumflex \^ Underscore \_ +% Grave accent \` Left brace \{ Vertical bar \| +% Right brace \} Tilde \~} +% +% \providecommand*{\url}{\texttt} +% \GetFileInfo{\jobname.sty} +% \title{The \textsf{mandi} package} +% \author{Paul J. Heafner +% (\href{mailto:heafnerj@gmail.com?subject=[Heafner]\%20mandi} +% {\nolinkurl{heafnerj@gmail.com}})} +% ^^A \date{Version \fileversion~dated \filedate} +% \date{Version \mandiversion} +% +% \newgeometry{left=1.0in,right=1.0in,top=4.0in} +% \pagenumbering{gobble} +% \hypersetup{pageanchor=false} +% \begin{titlepage} +% \maketitle +% \end{titlepage} +% \hypersetup{pageanchor=true} +% \pagenumbering{arabic} +% \restoregeometry +% +% ^^A \centerline{\textbf{PLEASE DO NOT DISTRIBUTE THIS VERSION.}} +% +% \newgeometry{left=1.0in,right=1.0in,top=1.0in,bottom=1.0in} +% \tableofcontents +% \newpage +% \phantomsection +% \addcontentsline{toc}{section}{Change History} +% \PrintChanges +% \newpage +% \phantomsection +% \addcontentsline{toc}{section}{Program Listings} +% \lstlistoflistings +% \newpage +% \restoregeometry +% +%\changes{v2.4.0}{2014/12/16}{Made option names consistent with default behavior.} +%\changes{v2.4.0}{2014/12/16}{Added option for boldface vector kernels.} +%\changes{v2.4.0}{2014/12/16}{Added option for approximate values of constants.} +%\changes{v2.4.0}{2014/12/16}{Added magnetic charge.} +%\changes{v2.4.0}{2014/12/16}{\cs{vpythonfile} now uses a uniform style.} +%\changes{v2.4.0}{2014/12/16}{Added table of all predefined quantities with units.} +%\changes{v2.4.0}{2014/12/16}{Added table of all predefined constants +% with their symbols and units.} +%\changes{v2.4.0}{2014/12/16}{Added Maxwell's equations in both integral +% and differential forms, both with and without magnetic monopoles.} +%\changes{v2.4.0}{2014/12/16}{Added Lorentz force, with and +% without magnetic monopoles.} +%\changes{v2.4.0}{2014/12/16}{\cs{vpythonline} now uses a uniform style.} +%\changes{v2.4.0}{2014/12/16}{\texttt{vpythonblock} now uses a uniform style.} +%\changes{v2.4.0}{2014/12/17}{Now coexists with the \pkgname{commath} package.} +%\changes{v2.4.0}{2014/12/19}{Removed compatibility check for the \pkgname{physymb} +% package.} +%\changes{v2.4.1}{2015/02/11}{\texttt{vpythonblock} now accepts an optional caption.} +%\changes{v2.4.1}{2015/02/11}{\cs{vpythonfile} now accepts an optional caption.} +%\changes{v2.4.1}{2015/02/14}{Commands that use \pkgname{mdframed} +% will not break over pages.} +%\changes{v2.4.1}{2015/02/20}{Added \cs{scompsCvect} for superscripted +% components.} +%\changes{v2.4.1}{2015/02/20}{Added \cs{scompsRvect} for superscripted +% components.} +%\changes{v2.4.1}{2015/01/23}{Added more VPython keywords.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{smallanswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{mediumanswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{largeanswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{largeranswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{hugeanswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{hugeranswerform}.} +%\changes{v2.4.2}{2015/06/08}{Added \cs{fullpageanswerform}.} +%\changes{v2.5.0}{2016/01/26}{Added explicit mention of VPython and GlowScript.} +%\changes{v2.5.0}{2016/01/26}{Added GlowScript keywords.} +%\changes{v2.5.0}{2016/01/26}{Added example showing how to handle long +% lines and suppressing numbers on broken lines.} +%\changes{v2.5.0}{2016/01/26}{\cs{vpythonfile} now begins listings on a new page.} +%\changes{v2.5.0}{2015/09/13}{Removed autosized parentheses in math mode.} +%\changes{v2.5.0}{2015/09/13}{Removed compatibility check for the \pkgname{commath} +% package.} +%\changes{v2.5.0}{2015/09/13}{Renamed \cs{abs} to \cs{absof}.} +%\changes{v2.5.0}{2015/09/13}{\cs{absof} now shows a placeholder for a +% blank argument.} +%\changes{v2.5.0}{2015/09/13}{\cs{magof} now shows a placeholder for a +% blank argument.} +%\changes{v2.5.0}{2015/09/13}{\cs{dimsof} now shows a placeholder for a +% blank argument.} +%\changes{v2.5.0}{2015/09/13}{\cs{unitsof} now shows a placeholder for a +% blank argument.} +%\changes{v2.5.0}{2015/09/13}{Added \cs{inparens} for grouping with +% parentheses.} +%\changes{v2.5.0}{2015/09/13}{Changed behavior of \cs{sneakyone}.} +%\changes{v2.5.0}{2015/10/08}{Added \cs{eulerlagrange} command to +% typeset the Euler-Lagrange equation.} +%\changes{v2.5.0}{2015/10/08}{Added \cs{Lagr} to get symbol for +% Lagrangian.} +%\changes{v2.5.0}{2015/10/08}{Added color to \cs{checkpoint}.} +%\changes{v2.5.0}{2015/10/08}{Added \cs{qed} symbol.} +%\changes{v2.5.0}{2015/10/09}{Added \cs{ueuzero} and friends.} +%\changes{v2.5.0}{2015/10/09}{Added commands for Dirac notation.} +%\changes{v2.5.0}{2015/10/09}{Documented precise and approximate +% constant values.} +%\changes{v2.5.0}{2015/10/14}{\cs{miderivation} now prints line numbers.} +%\changes{v2.5.0}{2015/10/14}{Added \cs{miderivation*} to suppress line +% numbers.} +%\changes{v2.5.0}{2015/10/14}{\cs{bwderivation} now shows line numbers.} +%\changes{v2.5.0}{2015/10/14}{Added \cs{bwderivation*} to suppress line +% numbers.} +%\changes{v2.5.0}{2015/10/14}{\cs{mysolution} now prints line numbers.} +%\changes{v2.5.0}{2015/10/14}{Added \cs{mysolution*} to suppress line numbers.} +%\changes{v2.5.0}{2015/10/16}{Added \cs{taigrad} to get Tai's gradient symbol.} +%\changes{v2.5.0}{2015/10/16}{Added \cs{taisvec} to get Tai's symbolic vector.} +%\changes{v2.5.0}{2015/10/16}{Added \cs{taigrad} to get Tai's divergence symbol.} +%\changes{v2.5.0}{2015/10/16}{Added \cs{taigrad} to get Tai's curl symbol.} +%\changes{v2.5.0}{2015/10/20}{Added \cs{scompsdirvect}.} +%\changes{v2.5.0}{2015/10/20}{Added \cs{compdirvect}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{componentalong}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{expcomponentalong}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{ucomponentalong}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{projectiononto}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{expprojectiononto}.} +%\changes{v2.5.0}{2015/11/29}{Added \cs{uprojectiononto}.} +%\changes{v2.5.0}{2015/11/29}{Fixed parentheses bug in \cs{magvectncomps}.} +%\changes{v2.5.0}{2015/12/27}{Added option for radians in certain angular +% quantities.} +%\changes{v2.5.1}{2016/03/13}{Fixed errors in build for uploading to CTAN.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectormomentum}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectordisplacement}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorvelocityc}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorvelocity}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectoracceleration}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorgravitationalfield}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorimpulse}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorforce}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorangularvelocity}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorangularacceleration}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorangularmomentum}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorangularimpulse}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectortorque}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorwavenumber}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorelectricfield}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorelectricdipolemoment}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectormagneticfield}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectormagneticdipolemoment}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorcurrentdensity}.} +%\changes{v2.6.0}{2016/04/30}{Added \cs{vectorcmagneticfield}.} +%\changes{v2.6.0}{2016/05/02}{Created a student guide.} +%\changes{v2.6.0}{2016/05/02}{Changed placeholder to underscore.} +%\changes{v2.6.0}{2016/05/02}{Changed placeholder to underscore.} +%\changes{v2.6.0}{2016/05/02}{Changed placeholder to underscore.} +%\changes{v2.6.0}{2016/05/02}{Changed placeholder to underscore.} +%\changes{v2.6.0}{2016/05/02}{Changed placeholder to underscore.} +%\changes{v2.6.0}{2016/05/02}{Added \cs{problem} environment.} +%\changes{v2.6.0}{2016/05/02}{Added \cs{reason}.} +%\changes{v2.6.0}{2016/05/03}{Added \cs{energyflux}.} +%\changes{v2.6.0}{2016/05/03}{Added \cs{momentumflux}.} +%\changes{v2.6.0}{2016/05/03}{Added \cs{poyntingvector}.} +%\changes{v2.6.0}{2016/05/03}{Added many new commands that format expressions +% with placeholders for numerical quantities.} +%\changes{v2.6.0}{2016/05/10}{Replaced \cs{evalfromto} with \cs{evaluatedfromto}.} +%\changes{v2.6.0}{2016/05/10}{Replaced \cs{evalat} with new \cs{evaluatedat}.} +%\changes{v2.6.0}{2016/05/10}{Removed deprecated commands.} +%\changes{v2.6.0}{2016/05/11}{Added \cs{direction}.} +%\changes{v2.6.0}{2016/05/11}{Added \cs{vectordirection}.} +%\changes{v2.6.0}{2016/05/11}{Added \cs{vectorenergyflux}.} +%\changes{v2.6.0}{2016/05/11}{Added \cs{vectormomentumflux}.} +%\changes{v2.6.0}{2016/05/12}{Added \cs{glowscriptline}.} +%\changes{v2.6.0}{2016/05/12}{Added \texttt{glowscriptblock}.} +%\changes{v2.6.0}{2016/05/12}{Added \cs{glowscriptfile}.} +%\changes{v2.6.0}{2016/05/16}{Extensive revisions to documentation.} +%\changes{v2.6.0}{2016/05/18}{Option \opt{singleabsbars} renamed to +% \opt{singlemagbars}.} +%\changes{v2.6.0}{2016/05/20}{Documented \cs{chkquantity}.} +%\changes{v2.6.0}{2016/05/20}{Documented \cs{chkconstant}.} +%\changes{v2.6.0}{2016/05/20}{Documented \cs{mandiversion}.} +%\changes{v2.6.0}{2016/05/23}{Loads the \pkgname{tensor} package for future use.} +%\changes{v2.6.1}{2016/06/30}{Fixed \cs{mandiversion} so it displays correctly +% in math mode.} +%\changes{v2.6.1}{2016/06/30}{Fixed errors in Student Quick Guide documentation.} +%\changes{v2.6.2}{2016/07/31}{Made minor changes to the documentation.} +%\changes{v2.6.3}{2016/09/02}{Added \cs{mistandard} for standards.} +%\changes{v2.6.3}{2016/09/02}{Added \cs{bwstandard} for standards.} +%\changes{v2.6.3}{2016/09/07}{Added \cs{infeetpersecond}.} +%\changes{v2.6.3}{2016/09/08}{Added scaling options to \cs{image}.} +%\changes{v2.6.3}{2016/09/08}{Tweaked \cs{image} to work in documentation.} +%\changes{v2.6.3}{2016/09/08}{Added \cs{infeet}.} +%\changes{v2.6.3}{2016/09/08}{Added \cs{infeetpersecondsquared}.} +%\changes{v2.6.3}{2016/09/11}{Loads the \pkgname{float} package for \cs{image}.} +%\changes{v2.7.0}{2016/12/16}{Changed \cs{vectdotvect} to use \cs{cdot}.} +%\changes{v2.7.0}{2016/12/16}{Added \cs{vectDotvect} to use \cs{bullet}.} +%\changes{v2.7.0}{2017/02/02}{Made numerous internal changes to eliminate warnings.} +%\changes{v2.7.0}{2017/02/02}{Added blank output lines around mandi messages +% during compilation.} +%\changes{v2.7.0}{2017/02/02}{Changed first line of VPython programs to match +% Jupyter Notebook syntax.} +%\changes{v2.7.0}{2017/02/02}{Changed \cs{reason} to use minipage.} +%\changes{v2.7.0}{2017/02/02}{Added fourth argument to \cs{image} for a label.} +%\changes{v2.7.0}{2017/03/17}{Added \cs{dslashx} for inexact differentials.} +%\changes{v2.7.0}{2017/04/13}{Added \cs{factorvect}.} +%\changes{v2.7.0}{2017/04/13}{Added \cs{circulation}.} +%\changes{v2.7.0}{2017/09/01}{Added better looking parallel symbol.} +%\changes{v2.7.0}{2017/09/01}{Added an alias for the perpendicular symbol.} +%\changes{v2.7.0}{2018/01/11}{Added instructions for Overleaf users.} +%\changes{v2.7.2}{2018/03/14}{Changed \emph{tradunits} to \opt{altnunits}.} +%\changes{v2.7.2}{2018/03/16}{Documented the \cs{redefinephysicsquantity} command.} +%\changes{v2.7.2}{2018/03/16}{Documented the \cs{redefinephysicsconstant} command.} +%\changes{v2.7.2}{2018/03/18}{Changed \cs{lorentz} to \cs{lorentzfactor}.} +%\changes{v2.7.2}{2018/03/19}{Made \opt{drvdunits} the default.} +%\changes{v2.7.2}{2018/03/19}{Adjusted units of some predefined quantities and +% constants.} +%\changes{v2.7.2}{2018/03/20}{Added expanded instructions for Overleaf users.} +%\changes{v2.7.3}{2018/04/06}{Reformatted source code to allow for better +% documentation of changes.} +%\changes{v2.7.3}{2018/11/10}{Added \cs{emptyunit}. Thanks to Dr. Brian Lane +% for suggesting this implementation.} +%\changes{v2.7.3}{2018/11/11}{Added \cs{anglebetween}.} +%\changes{v2.7.3}{2018/11/13}{Made variable in series expansions a parameter +% with \(x\) as the default.} +%\changes{v2.7.3}{2018/12/27}{Modified \cs{vpythonfile} and \cs{vpythonblock} to +% include both captions and labels.} +%\changes{v2.7.4}{2019/01/12}{Revised Overleaf instructions to reflect new version.} +%\changes{v.2.7.5}{2019/01/12}{Revised documentation for Overleaf yet again.} +% +% \section{Introduction} +% This package provides a collection of commands useful in introductory physics +% and astronomy. The underlying philosophy is that the user, potentially an +% introductory student, should just type the name of a physical quantity, with a +% numerical value if needed, without having to think about the units. \mandi\ +% will typeset everything correctly. For symbolic quantities, the user should +% type only what is necessary to get the desired result. What one types should +% correspond as closely as possible to what one thinks when writing. The package +% name derives from \mi +% \footnote{See the \mi\ home page at \url{https://www.matterandinteractions.org/} +% for more information about this innovative introductory calculus-based physics +% curriculum.} by Ruth Chabay and Bruce Sherwood. The package certainly is rather +% tightly tied to that textbook but can be used for typesetting any document that +% requires consistent physics notation. With \mandi\ many complicated expressions +% can be typeset with just a single command. Great thought has been given to +% command names and I hope users find the conventions logical and easy to remember. +% +% There are other underlying philosophies and goals embedded within \mandi, +% all of which are summarized here. These philosophies are +% \begin{itemize} +% \item to employ a \emph{type what you think} model for remembering commands, +% \item to relieve the user of having to explicitly worry about typesetting SI +% units, +% \item to enforce certain concepts that are too frequently merged, such as the +% distinction between a vector quantity and its magnitude (e.g.\ we often use +% the same name for both), +% \item to enforce consistent terminology in the naming of quantities, with names +% that are both meaningful to introductory students and accurate +% (e.g.\ \emph{duration} vs.\ \emph{time}), and +% \item to enforce consistent notation, especially for vector quantities. +% \end{itemize} +% +% I hope that using \mandi\ will cause users to form good habits that +% benefit physics students. +% +% \section{Building From Source} +% I am assuming the user will use pdf\LaTeX, which creates PDF files as output, +% to build the documentation. I have not tested the build with with standard \LaTeX, +% which creates DVI files. +% +% The latest useable version is always found on the \mandi\ home page at +% \url{https://tensortime.sticksandshadows.com/mandi} and note that the version there +% may not yet have been pushed to \href{https://ctan.org}{CTAN}. +% +% \newpage +% \section{Loading the Package}\label{LoadingthePackage} +% To load \mandi\ with its default options, simply put the line |\usepackage{mandi}| +% in your document's preamble. To use the package's available options, put the line +% |\usepackage|\textbf{[}\opt{options}\textbf{]}|{mandi}| in your document's +% preamble. There are eight available options, all of which are described below. +% +% \begin{itemize} +% \item \opt{boldvectors} gives bold letters for the kernels of vector names. +% No arrows are used above the kernel. +% \item \opt{romanvectors} gives Roman letters for the kernels of vectors names. +% An arrow appears over the kernel. +% \end{itemize} +% +% If neither \opt{boldvectors} nor \opt{romanvectors} is specified (the +% default), vectors are displayed with italic letters for the kernels of vector +% names and an arrow appears over the kernel. +% +% \begin{itemize} +% \item \opt{singlemagbars} gives single bars in symbols for vector magnitudes +% instead of the default double bars. Double bars may be more familiar to +% students from their calculus courses. +% \item \opt{approxconsts} gives approximate values of constants to one or two +% significant figures, depending on how they appear in \mi, instead of the +% default precise values. +% \item \opt{useradians} gives radians in the units of angular momentum, +% angular impulse, and torque. The default is to not use radians in the units +% of these quantities. +% \item \opt{baseunits} causes all units to be displayed in \baseunits\ form, with +% SI base units. No solidi (slashes) are used. Positive and negative exponents +% are used to denote powers of various base units. +% \item \opt{drvdunits} causes all units to be displayed, when possible, in +% \drvdunits\ form, with SI derived units. Students may already be familiar with +% many of these derived units. +% \item \opt{altnunits} causes all units to be displayed in \altnunits\ form, +% which is intended to allow for custom units when desired. This is sometimes +% helpful for enhancing conceptual understanding in some situations. +% \end{itemize} +% +% If neither \opt{baseunits} nor \opt{altnunits} is specified, units are +% displayed in \drvdunits\ form, which is typically the way they would usually +% appear in textbooks. Units in this form may hide the underlying physical +% meaning or indeed may do precisely the opposite and enhance conceptual +% understanding. In this document, the default is to use +% \ifthenelse{\boolean{@optbaseunits}} +% {base} +% {\ifthenelse{\boolean{@optaltnunits}} +% {alternate} +% {derived}} +% units. As you will see later, there are ways to override these options either +% temporarily or permanently. +% +% \mandi\ coexists with the \pkgname{siunitx} package. While there is some +% functional overlap between the two packages, \mandi\ is completely independent of +% \pkgname{siunitx}. The two are designed for different purposes and probably also +% for different audiences, but can be used together if desired. \mandi\ coexists with +% the \pkgname{commath} package. There is no longer a conflict because \mandi's +% |\abs| command has been renamed to \refCom{absof}. \mandi\ no longer checks for the +% presence of the \pkgname{physymb} package. That package now incorporates \mandi\ +% dependencies, and the two are completely compatible as far as I know. +% +%\mandi\ loads the \pkgname{tensor} for likely future use. See that package's +% documentation for its commands and how to use them. There are no known conflicts +% between \mandi\ and \pkgname{tensor}. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mandiversion}{} +Gives the current package version number and build date. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\mandiversion +\end{dispExample*} +%\iffalse +% +%\fi +% +% \newpage +% \section{Overleaf Users} +% \href{https://www.overleaf.com}{Overleaf.com} is an online \LaTeX\ environment +% with widespread use. It uses a full \TeX/\LaTeX\ installation but may not always +% have the latest version of every package installed (for stability reasons). +% Sometimes packages are updated more frequently than the large distributions are +% updated. If you want to always be sure you're using the latest version of \mandi\ +% make sure the files \pkgname{mandi.sty} and \pkgname{mandi.pdf} are in your +% Overleaf project folder. The package can now be used in your documents. +% +% If you are a student, here are detailed instructions on how to use \mandi\ +% in your Overleaf project. +% \begin{enumerate} +% \item Direct your browser to +% \href{https://tensortime.sticksandshadows.com/mandi} +% {https://tensortime.sticksandshadows.com/mandi} and fetch the file named +% \texttt{overleaf-template.zip}. Download it and open the zip file into a +% temporary folder on your computer. +% \item Go to the \href{https://www.overleaf.com}{Overleaf.com} website and +% create a free account and then sign into that account. +% \item Upon signing in, you should see a list of your current projects. Look +% for the New Project button on the left and click on it. Click on Blank Project. +% You will be asked to name your new project. Choose this name very carefully +% because it will also be the name of the compiled PDF file generated by compiling +% the project's main file. +% \item Once named, your new project will be created and you will be taken to its +% new folder. You will see a file named \texttt{main.tex}. For now, just leave it +% alone. +% \item Click the user interface element resembling an upward arrow attached to +% a tray (a popup labeled \texttt{Upload} appears when you hover over it) to open +% the file upload dialog. Select all the files (there should be six) in the +% temporary overleaf-template folder you previously created. Upload them +% into your project's folder. You can now delete the \texttt{main.tex} file. +% \item Click on the word \texttt{Menu} in the upper left corner of the window, +% then scroll down and look for the Main document setting. Make sure +% \texttt{NnnnnnnnCCPxx.tex} is selected as the project's main file. +% \item From now on, to start a new project, begin by copying this master +% project template and creating a new name for the new project. This way, +% you will build a neatly organized collection of logically named projects +% and the original Master Template will never have to be modified (but see +% next step) and every project will have \mandi\ available for use. +% \item If \mandi\ is updated by the developer, all you need to do is make +% sure the new \texttt{mandi.sty} and \texttt{mandi.pdf} files, and perhaps +% a few others if the developer has modified them, are uploaded to your project +% folders. +% \item You can now delete the \texttt{overleaf-template.zip} file and the +% temporary folder you created on your computer. +% \end{enumerate} +% +% \newpage +% \section{Student Quick Guide} +% Use \refCom{vect} to put an arrow over a symbol to make it the symbol for a vector. +% Typing |\vect{p}| gives \vect{p}. +% +% Use \refCom{vectsub} if the symbol needs a subscript. Typing |\vectsub{p}{ball}| +% gives \vectsub{p}{ball}. +% +% Use \refCom{magvect} or \refCom{magvectsub} to get the symbol for a vector's +% magnitude. Typing |\magvect{p}| gives \magvect{p}. Typing |\magvectsub{p}{ball}| +% gives \magvectsub{p}{ball}. +% +% Use \refCom{dirvect} or \refCom{dirvectsub} to get the symbol for a vector's +% direction. Typing |\dirvect{p}| or |\dirvectsub{p}{ball}| gives \dirvect{p} or +% \dirvectsub{p}{ball}. +% +% Use \refCom{compvect} to write the symbol for one of a vector's coordinate +% components. Typing |\compvect{v}{z}| gives \compvect{v}{z}. +% +% Use a \hyperlink{target2}{physical quantity's} name followed by a numerical value +% in curly braces to typeset that numerical value and an appropriate +% \hyperlink{target1}{SI unit}. +% Using \refCom{velocity} by typing |\velocity{2.5}| gives +% \velocity{2.5}. Use \refCom{newphysicsquantity} to define any new quantity +% you need. +% +% Many \hyperlink{target3}{physical constants} are defined in \mandi\ and are +% well documented in the corresponding section. +% +% Use \refCom{mivector} to write the coordinate representation of a vector. +% Typing |\mivector{3,2,-4}| gives \mivector{3,2,-4}. Typing |\mivector{a,b,c}| +% gives \mivector{a,b,c}. +% +% Use \refCom{direction} to write the coordinate representation of a unit vector, +% which some authors call a direction. Typing |\direction{1,0,0}| gives +% \direction{1,0,0}. Directions have no units. +% +% To specify a vector quantity in terms of its coordinate components, you have two +% options. One way is to type the vector quantity's name as above, but use +% \refCom{mivector} to specify a list of three components separated by commas in +% curly braces as in |\velocity{\mivector{3,2,-4}}| to get +% \velocity{\mivector{3,2,-4}}. Another way is to prefix |\vector| to the quantity's +% name (with no leading backslash) and specify a list of three components separated +% by commas in curly braces as in |\vectorvelocity{3,2,-4}| to get +% \vectorvelocity{3,2,-4}. The output is the same either way. +% +% Use \refCom{timestento} or \refCom{xtento} to get scientific notation. +% Typing either |2.54\timestento{-4}| or |2.54\xtento{-4}| gives 2.54\timestento{-4}. +% +% Use \refCom{inparens} to surround quantities with nicely formatted parentheses. +% Typing |\inparens{x^2 + 4}| gives \inparens{x^2 + 4}. +% +% Use \refCom{define} to create a variable that can be used in an intermediate +% step in a solution. This is discussed \hyperlink{target5}{later in this section}. +% +% To typeset a matrix in parentheses, use the \cs{pmatrix} environment by putting +% the rows, between |\begin{pmatrix}| and |\end{pmatrix}|. Each row, except the +% last, must end with |\\|. Within each row, separate the columns with |&|. Note +% that \cs{pmatrix} typesets the matrix in parentheses. Use \cs{bmatrix} to typeset +% it in square brackets and \cs{vmatrix} to typeset it in single vertical bars +% to indicate a determinant. Use \cs{Vmatrix} to typeset it in double vertical +% bars. +% +%\iffalse +%<*example> +%\fi + \begin{dispExample*}{sidebyside,colframe=white,colback=white, lefthand ratio=0.70} + A second rank tensor represented as a matrix. + \[\begin{pmatrix} + \hphantom{-}T_{00} & T_{01} & -T_{02} \\ + -T_{10} & T_{11} & -T_{12} \\ + \hphantom{-}T_{20} & T_{21} & \hphantom{-}T_{22} + \end{pmatrix}\] + Alternate notation for a matrix. + \[\begin{bmatrix} + \hphantom{-}T_{00} & T_{01} & -T_{02} \\ + -T_{10} & T_{11} & -T_{12} \\ + \hphantom{-}T_{20} & T_{21} & \hphantom{-}T_{22} + \end{bmatrix}\] + The determinant of a matrix. + \[\begin{vmatrix} + \hphantom{-}T_{00} & T_{01} & -T_{02} \\ + -T_{10} & T_{11} & -T_{12} \\ + \hphantom{-}T_{20} & T_{21} & \hphantom{-}T_{22} + \end{vmatrix}\] + Alternate notation for the determinant of a matrix. + \[\begin{Vmatrix} + \hphantom{-}T_{00} & T_{01} & -T_{02} \\ + -T_{10} & T_{11} & -T_{12} \\ + \hphantom{-}T_{20} & T_{21} & \hphantom{-}T_{22} + \end{Vmatrix}\] + \end{dispExample*} +%\iffalse +% +%\fi +% +% Encapsulate an entire problem solution in a \refEnv{problem} environment by +% putting it between |\begin{problem}| and |\end{problem}|. +% +% Show the steps in a calculation in a \refEnv{mysolution} environment by putting +% them between |\begin{mysolution}| and |\end{mysolution}|. +% +% Use \cs{href} from the \pkgname{hyperref} package to link to URLs. +% |\href{http://glowscript.org}{GlowScript}| gives +% \href{http://glowscript.org}{GlowScript}. You can link to a specific +% \href{http://goo.gl/wPMqjp}{GlowScript program} when necessary. Links are +% active. +% +% Use \refCom{image} to insert diagrams. The diagram should be a PDF file. You +% \emph{must} remember to specify a meaningful caption for the diagram. You must +% also provide a unique label for the image so you can easily refer back to it +% elsewhere in your document. +% +% There are two main design goals behind this package. The first is to typeset +% numerical values of scalar and vector physical quantities and their SI units. The +% idea is to simply type a command corresponding to the quantity's name, specifying +% as an argument a single scalar value or the numerical components of a traditional +% Cartesian 3-vector, and let \mandi\ take care of the units. Every physical quantity +% you are likely to encounter in an introductory course is probably already defined, +% but there's a facility for defining new quantities if you need to. +% +% The second main design goal provides a similar approach to typesetting the most +% frequently used symbolic expressions in introductory physics. If you want to save +% time in writing out the expression for the electric field of a particle, just use +% +%\iffalse +%<*example> +%\fi +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Efieldofparticle +\end{dispExample*} +%\iffalse +% +%\fi +% +% which, as you can see, takes fewer keystrokes and it's easier to remember. Correct +% vector notation is automatically enforced, leading students to get used to seeing +% it and, hopefully, using it in their own calculations. Yes, this is a bit of an +% agenda on my part, but my experience has been that students don't recognize or +% appreciate the utility of vector notation and thus their physical reasoning may +% suffer as a result. So by using \mandi\ they use simple commands that mirror what +% they're thinking, or what they're supposed to be thinking (yes, another agenda), +% and in the process see the correct typeset output. +% +% There is another persistent problem with introductory physics textbooks, and that +% is that many authors do not use consistent notation. Many authors define the +% notation for a vector's magnitude to be either \magvect{a} or \absof{\vect{a}} in +% an early chapter, but then completely ignore that notation and simply use \(a\) +% later in the book. I have never understood the (lack of) logic behind this practice +% and find it more than annoying. Textbooks authors should know better, and should +% set a better example for introductory students. I propose that using \mandi\ +% would eliminate all last vestiges of all excuses for not setting this one good +% example for introductory students. +% +% If you are a student, using this package will very likely begin with using a +% pre-made document template supplied by your instructor. There will likely be a +% lot about the document that you won't understand at first. Look for a line that +% says |\begin{document}| and a corresponding line that says |\end{document}| You +% will add content between these two lines. Most of your content will be within the +% \refEnv{problem} environment. Each use of this environment is intended to +% encapsulate one complete written solution to one physics problem. In this way, +% you can build a library of problem solutions for your own convenience. +% +% Since students are this package's primary audience, nearly all of the commands +% have been defined with students in mind. Writing a problem solution in \LaTeX\ +% can be tedious to the beginner and some of the commands have been designed to +% minimize the tedium. For example, if you want to calculate something using an +% equation, you typically must write the equation, substitute numerical quantities +% with units if necessary, do the actual calculation, and then state the final +% result.Sometimes it is necessary to show intermediate steps in a calculation. +% \mandi\ can help with this. +% +% Here is a set of commands that typeset standard equations with placeholders where +% numerical quantities must be eventually inserted. Note that all of these commands +% end with the word |places| as a reminder that they generate placeholders. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{genericinteractionplaces} +{\marg{const}\marg{thing1}\marg{thing2}\marg{dist}\marg{direction}} +Command for generic expression for an inverse square interaction. The five +required arguments are, from left to right, a constant of proportionality, a +physical property of object 1, a physical property of object 2, the objects' +mutual separation, and a vector direction. In practice, these should all be +provided in numerical form. Note that negative signs must be placed manually. +\end{docCommand} +\begin{dispExample} +\genericinteractionplaces{}{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{genericfieldofparticleplaces} +{\marg{const}\marg{thing}\marg{dist}\marg{direction}} +Command for generic expression for an inverse square field. The four required +arguments are, from left to right, a constant of proportionality, a physical +property, relative distance to field point, and a vector direction. In practice, +these should all be provided in numerical form. Note that negative signs must be +placed manually. +\end{docCommand} +\begin{dispExample} +\genericfieldofparticleplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{genericpotentialenergyplaces} +{\marg{const}\marg{thing1}\marg{thing2}\marg{dist}} +Command for generic expression for an inverse square energy. The four required +arguments are, from left to right, a constant of proportionality, a physical +property of object 1, a physical property of object 2, and the objects' mutual +separation. In practice, these should all be provided in numerical form. Note that +negative signs must be placed manually. +\end{docCommand} +\begin{dispExample} +\genericpotentialenergyplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalinteractionplaces} +{\marg{mass1}\marg{mass2}\marg{distance}\marg{direction}} +Command for gravitational interaction. The four required arguments are, from +left to right, the first object's mass, the second object's mass, the objects' +mutual separation, and a vector direction. In practice, these should all be +provided in numerical form. Note that negative signs must be placed manually. +\end{docCommand} +\begin{dispExample} +\gravitationalinteractionplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gfieldofparticleplaces} +{\marg{mass}\marg{distance}\marg{direction}} +Command for gravitational field of a particle. The three required arguments are, +from left to right, the object's mass, the distance from the source to the field +point, and a vector direction. In practice, these should all be provided in +numerical form. Note that negative signs must be placed manually. +\end{docCommand} +\begin{dispExample} +\gfieldofparticleplaces{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalpotentialenergyplaces} +{\marg{mass1}\marg{mass2}\marg{distance}} +Command for gravitational potential energy. The three required arguments are, +from left to right, the first object's mass, the second object's mass, and +the object's mutual distance. In practice, these should all be provided in +numerical form. Note the inclusion of the leading negative sign. +\end{docCommand} +\begin{dispExample} +\gravitationalpotentialenergyplaces{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springinteractionplaces} +{\marg{stiffness}\marg{stretch}\marg{direction}} +Command for a spring interaction. The three required arguments are, from left +to right, the spring stiffness, the spring's stretch, and a vector direction. +In practice, these should all be provided in numerical form. Note that negative +signs must be placed manually or absorbed into the displacement vector. +\end{docCommand} +\begin{dispExample} +\springinteractionplaces{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springpotentialenergyplaces} +{\marg{stiffness}\marg{stretch}} +Command for spring potential energy. The two required arguments are, from left +to right, the spring stiffness and the spring stretch. In practice, these should +be provided in numerical form. +\end{docCommand} +\begin{dispExample} +\springpotentialenergyplaces{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{genericelectricdipoleonaxisplaces} +{\marg{const}\marg{charge}\marg{separation}\marg{dist}\marg{direction}} +Command for generic expression for dipole field on the dipole's axis. The five +required arguments are, from left to right, a constant of proportionality, a charge, +a dipole separation, the distance to the field point, and a vector direction. In +practice, these should all be provided in numerical form. +\end{docCommand} +\begin{dispExample} +\genericelectricdipoleonaxisplaces{}{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{genericelectricdipoleplaces} +{\marg{const}\marg{charge}\marg{separation}\marg{dist}\marg{direction}} +Command for generic expression for dipole field. The five required arguments are, +from left to right, a constant of proportionality, a charge, a dipole separation, +the distance to the field point, and a vector direction. In practice, these should +all be provided in numerical form. +\end{docCommand} +\begin{dispExample} +\genericelectricdipoleplaces{}{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricinteractionplaces} +{\marg{charge1}\marg{charge2}\marg{distance}\marg{direction}} +Command for electric interaction. The four required arguments are, from left to +right, the first object's charge, the second object's charge, the objects' mutual +separation, and a vector direction. In practice, these should all be provided in +numerical form. +\end{docCommand} +\begin{dispExample} +\electricinteractionplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Efieldofparticleplaces} +{\marg{charge}\marg{distance}\marg{direction}} +Command for electric field of a particle. The three required argument are, from +left to right, the particle's charge, the distance form the source to the field +point, and a vector direction. In practice, these should all be provided in +numerical form. +\end{docCommand} +\begin{dispExample} +\Efieldofparticleplaces{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Bfieldofparticleplaces} +{\marg{charge}\marg{magvel}\marg{magr}\marg{vhat}\marg{rhat}} +Command for magnetic field of a particle. The five required arguments are, from +left to right, the particle's charge, the particle's velocity, the distance from +the source to the field point, the velocity's direction, and a direction vector +from the source to the field point. In practice, these should all be provided in +numerical form. +\end{docCommand} +\begin{dispExample} +\Bfieldofparticleplaces{}{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricpotentialenergyplaces} +{\marg{charge1}\marg{charge2}\marg{distance}} +Command for electric potential energy. The three required arguments are, from +left to right, the first object's charge, the second object's charge, and the +objects' mutual distance. In practice, these should all be provided in numerical +form. +\end{docCommand} +\begin{dispExample} +\electricpotentialenergyplaces{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricdipoleonaxisplaces} +{\marg{charge}\marg{separation}\marg{dist}\marg{direction}} +Command for dipole electric field on the dipole's axis. The four required arguments +are, from left to right, a charge, a dipole separation, the distance to the field +point, and a vector direction. In practice, these should all be provided in numerical +form. +\end{docCommand} +\begin{dispExample} +\electricdipoleonaxisplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricdipoleonbisectorplaces} +{\marg{charge}\marg{separation}\marg{dist}\marg{direction}} +Command for dipole electric field. The four required arguments are, from left +to right, a charge, a dipole separation, the distance to the field point, and +a vector direction. In practice, these should all be provided in numerical form. +\end{docCommand} +\begin{dispExample} +\electricdipoleonbisectorplaces{}{}{}{} +\end{dispExample} +%\iffalse +% +%\fi +% +% The underlying strategy is to \emph{think about how you would say what you want +% to write and then write it the way you would say it}. With a few exceptions, this +% is how \mandi\ works. You need not worry about units because \mandi\ knows what +% SI units go with which physical quantities. You can define new quantities so that +% \mandi\ knows about them and in doing so, you give the new quantities the same +% names they would normally have. +% +% \hypertarget{target5}{So} now how to you go about getting numerical values (with +% units) into the placeholders? Use the \refCom{define} command to define a variable +% containing a desired quantity, and then pass that variable to the above commands +% and that quantity will appear in the corresponding placeholder. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{define}{\marg{variablename}\marg{quantity}} +Defines a variable, actually a new command, named \cs{variablename} and sets its +value to \cs{quantity}. \textbf{Note that digits are not permitted in command names +in \LaTeX.} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\define{\massone}{\mass{25}} +\end{dispExample*} +%\iffalse +% +%\fi +% +% Suppose you want to calculate the gravitational force on one object due to +% another. You need two masses, and their mutual distance, and a direction. You +% can say, for example, |\define{\massone}{\mass{5}| to create a variable |\massone| +% containing a mass of \mass{5}. Note that you don't have to worry about units +% because the \refCom{mass} command handles that for you. Similarly, you can go on +% and say |\define{\masstwo}{\mass{12}| and |\define{\myr}{\displacement{5}| and +% |\define{\mydir}{\mivector{0,-1,0}|. Now just call the +% \refCom{gravitationalinteractionplaces} command with these arguments (in the +% correct order of course) and \LaTeX\ will do the rest when you compile your +% document. The entire process would look like this: +% +%\iffalse +%<*example> +%\fi +\begin{dispExample} +\define{\massone}{\mass{5}} +\define{\masstwo}{\mass{12}} +\define{\myr}{\displacement{5}} +\define{\mydir}{\mivector{0,-1,0}} +\gravitationalinteractionplaces{\massone}{\masstwo}{\myr}{\mydir} = +\vectorforce{0,-1.60\xtento{-10},0} +\end{dispExample} +%\iffalse +% +%\fi +% +% Of course you must calculate the final numerical result yourself because \mandi\ +% doesn't (yet) do calculations. One very important restriction on variable names is +% that \LaTeX\ doesn't allow digits in command or variable names and thus that +% restriction applies here too. +% +% This barely scratches the surface in describing \mandi\ so continue reading this +% document to see everything it can do. You will learn new commands as you need +% them in your work. To start with, you should at least read the section on +% \hyperlink{target1}{SI units} and the section on +% \hyperlink{target2}{physical quantities}. +% +% \newpage +% \section{Features and Commands} +% \hypertarget{target1}{\subsection{SI Base Units and Dimensions}} +% This is not a tutorial on SI units and the user is assumed +% to be familiar with SI rules and usage. Begin by defining shortcuts for the units +% for the seven SI base quantities: +% \emph{spatial displacement} (what others call \emph{length}), \emph{mass}, +% \emph{temporal displacement} (what others call \emph{time}, but we will call +% it \emph{duration} in most cases), \emph{electric current}, \emph +% {thermodynamic temperature}, \emph{amount}, and \emph{luminous intensity}. +% These shortcuts are used internally and need not explicitly be invoked by the +% user. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{m}{} + Command for \href{https://en.wikipedia.org/wiki/metre}{metre}, the SI unit of + spatial displacement (length). +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{kg}{} + Command for \href{https://en.wikipedia.org/wiki/kilogram}{kilogram}, the SI unit + of mass. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{s}{} + Command for \href{https://en.wikipedia.org/wiki/second}{second}, the SI unit + of temporal displacement (duration). +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{A}{} + Command for \href{https://en.wikipedia.org/wiki/ampere}{ampere}, the SI unit + of electric current. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{K}{} + Command for \href{https://en.wikipedia.org/wiki/kelvin}{kelvin}, the SI unit + of thermodynamic temperature. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mol}{} + Command for \href{https://en.wikipedia.org/wiki/mole}{mole}, the SI unit of + amount. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{cd}{} + Command for \href{https://en.wikipedia.org/wiki/candela}{candela}, the SI + unit of luminous intensity. +\end{docCommand} +%\iffalse +% +%\fi +% +% If \mandi\ was loaded with \opt{baseunits}, then every physical quantity will +% have a unit that is some product of powers of these seven base SI units. +% Exceptions are angular quantities, which will include either degrees or radians +% depending upon the application. Again, this is what we mean by \baseunits\ form. +% +% Certain combinations of the SI base units have nicknames and each such +% combination and nickname constitutes a \emph{derived unit}. Derived units are +% no more physically meaningful than the base units, they are merely nicknames for +% particular combinations of base units. An example of a derived unit is the +% newton, for which the symbol (it is not an abbreviation) is \newton. However, +% the symbol \newton\ is merely a nickname for a particular combination of base +% units. It is not the case that every unique combination of base units has a +% nickname, but those that do are usually named in honor of a scientist. +% Incidentally, in such cases, the symbol is capitalized but the \emph{name} +% of the unit is \emph{never} capitalized. Thus we would write the name of the +% derived unit of force as newton and not Newton. Again, using these select +% nicknames for certain combinations of base units is what we mean by \drvdunits\ +% form. +% +% \subsection{SI Dimensions} +% For each SI unit, there is at least one corresponding dimension. Every physical +% quantity is some multiplicative product of each of the seven basic SI dimensions +% raised to a power. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimddisplacement}{} +Command for the symbol for the dimension of displacement. +\end{docCommand} +\begin{dispExample*}{sidebyside} +displacement has dimension of \dimdisplacement +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimmass}{} +Command for the symbol for the dimension of mass. +\end{docCommand} +\begin{dispExample*}{sidebyside} +mass has dimension of \dimmass +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimduration}{} +Command for the symbol for the dimension of duration. +\end{docCommand} +\begin{dispExample*}{sidebyside} +duration has dimension of \dimduration +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimcurrent}{} +Command for the symbol for the dimension of current. +\end{docCommand} +\begin{dispExample*}{sidebyside} +current has dimension of \dimcurrent +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimtemperature}{} +Command for the symbol for the dimension of temperature. +\end{docCommand} +\begin{dispExample*}{sidebyside} +temperature has dimension of \dimtemperature +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimamount}{} +Command for the symbol for the dimension of amount. +\end{docCommand} +\begin{dispExample*}{sidebyside} +amount has dimension of \dimamount +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimluminous}{} +Command for the symbol for the dimension of luminous intensity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +luminous has dimension of \dimluminous +\end{dispExample*} +%\iffalse +% +%\fi +% +% \hypertarget{target2}{\subsection{Defining Physical Quantities}} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{newphysicsquantity} +{\marg{newname}\marg{\baseunits}\oarg{\drvdunits}\oarg{\altnunits}} +Defines a new physical quantity and its associated commands. +\end{docCommand} +%\iffalse +% +%\fi +% +% Using this command causes several things to happen. +% \begin{itemize} +% \item A command \colDef{\cs{newname}}\marg{magnitude}, where \colDef{newname} +% is the first argument of \colDef{\cs{newphysicsquantity}}, is created that +% takes one mandatory argument, a numerical magnitude. Subsequent use of your +% defined scalar quantity can be invoked by typing \colDef{\cs{newname}} +% \marg{magnitude} and the units will be typeset according to the options +% given when \mandi\ was loaded. Note that if the \drvdunits\ and \altnunits\ +% forms are not specified, they will be populated with the \baseunits\ form. +% \item A command \colDef{\cs{newnamebaseunit}}\marg{magnitude} is created that +% expresses the quantity and its units in \baseunits\ form. +% \item A command \colDef{\cs{newnamedrvdunit}}\marg{magnitude} is created that +% expresses the quantity and its units in \drvdunits\ form. This command is +% created whether or not the first optional argument is provided. +% \item A command \colDef{\cs{newnamealtnunit}}\marg{magnitude} is created that +% expresses the quantity and its units in \altnunits\ form. This command is +% created whether or not the first optional argument is provided. +% \item A command \colDef{\cs{newnameonlybaseunit}}\marg{magnitude} is created +% that expresses \textbf{only} the quantity's units in \baseunits\ form. +% \item A command \colDef{\cs{newnameonlydrvdunit}}\marg{magnitude} is created +% that expresses \textbf{only} the quantity's units in \drvdunits\ form. +% \item A command \colDef{\cs{newnameonlyaltnunit}}\marg{magnitude} is created +% that expresses \textbf{only} the quantity's units in \altnunits\ form. +% \item A command \colDef{\cs{newnamevalue}}\marg{magnitude} is created that +% expresses \textbf{only} the quantity's numerical value. +% \end{itemize} +% +% As an example, consider momentum. The following commands are defined: +% +% \begin{quotation} +% \begin{tabular}{l l l} +% |\momentum{3}| &\momentum{3} & unit set by global options \\ +% |\momentumbaseunit{3}| &\momentumbaseunit{3} & quantity with base unit \\ +% |\momentumdrvdunit{3}| &\momentumdrvdunit{3} & quantity with derived unit \\ +% |\momentumaltnunit{3}| &\momentumaltnunit{3} & quantity with alternate unit \\ +% |\momentumvalue{3}| &\momentumvalue{3} & selects only numerical value \\ +% |\momentumonlybaseunit|&\momentumonlybaseunit & selects only base unit \\ +% |\momentumonlydrvdunit|&\momentumonlydrvdunit & selects only derived unit \\ +% |\momentumonlyaltnunit|&\momentumonlyaltnunit & selects only alternate unit +% \end{tabular} +% \end{quotation} +% +% Momentum is a vector quantity, so obviously this command really refers to the +% magnitude of a momentum vector. There is an interesting, and as far as I can +% tell unwritten, convention in physics that we use the same name for a vector +% and its magnitude with one exception, and that is for velocity, the magnitude +% of which we sometimes call speed. Conceptually, however, velocity and speed are +% different entities. Therefore, \mandi\ has different commands for them. Actually, +% the \refCom{speed} command is just an alias for \refCom{velocity} and should only +% be used for scalars and never for vectors. This convention means that the same +% name is used for vector quantities and the corresponding magnitudes. +% +% \subsubsection{Defining Vector Quantities} +% +% All physical quantities are defined as in the momentum example above regardless +% of whether the quantity is a scalar or a vector. To typeset a vector quantity +% in terms of its components in some coordinate system (usually an orthonormal +% cartesian system, either specify an argument consisting of a vector with components +% as a comma separated list in a \refCom{mivector} command or prepend the quantity +% name with |vector|. So specifying a momentum vector is as simple as +% +%\iffalse +%<*example> +%\fi +\begin{dispExample} +\momentum{\mivector{3,2,-1}} \\ +\vectormomentum{3,2,-1} +\end{dispExample} +%\iffalse +% +%\fi +% +% where the notation corresponds to that used in \mi. +% +% \subsubsection{First Semester Physics} +% The first semester of most introductory calculus-based physics courses focuses +% on mechanics, dynamics, and statistical mechanics. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{displacement}{\marg{magnitude or vector}} +Command for displacement. +\end{docCommand} +\begin{docCommand}{vectordisplacement}{\marg{commadelimitedlistofcomps}} +Command for vector displacement. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\displacement{5} \\ +\displacement{\mivector{3,2,-1}} \\ +\vectordisplacement{1,2,3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mass}{\marg{magnitude}} +Command for mass. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\mass{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{duration}{\marg{magnitude}} +Command for duration. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\duration{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{current}{\marg{magnitude}} +Command for current. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\current{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{temperature}{\marg{magnitude}} +Command for temperature. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\temperature{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{amount}{\marg{magnitude}} +Command for amount. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\amount{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{luminous}{\marg{magnitude}} +Command for luminous intensity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\luminous{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +% While we're at it, let's also go ahead and define a few non-SI units from +% astronomy, astrophysics, and old school physics. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{infeet}{\marg{magnitude}} +Command for magnitude of displacement in feet. This is still sometimes used +in engineering applications and is frequently seen in older physics textbooks. +\end{docCommand} +\begin{docCommand}{infeetpersecond}{\marg{magnitude}} +Command for magnitude of velocity in feet per second. This is still sometimes used +in engineering applications and is frequently seen in older physics textbooks. +\end{docCommand} +\begin{docCommand}{infeetpersecondsquared}{\marg{magnitude}} +Command for magnitude of acceleration in feet per second. This is still sometimes +used in engineering applications and is frequently seen in older physics textbooks. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\infeet{5} \\ +\infeetpersecond{5} \\ +\infeetpersecondsquared{32} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planeangle}{\marg{magnitude}} +Command for plane angle in radians. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\planeangle{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{solidangle}{\marg{magnitude}} +Command for solidangle. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\solidangle{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{indegrees}{\marg{magnitude}} +Command for plane angle in degrees. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\indegrees{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inarcminutes}{\marg{magnitude}} +Command for plane angle in minutes of arc. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inarcminutes{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inarcseconds}{\marg{magnitude}} +Command for plane angle in seconds of arc. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inarcseconds{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inFarenheit}{\marg{magnitude}} +Command for temperature in degrees Farenheit. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inFarenheit{68} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inCelsius}{\marg{magnitude}} +Command for temperature in degrees Celsius. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inCelsius{20} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ineV}{\marg{magnitude}} +Command for energy in electron volts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ineV{10.2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ineVocs}{\marg{magnitude}} +Command for mass in \(\mathrm{eV}\per c^2\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ineVocs{1.1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ineVoc}{\marg{magnitude}} +Command for momentum in \(\mathrm{eV}\per c\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ineVoc{3.6} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inMeV}{\marg{magnitude}} +Command for energy in millions of electron volts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inMeV{2.2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inMeVocs}{\marg{magnitude}} +Command for mass in \(\mathrm{MeV}\per c^2\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inMeVocs{0.511} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inMeVoc}{\marg{magnitude}} +Command for momentum in \(\mathrm{MeV}\per c\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inMeVoc{3.6} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inGeV}{\marg{magnitude}} +Command for energy in millions of electron volts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inGeV{2.2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inGeVocs}{\marg{magnitude}} +Command for mass in \(\mathrm{GeV}\per c^2\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inGeVocs{0.511} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inGeVoc}{\marg{magnitude}} +Command for momentum in \(\mathrm{GeV}\per c\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inGeVoc{3.6} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inamu}{\marg{magnitude}} +Command for mass in atomic mass units. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inamu{4.002602} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inAU}{\marg{magnitude}} +Command for displacement in astronomical units. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inAU{5.2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inly}{\marg{magnitude}} +Command for displacement in light years. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inly{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{incyr}{\marg{magnitude}} +Command for displacement in light years written differently. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\incyr{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inpc}{\marg{magnitude}} +Command for displacement in parsecs. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inpc{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarL}{\marg{magnitude}} +Command for luminosity in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarL{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarT}{\marg{magnitude}} +Command for temperature in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarT{2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarR}{\marg{magnitude}} +Command for radius in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarR{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarM}{\marg{magnitude}} +Command for mass in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarM{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarF}{\marg{magnitude}} +Command for flux in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarF{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarf}{\marg{magnitude}} +Command for apparent flux in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarf{4.3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarMag}{\marg{magnitude}} +Command for absolute magnitude in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarMag{2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarmag}{\marg{magnitude}} +Command for apparent magnitude in solar multiples. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarmag{2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{insolarD}{\marg{magnitude}} +Command for distance in solar multiples. +\end{docCommand} +\begin{docCommand}{insolard}{\marg{magnitude}} +Identical to \refCom{insolarD} but uses \(d\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\insolarD{2} \\ +\insolard{2} +\end{dispExample*} +%\iffalse +% +%\fi +% +% Angles are confusing in introductory physics because sometimes we write +% the unit and sometimes we do not. Some concepts, such as flux, are simplified +% by introducing solid angle. +% +% Now let us continue into first semester physics, defining quantities in the +% approximate order in which they appear in such a course. Use \refCom{timestento} +% or \refCom{xtento} to get scientific notation, with the mantissa immediately +% preceding the command and the power as the required argument. \refCom{timestento} +% has an optional second argument that specifies a unit, but that is not needed or +% used in the following examples. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{direction}{\marg{commadelimitedlistofcomps}} +Command for coordinate representation of a vector direction. Direction has no unit. +\end{docCommand} +\begin{docCommand}{vectordirection}{\marg{commadelimitedlistofcomps}} +This is an alias for \refCom{direction}. +\end{docCommand} +\begin{dispExample} +\direction{a,b,c} \\ +\direction{\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}} \\ +\vectordirection{a,b,c} \\ +\vectordirection{\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{velocityc}{\marg{magnitude or vector}} +Command for velocity as a fraction of \(c\). +\end{docCommand} +\begin{docCommand}{vectorvelocityc}{\marg{commadelimitedlistofcomps}} +Command for vector velocity as a fraction of \(c\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\velocityc{0.9987} \\ +\velocityc{\mivector{0,0.9987,0}} \\ +\mivector{\velocityc{\frac{1}{\sqrt{3}}} \\ +\velocityc{\frac{1}{\sqrt{3}}} \\ +\velocityc{\frac{1}{\sqrt{3}}}} \\ +\vectorvelocityc{0,0.9987,0} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{velocity}{\marg{magnitude or vector}} +Command for velocity. +\end{docCommand} +\begin{docCommand}{vectorvelocity}{\marg{commadelimitedlistofcomps}} +Command for vector velocity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\velocity{2.34} \\ +\velocity{\mivector{3,2,-1}} \\ +\vectorvelocity{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{speed}{\marg{magnitude}} +Command for speed. Technically, velocity is defined as the quotient of +displacement and duration while speed is defined as the quotient of distance +traveled and duration. They have the same dimension and unit, but are +conceptually different so separate commands are provided. I've never seen speed +used as anything other than a scalar. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\velocity{8.25} +\end{dispExample*} +%\iffalse +% +%\fi +% + +%\iffalse +%<*example> +%\fi +\begin{docCommand}{lorentzfactor}{\marg{magnitude}} +Command for relativistic Lorentz factor. Obviously this command doesn't do +anything visually, but is included for thinking about calculations where this +quantity is needed. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\lorentzfactor{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{momentum}{\marg{magnitude or vector}} +Command for momentum. +\end{docCommand} +\begin{docCommand}{vectormomentum}{\marg{commadelimitedlistofcomps}} +Command for vector momentum. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\momentum{2.34} \\ +\momentum{\mivector{3,2,-1}} \\ +\vectormomentum{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{acceleration}{\marg{magnitude or vector}} +Command for acceleration. +\end{docCommand} +\begin{docCommand}{vectoracceleration}{\marg{commadelimitedlistofcomps}} +Command for vector acceleration. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\acceleration{2.34} \\ +\acceleration{\mivector{3,2,-1}} \\ +\vectoracceleration{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalfield}{\marg{commadelimitedlistofcomps}} +Command for gravitational field. +\end{docCommand} +\begin{docCommand}{vectorgravitationalfield}{\marg{magnitude or vector}} +Command for vector gravitational field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\gravitationalfield{2.34} \\ +\gravitationalfield{\mivector{3,2,-1}} \\ +\vectorgravitationalfield{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalpotential}{\marg{magnitude}} +Command for gravitational potential. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\gravitationalpotential{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{impulse}{\marg{magnitude or vector}} +Command for impulse. Impulse and change in momentum are conceptually different +and a case can be made for expressing the in different, but equivalent, units. +\end{docCommand} +\begin{docCommand}{vectorimpulse}{\marg{commadelimitedlistofcomps}} +Command for vector impulse. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\impulse{2.34} \\ +\impulse{\mivector{3,2,-1}} \\ +\vectorimpulse{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{force}{\marg{magnitude or vector}} +Command for force. +\end{docCommand} +\begin{docCommand}{vectorforce}{\marg{commadelimitedlistofcomps}} +Command for vector force. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\force{2.34} \\ +\force{\mivector{3,2,-1}} \\ +\vectorforce{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springstiffness}{\marg{magnitude}} +Command for spring stiffness. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\springstiffness{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springstretch}{\marg{magnitude}} +Command for spring stretch. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\springstretch{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{area}{\marg{magnitude}} +Command for area. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\area{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{volume}{\marg{magnitude}} +Command for volume. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\volume{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{linearmassdensity}{\marg{magnitude}} +Command for linear mass density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\linearmassdensity{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{areamassdensity}{\marg{magnitude}} +Command for area mass density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\areamassdensity{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{volumemassdensity}{\marg{magnitude}} +Command for volume mass density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\volumemassdensity{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{youngsmodulus}{\marg{magnitude}} +Command for Young's modulus. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\youngsmodulus{2.34\timestento{9}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{work}{\marg{magnitude}} +Command for work. Energy and work are conceptually different and a case can +be made for expressing them in different, but equivalent, units. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\work{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{energy}{\marg{magnitude}} +Command for energy. Work and energy are conceptually different and a case can +be made for expressing them in different, but equivalent, units. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\energy{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{power}{\marg{magnitude}} +Command for power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\power{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{specificheatcapacity}{\marg{magnitude}} +Command for specific heat capacity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\specificheatcapacity{4.18\xtento{3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularvelocity}{\marg{magnitude or vector}} +Command for angular velocity. +\end{docCommand} +\begin{docCommand}{vectorangularvelocity}{\marg{commadelimitedlistofcomps}} +Command for vector angular velocity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\angularvelocity{2.34} \\ +\angularvelocity{\mivector{3,2,-1}} \\ +\vectorangularvelocity{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularacceleration}{\marg{magnitude or vector}} +Command for angular acceleration. +\end{docCommand} +\begin{docCommand}{vectorangularacceleration}{\marg{commadelimitedlistofcomps}} +Command for vector angular acceleration. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\angularacceleration{2.34} \\ +\angularacceleration{\mivector{3,2,-1}} \\ +\vectorangularacceleration{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularmomentum}{\marg{magnitude or vector}} +Command for angular momentum. Whether or not the units contain radians +is determined by whether the \opt{useradians} option was used when +\pkgname{mandi} was loaded. +\end{docCommand} +\begin{docCommand}{vectorangularmomentum}{\marg{commadelimitedlistofcomps}} +Command for vector angular momentum. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\angularmomentum{2.34} \\ +\angularmomentum{\mivector{3,2,-1}} \\ +\vectorangularmomentum{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularimpulse}{\marg{magnitude or vector}} +Command for angular impulse. Whether or not the units contain radians is +determined by whether the \opt{useradians} option was used when +\pkgname{mandi} was loaded. +\end{docCommand} +\begin{docCommand}{vectorangularimpulse}{\marg{commadelimitedlistofcomps}} +Command for vector angular impulse. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\angularimpulse{2.34} \\ +\angularimpulse{\mivector{3,2,-1}} \\ +\vectorangularimpulse{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{torque}{\marg{magnitude or vector}} +Command for torque. Whether or not the units contain radians is +determined by whether the \opt{useradians} option was used when +\pkgname{mandi} was loaded. +\end{docCommand} +\begin{docCommand}{vectortorque}{\marg{commadelimitedlistofcomps}} +Command for vector torque. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\torque{2.34} \\ +\torque{\mivector{3,2,-1}} \\ +\vectortorque{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{momentofinertia}{\marg{magnitude}} +Command for moment of inertia. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\momentofinertia{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{entropy}{\marg{magnitude}} +Command for entropy. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\entropy{2.34} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{wavelength}{\marg{magnitude}} +Command for wavelength. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\wavelength{4.00\timestento{-7}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{wavenumber}{\marg{magnitude or vector}} +Command for wavenumber. +\end{docCommand} +\begin{docCommand}{vectorwavenumber}{\marg{commadelimitedlistofcomps}} +Command for vector wavenumber. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\wavenumber{2.50\timestento{6}} \\ +\wavenumber{\mivector{3,2,-1}} \\ +\vectorwavenumber{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{frequency}{\marg{magnitude}} +Command for frequency. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\frequency{7.50\timestento{14}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularfrequency}{\marg{magnitude}} +Command for angularfrequency. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\angularfrequency{4.70\timestento{15}} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Second Semester Physics} +% The second semester of introductory physics focuses on electromagnetic theory, +% and there are many primary and secondary quantities. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{charge}{\marg{magnitude}} +Command for electric charge. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\charge{2\timestento{-9}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{permittivity}{\marg{magnitude}} +Command for permittivity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\permittivity{9\timestento{-12}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricfield}{\marg{magnitude or vector}} +Command for electric field. +\end{docCommand} +\begin{docCommand}{vectorelectricfield}{\marg{commadelimitedlistofcomps}} +Command for vector electric field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\electricfield{2\timestento{5}} \\ +\electricfield{\mivector{3,2,-1}} \\ +\vectorelectricfield{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricdipolemoment}{\marg{magnitude or vector}} +Command for electric dipole moment. +\end{docCommand} +\begin{docCommand}{vectorelectricdipolemoment}{\marg{commadelimitedlistofcomps}} +Command for vector electric dipole moment. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\electricdipolemoment{2\timestento{5}} \\ +\electricdipolemoment{\mivector{3,2,-1}} \\ +\vectorelectricdipolemoment{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{permeability}{\marg{magnitude}} +Command for permeability. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\permeability{4\pi\timestento{-7}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magneticfield}{\marg{magnitude or vector}} +Command for magnetic field (also called magnetic induction). +\end{docCommand} +\begin{docCommand}{vectormagneticfield}{\marg{commadelimitedlistofcomps}} +Command for vector magnetic field (also called magnetic induction). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magneticfield{1.25} \\ +\magneticfield{\mivector{3,2,-1}} \\ +\vectormagneticfield{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{cmagneticfield}{\marg{magnitude or vector}} +Command for product of \(c\) and magnetic field. This quantity is +convenient for symmetry. +\end{docCommand} +\begin{docCommand}{vectorcmagneticfield}{\marg{commadelimitedlistofcomps}} +Command for product of \(c\) and magnetic field as a vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\cmagneticfield{1.25} \\ +\cmagneticfield{\mivector{3,2,-1}} \\ +\vectorcmagneticfield{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{linearchargedensity}{\marg{magnitude}} +Command for linear charge density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\linearchargedensity{4.5\timestento{-3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{areachargedensity}{\marg{magnitude}} +Command for area charge density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\areachargedensity{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{volumechargedensity}{\marg{magnitude}} +Command for volume charge density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\volumechargedensity{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mobility}{\marg{magnitude}} +Command for electron mobility. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\areachargedensity{4.5\timestento{-3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{numberdensity}{\marg{magnitude}} +Command for electron number density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\numberdensity{2\timestento{18}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{polarizability}{\marg{magnitude}} +Command for polarizability. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\polarizability{1.96\timestento{-40}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricpotential}{\marg{magnitude}} +Command for electric potential. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\electricpotential{1.5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{emf}{\marg{magnitude}} +Command for emf. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\emf{1.5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dielectricconstant}{\marg{magnitude}} +Command for dielectric constant. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dielectricconstant{1.5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{indexofrefraction}{\marg{magnitude}} +Command for index of refraction. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\indexofrefraction{1.5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{relativepermittivity}{\marg{magnitude}} +Command for relative permittivity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\relativepermittivity{0.9} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{relativepermeability}{\marg{magnitude}} +Command for relative permeability. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\relativepermeability{0.9} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{poyntingvector}{\marg{commadelimitedlistofcomps}} +Command for Poynting vector. This is an alias for \refCom{vectorenergyflux}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\poyntingvector{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{energydensity}{\marg{magnitude}} +Command for energy density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\energydensity{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{energyflux}{\marg{magnitude or vector}} +Command for energy flux. +\end{docCommand} +\begin{docCommand}{vectorenergyflux}{\marg{commadelimitedlistofcomps}} +Command for vector energy flux. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\energyflux{4\timestento{26}} \\ +\energyflux{\mivector{3,2,-1}} \\ +\vectorenergyflux{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{momentumflux}{\marg{magnitude or vector}} +Command for momentum flux. +\end{docCommand} +\begin{docCommand}{vectormomentumflux}{\marg{commadelimitedlistofcomps}} +Command for vector momentum flux. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\momentumflux{4\timestento{26}} \\ +\momentumflux{\mivector{3,2,-1}} \\ +\vectormomentumflux{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electroncurrent}{\marg{magnitude}} +Command for electron current. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\electroncurrent{2\timestento{18}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{conventionalcurrent}{\marg{magnitude}} +Command for conventional current. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\conventionalcurrent{0.003} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magneticdipolemoment}{\marg{magnitude or vector}} +Command for magnetic dipole moment. +\end{docCommand} +\begin{docCommand}{vectormagneticdipolemoment}{\marg{commadelimitedlistofcomps}} +Command for vector magnetic dipole moment. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magneticdipolemoment{1.25} \\ +\magneticdipolemoment{\mivector{3,2,-1}} \\ +\vectormagneticdipolemoment{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{currentdensity}{\marg{magnitude or vector}} +Command for current density. +\end{docCommand} +\begin{docCommand}{vectorcurrentdensity}{\marg{commadelimitedlistofcomps}} +Command for vector current density. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\currentdensity{1.25} \\ +\currentdensity{\mivector{3,2,-1}} \\ +\vectorcurrentdensity{3,2,-1} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricflux}{\marg{magnitude}} +Command for electric flux. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\electricflux{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magneticflux}{\marg{magnitude}} +Command for magnetic flux. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magneticflux{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{capacitance}{\marg{magnitude}} +Command for capacitance. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\capacitance{1.00} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inductance}{\marg{magnitude}} +Command for inductance. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inductance{1.00} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{conductivity}{\marg{magnitude}} +Command for conductivity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\conductivity{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{resistivity}{\marg{magnitude}} +Command for resistivity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\resistivity{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{resistance}{\marg{magnitude}} +Command for resistance. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\resistance{1\timestento{6}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{conductance}{\marg{magnitude}} +Command for conductance. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\conductance{1\timestento{6}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magneticcharge}{\marg{magnitude}} +Command for magnetic charge, in case it actually exists. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magneticcharge{1.25} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Further Words on Units} +% The form of a quantity's unit can be changed on the fly regardless of the +% global format determined by \opt{baseunits} and \opt{drvdunits}. One way, +% as illustrated in the table above, is to append |baseunit|, |drvdunit|, +% |altnunit| to the quantity's name, and this will override the global options +% for that instance. +% +% A second way is to use the commands that change a quantity's unit on the fly. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hereusebaseunit}{\marg{magnitude}} +Command for using base units in place. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\hereusebaseunit{\momentum{3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hereusedrvdunit}{\marg{magnitude}} +Command for using derived units in place. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\hereusedrvdunit{\momentum{3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hereusealtnunit}{\marg{magnitude}} +Command for using alternate units in place. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\hereusealtnunit{\momentum{3}} +\end{dispExample*} +%\iffalse +% +%\fi +% +% A third way is to use the environments that change a quantity's unit +% for the duration of the environment. +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{usebaseunit}{} +Environment for using base units. +\end{docEnvironment} +\begin{dispExample*}{sidebyside} +\begin{usebaseunit} + \momentum{3} +\end{usebaseunit} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{usedrvdunit}{} +Environment for using derived units. +\end{docEnvironment} +\begin{dispExample*}{sidebyside} +\begin{usedrvdunit} + \momentum{3} +\end{usedrvdunit} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{usealtnunit}{} +Environment for using alternate units. +\end{docEnvironment} +\begin{dispExample*}{sidebyside} +\begin{usealtnunit} + \momentum{3} +\end{usealtnunit} +\end{dispExample*} +%\iffalse +% +%\fi +% +% A fourth way is to use the three global switches that perpetually change the +% default unit. \textbf{It's important to remember that these switches override +% the global options for the rest of the document or until overridden by one of +% the other two switches.} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{perpusebaseunit}{} +Command for perpetually using base units. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{perpusedrvdunit}{} +Command for perpetually using derived units. +\end{docCommand} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{perpusealtnunit}{} +Command for perpetually using alternate units. +\end{docCommand} +%\iffalse +% +%\fi +% +%\subsubsection{Using Alternate Units} +% In some cases it may be helpful to use unconventional, but pedagogically +% appropriate, units for certain physical quantities. As an example, consider +% force. It is normally expressed in newtons, but it can also be expressed in +% joules per meter. You can redefine a quantity's units on the fly with the +% \cs{redefinephysicsquantity} command. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{redefinephysicsquantity} +{\marg{newname}\marg{\baseunits}\oarg{\drvdunits}\oarg{\altnunits}} +Redefines an existing physical quantity, allowing for new alternate units. You can +also change the other units but it strongly discouraged. The new definition takes +effect immediately. +\end{docCommand} +%\iffalse +% +%\fi +% +%\subsubsection{All Predefined Quantities} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{chkquantity}{\marg{quantityname}} +Diagnostic command for all of the units for a defined physical quantity. See table +below. +\end{docCommand} +%\iffalse +% +%\fi +% +% Here are all the predefined quantities and their units. +%\begin{adjustwidth}{-0.5in}{-0.5in} +% +%\chkquantity{displacement} +%\chkquantity{mass} +%\chkquantity{duration} +%\chkquantity{current} +%\chkquantity{temperature} +%\chkquantity{amount} +%\chkquantity{luminous} +%\chkquantity{infeetpersecond} +%\chkquantity{infeet} +%\chkquantity{planeangle} +%\chkquantity{solidangle} +%\chkquantity{velocity} +%\chkquantity{acceleration} +%\chkquantity{gravitationalfield} +%\chkquantity{gravitationalpotential} +%\chkquantity{momentum} +%\chkquantity{impulse} +%\chkquantity{force} +%\chkquantity{springstiffness} +%\chkquantity{springstretch} +%\chkquantity{area} +%\chkquantity{volume} +%\chkquantity{linearmassdensity} +%\chkquantity{areamassdensity} +%\chkquantity{volumemassdensity} +%\chkquantity{youngsmodulus} +%\chkquantity{stress} +%\chkquantity{pressure} +%\chkquantity{strain} +%\chkquantity{work} +%\chkquantity{energy} +%\chkquantity{power} +%\chkquantity{specificheatcapacity} +%\chkquantity{angularvelocity} +%\chkquantity{angularacceleration} +%\chkquantity{momentofinertia} +%\chkquantity{angularmomentum} +%\chkquantity{angularimpulse} +%\chkquantity{torque} +%\chkquantity{entropy} +%\chkquantity{wavelength} +%\chkquantity{wavenumber} +%\chkquantity{frequency} +%\chkquantity{angularfrequency} +%\chkquantity{charge} +%\chkquantity{permittivity} +%\chkquantity{permeability} +%\chkquantity{linearchargedensity} +%\chkquantity{areachargedensity} +%\chkquantity{volumechargedensity} +%\chkquantity{electricfield} +%\chkquantity{electricdipolemoment} +%\chkquantity{electricflux} +%\chkquantity{magneticfield} +%\chkquantity{magneticflux} +%\chkquantity{cmagneticfield} +%\chkquantity{mobility} +%\chkquantity{numberdensity} +%\chkquantity{polarizability} +%\chkquantity{electricpotential} +%\chkquantity{emf} +%\chkquantity{dielectricconstant} +%\chkquantity{indexofrefraction} +%\chkquantity{relativepermittivity} +%\chkquantity{relativepermeability} +%\chkquantity{energydensity} +%\chkquantity{momentumflux} +%\chkquantity{energyflux} +%\chkquantity{electroncurrent} +%\chkquantity{conventionalcurrent} +%\chkquantity{magneticdipolemoment} +%\chkquantity{currentdensity} +%\chkquantity{capacitance} +%\chkquantity{inductance} +%\chkquantity{conductivity} +%\chkquantity{resistivity} +%\chkquantity{resistance} +%\chkquantity{conductance} +%\chkquantity{magneticcharge} +%\end{adjustwidth} +% +% \subsection{When to Write Radians}\label{WhentoWriteRadians} +% A word of clarification is in order for plane angles, solid angles, and other +% angular quantities. There is the perpetually confusing issue of when to explicitly +% write radians as a unit and when to omit it. The answer is that if the numerical +% value of a quantity explicitly depends on the angular unit, then the unit should +% be written. An example would be angular displacement; the numerical value obviously +% depends on the unit used. If the numerical value of a quantity does not explicitly +% depend on the angular unit, then the unit is omitted. An example would be the linear, +% or translational, velocity or a particle in circular motion. This quantity doesn't +% explicitly depends on the angular unit, so the angular unit is not written. +% +% Torque, angular impulse, and angular momentum present special a special problem +% in that it is sometimes pedagogically helpful to explicitly include angular units +% in their operational definitions. While this may not be in strict accordance +% with SI standards, loading \mandi\ with the \opt{useradians} option includes +% angular units in these quantities. See \nameref{LoadingthePackage} for details. +% +% \subsection{The Empty Unit} +% Sometimes, when discussing manipulation of units, it is helpful to have a generic +% symbol that does not correspond to any particular existing unit. The +% \cs{emptyunit} is provided for this purpose. It serves as a visual placeholder +% for any unit. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{emptyunit}{} +Command for a generic visual placeholder symbolizing any actual unit. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \frac{\emptyunit\squared}{\cubic\emptyunit} = \emptyunit^{-1} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +% \newpage +% \hypertarget{target3}{\subsection{Physical Constants}} +% \subsubsection{Defining Physical Constants} +% \mandi\ has many predefined physical constants. +% This section explains how to use them. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{newphysicsconstant} +{\marg{name}\marg{symbol}{\{\cs{mi@p\marg{approx}\marg{precise}}\}}\marg{\baseunits} +\\ +\oarg{\drvdunits}\oarg{\altnunits}% +}% + +Defines a new physical constant with a name, a symbol, approximate and +precise numerical values, required base units, optional derived units, +and optional alternate units. The \cs{mi@p} command is defined +internally and is not meant to be otherwise used. +\end{docCommand} +\begin{dispListing} +Here is how \planck (Planck's constant) is defined internally, showing +each part of the definition on a separate line. +\newphysicsconstant{planck} + {\ensuremath{h}} + {\mi@p{6.6}{6.626070040}\timestento{-34}} + {\m\squared\usk\kg\usk\reciprocal\s} + [\J\usk\s] + [\J\usk\s] +\end{dispListing} +%\iffalse +% +%\fi +% +% Using this command causes several things to happen. +% \begin{itemize} +% \item A command \cs{name} is created and contains the constant and +% units typeset according to the options given when \mandi\ was loaded. +% \item A command \cs{namemathsymbol} is created that expresses +% \textbf{only} the constant's mathematical symbol. +% \item A command \cs{namevalue} is created that expresses +% \textbf{only} the constant's approximate or precise numerical value. +% Note that both values must be present when the constant is defined. +% By default, precise values are always used but this can be changed +% when \mandi\ is loaded. Note how the values are specified in the +% definition of the constant. +% \item A command \cs{namebaseunit} is created that expresses +% the constant and its units in \baseunits\ form. +% \item A command \cs{namedrvdunit} is created that expresses +% the constant and its units in \drvdunits\ form. +% \item A command \cs{namealtnunit} is created that +% expresses the constant and its units in \altnunits\ form. +% \item A command \cs{nameonlybaseunit} is created that expresses +% \textbf{only} the constant's units in \baseunits\ form. +% \item A command \cs{nameonlydrvdunit} is created that +% expresses \textbf{only} the constant's units in \drvdunits\ form. +% \item A command \cs{nameonlyaltnunit} is created that +% expresses \textbf{only} the constant's units in \altnunits\ form. +% \end{itemize} +% None of these commands takes any arguments. +% +% +% There is a command similar to \refCom{redefinephysicsquantity} that allows for +% redefining physical constants. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{redefinephysicsconstant} +{\marg{name}\marg{symbol}{\{\cs{mi@p\marg{approx}\marg{precise}}\}}\marg{\baseunits} +\\ +\oarg{\drvdunits}\oarg{\altnunits}% +}% +Redefines an existing physical constant. +The new definition takes effect immediately. +\end{docCommand} +%\iffalse +% +%\fi +% +% \newpage +% \subsubsection{Predefined Physical Constants} +% +% In this section, precise values of constants are used. Approximate +% values are available as an option when the package is loaded. Precise values +% are sourced as accurately as possible, beginning with Wikipedia and following +% sources therein. I tried to use the most recent NIST or similarly authoritative +% values. In no case did I make up any values. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{oofpez}{} +Coulomb constant. +\end{docCommand} +\begin{dispExample} +\(\oofpezmathsymbol \approx \oofpez\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{oofpezcs}{} +Alternate form of Coulomb constant. +\end{docCommand} +\begin{dispExample} +\(\oofpezcsmathsymbol \approx \oofpezcs\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vacuumpermittivity}{} +Vacuum permittivity. +\end{docCommand} +\begin{dispExample} +\(\vacuumpermittivitymathsymbol \approx \vacuumpermittivity\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mzofp}{} +Biot-Savart constant. +\end{docCommand} +\begin{dispExample} +\(\mzofpmathsymbol \approx \mzofp\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vacuumpermeability}{} +Vacuum permeability. +\end{docCommand} +\begin{dispExample} +\(\vacuumpermeabilitymathsymbol \approx \vacuumpermeability\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{boltzmann}{} +Boltzmann constant. +\end{docCommand} +\begin{dispExample} +\(\boltzmannmathsymbol \approx \boltzmann\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{boltzmannineV}{} +Alternate form of Boltlzmann constant. +\end{docCommand} +\begin{dispExample} +\(\boltzmannineVmathsymbol \approx \boltzmannineV\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{stefan}{} +Stefan-Boltzmann constant. +\end{docCommand} +\begin{dispExample} +\(\stefanboltzmannmathsymbol \approx \stefanboltzmann\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planck}{} +Planck constant. +\end{docCommand} +\begin{dispExample} +\(\planckmathsymbol \approx \planck\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planckineV}{} +Alternate form of Planck constant. +\end{docCommand} +\begin{dispExample} +\(\planckmathsymbol \approx \planckineV\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planckbar}{} +Reduced Planck constant (Dirac constant). +\end{docCommand} +\begin{dispExample} +\(\planckbarmathsymbol \approx \planckbar\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planckbarineV}{} +Alternate form of reduced Planck constant (Dirac constant). +\end{docCommand} +\begin{dispExample} +\(\planckbarmathsymbol \approx \planckbarineV\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planckc}{} +Planck constant times light speed. +\end{docCommand} +\begin{dispExample} +\(\planckcmathsymbol \approx \planckc\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{planckcineV}{} +Alternate form of Planck constant times light speed. +\end{docCommand} +\begin{dispExample} +\(\planckcineVmathsymbol \approx \planckcineV\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{rydberg}{} +Rydberg constant. +\end{docCommand} +\begin{dispExample} +\(\rydbergmathsymbol \approx \rydberg\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{bohrradius}{} +Bohr radius. +\end{docCommand} +\begin{dispExample} +\(\bohrradiusmathsymbol \approx \bohrradius\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{finestructure}{} +Fine structure constant. +\end{docCommand} +\begin{dispExample} +\(\finestructuremathsymbol \approx \finestructure\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{avogadro}{} +Avogadro constant. +\end{docCommand} +\begin{dispExample} +\(\avogadromathsymbol \approx \avogadro\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{universalgrav}{} +Universal gravitational constant. +\end{docCommand} +\begin{dispExample} +\(\universalgravmathsymbol \approx \universalgrav\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{surfacegravfield}{} +Earth's surface gravitational field strength. +\end{docCommand} +\begin{dispExample} +\(\surfacegravfieldmathsymbol \approx \surfacegravfield\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{clight}{} +Magnitude of light's velocity (photon constant). +\end{docCommand} +\begin{dispExample} +\(\clightmathsymbol \approx \clight\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{clightinfeet}{} +Alternate of magnitude of light's velocity (photon constant). +\end{docCommand} +\begin{dispExample} +\(\clightinfeetmathsymbol \approx \clightinfeet\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ratom}{} +Approximate atomic radius. +\end{docCommand} +\begin{dispExample} +\(\Ratommathsymbol \approx \Ratom\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Mproton}{} +Proton mass. +\end{docCommand} +\begin{dispExample} +\(\Mprotonmathsymbol \approx \Mproton\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Mneutron}{} +Neutron mass. +\end{docCommand} +\begin{dispExample} +\(\Mneutronmathsymbol \approx \Mneutron\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Mhydrogen}{} +Hydrogen atom mass. +\end{docCommand} +\begin{dispExample} +\(\Mhydrogenmathsymbol \approx \Mhydrogen\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Melectron}{} +Electron mass. +\end{docCommand} +\begin{dispExample} +\(\Melectronmathsymbol \approx \Melectron\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{echarge}{} +Elementary charge quantum. +\end{docCommand} +\begin{dispExample} +\(\echargemathsymbol \approx \echarge\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Qelectron}{} +Electron charge. +\end{docCommand} +\begin{docCommand}{qelectron}{} +Alias for \cs{Qelectron}. +\end{docCommand} +\begin{dispExample} +\(\Qelectronmathsymbol \approx \Qelectron\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Qproton}{} +Proton charge. +\end{docCommand} +\begin{docCommand}{qproton}{} +Alias for \cs{Qproton}. +\end{docCommand} +\begin{dispExample} +\(\Qprotonmathsymbol \approx \Qproton\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{MEarth}{} +Earth's mass. +\end{docCommand} +\begin{dispExample} +\(\MEarthmathsymbol \approx \MEarth\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{MMoon}{} +Moon's mass. +\end{docCommand} +\begin{dispExample} +\(\MMoonmathsymbol \approx \MMoon\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{MSun}{} +Sun's mass. +\end{docCommand} +\begin{dispExample} +\(\MSunmathsymbol \approx \MSun\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{REarth}{} +Earth's radius. +\end{docCommand} +\begin{dispExample} +\(\REarthmathsymbol \approx \REarth\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RMoon}{} +Moon's radius. +\end{docCommand} +\begin{dispExample} +\(\RMoonmathsymbol \approx \RMoon\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RSun}{} +Sun's radius. +\end{docCommand} +\begin{dispExample} +\(\RSunmathsymbol \approx \RSun\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ESdist}{} +Earth-Sun distance. +\end{docCommand} +\begin{docCommand}{SEdist}{} +Alias for \refCom{ESdist}. +\end{docCommand} +\begin{dispExample} +\(\ESdistmathsymbol \approx \SEdist\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{EMdist}{} +Earth-Moon distance. +\end{docCommand} +\begin{docCommand}{MEdist}{} +Alias for \refCom{EMdist}. +\end{docCommand} +\begin{dispExample} +\(\EMdistmathsymbol \approx \EMdist\) +\end{dispExample} +%\iffalse +% +%\fi +% +%\subsubsection{All Predefined Constants} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{chkconstant}{\marg{constantname}} +Diagnostic command for the symbol, value (either approximate or precise depending +on how the package was loaded), and units for a defined physical constant. See table +below. +\end{docCommand} +%\iffalse +% +%\fi +% +% Here are all the predefined constants and their units. +%\begin{adjustwidth}{}{} +% +%\chkconstant{oofpez} +%\chkconstant{oofpezcs} +%\chkconstant{vacuumpermittivity} +%\chkconstant{mzofp} +%\chkconstant{vacuumpermeability} +%\chkconstant{boltzmann} +%\chkconstant{boltzmannineV} +%\chkconstant{stefanboltzmann} +%\chkconstant{planck} +%\chkconstant{planckineV} +%\chkconstant{planckbar} +%\chkconstant{planckbarineV} +%\chkconstant{planckc} +%\chkconstant{planckcineV} +%\chkconstant{rydberg} +%\chkconstant{bohrradius} +%\chkconstant{finestructure} +%\chkconstant{avogadro} +%\chkconstant{universalgrav} +%\chkconstant{surfacegravfield} +%\chkconstant{clight} +%\chkconstant{clightinfeet} +%\chkconstant{Ratom} +%\chkconstant{Mproton} +%\chkconstant{Mneutron} +%\chkconstant{Mhydrogen} +%\chkconstant{Melectron} +%\chkconstant{echarge} +%\chkconstant{Qelectron} +%\chkconstant{qelectron} +%\chkconstant{Qproton} +%\chkconstant{qproton} +%\chkconstant{MEarth} +%\chkconstant{MMoon} +%\chkconstant{MSun} +%\chkconstant{REarth} +%\chkconstant{RMoon} +%\chkconstant{RSun} +%\chkconstant{ESdist} +%\chkconstant{EMdist} +%\chkconstant{LSun} +%\chkconstant{TSun} +%\chkconstant{MagSun} +%\chkconstant{magSun} +%\end{adjustwidth} +% +% \subsection{Astronomical Constants and Quantities} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LSun}{} +Sun's luminosity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\LSunmathsymbol \approx \LSun\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{TSun}{} +Sun's effective temperature. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\TSunmathsymbol \approx \TSun\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{MagSun}{} +Sun's absolute magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\MagSunmathsymbol \approx \MagSun\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magSun}{} +Sun's apparent magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\magSunmathsymbol \approx \magSun\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Lstar}{\oarg{object}} +Symbol for stellar luminosity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Lstar or \Lstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Lsolar}{} +Symbol for solar luminosity as a unit. Really just an alias for +|\Lstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Lsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Tstar}{\oarg{object}} +Symbol for stellar temperature. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Tstar or \Tstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Tsolar}{} +Symbol for solar temperature as a unit. Really just an alias for +|\Tstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Tsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Rstar}{\oarg{object}} +Symbol for stellar radius. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Rstar or \Rstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Rsolar}{} +Symbol for solar radius as a unit. Really just an alias for +|\Rstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Rsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Mstar}{\oarg{object}} +Symbol for stellar mass. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Mstar or \Mstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Msolar}{} +Symbol for solar mass as a unit. Really just an alias for +|\Mstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Msolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Fstar}{\oarg{object}} +Symbol for stellar flux. +\end{docCommand} +\begin{docCommand}{fstar}{} +Alias for \refCom{Fstar}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Fstar or \Fstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Fsolar}{} +Symbol for solar flux as a unit. Really just an alias for +|\Fstar[\(\odot\)]|. +\end{docCommand} +\begin{docCommand}{fsolar}{} +Alias for \refCom{fsolar}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Fsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Magstar}{\oarg{object}} +Symbol for stellar absolute magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Magstar or \Magstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Magsolar}{} +Symbol for solar absolute magnitude as a unit. Really just an alias for +|\Magstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Magsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magstar}{\oarg{object}} +Symbol for stellar apparent magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magstar or \magstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magsolar}{} +Symbol for solar apparent magnitude as a unit. Really just an alias for +|\magstar[\(\odot\)]|. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Dstar}{\oarg{object}} +Symbol for stellar distance. +\end{docCommand} +\begin{docCommand}{dstar}{} +Alias for \refCom{Dstar} that uses a lower case d. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Dstar or \Dstar[Sirius] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Dsolar}{} +Symbol for solar distance as a unit. Really just an alias for +|\Dstar[\(\odot\)]|. +\end{docCommand} +\begin{docCommand}{dsolar}{} +Alias for \refCom{Dsolar} that uses a lower case d. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Dsolar +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{Symbolic Expressions with Vectors} +% \subsubsection{Basic Vectors} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vect}{\marg{kernel}} +Symbol for a vector quantity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vect{p} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magvect}{\marg{kernel}} +Symbol for magnitude of a vector quantity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magvect{p} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magsquaredvect}{\marg{kernel}} +Symbol for squared magnitude of a vector quantity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magsquaredvect{p} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magnvect}{\marg{kernel}\marg{exponent}} +Symbol for magnitude of a vector quantity to arbitrary power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magnvect{r}{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dirvect}{\marg{kernel}} +Symbol for direction of a vector quantity. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dirvect{p} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{factorvect}{\marg{kernel}} +Symbol for a vector factored into its magnitude and direction. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\factorvect{E} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{componentalong}{\marg{alongvector}\marg{ofvector}} +Symbol for the component along a vector of another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\componentalong{\vect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{expcomponentalong}{\marg{alongvector}\marg{ofvector}} +Symbolic expression for the component along a vector of another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\expcomponentalong{\vect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ucomponentalong}{\marg{alongvector}\marg{ofvector}} +Symbolic expression with unit vectors for the component along a vector of +another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ucomponentalong{\dirvect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{projectiononto}{\marg{ontovector}\marg{ofvector}} +Symbol for the projection onto a vector of another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\projectiononto{\vect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{expprojectiononto}{\marg{alongvector}\marg{ofvector}} +Symbolic expression for the projection onto a vector of another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\expprojectiononto{\vect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{uprojectiononto}{\marg{alongvector}\marg{ofvector}} +Symbolic expression with unit vectors for the projection onto a vector of +another vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\uprojectiononto{\dirvect{v}}{\vect{u}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mivector} + {\oarg{printeddelimiter}\marg{commadelimitedlistofcomps}\oarg{unit}} +Generic workhorse command for vectors formatted as in \mi. Unless the first +optional argument is specified, a comma is used in the output. Commas are +always required in the mandatory argument. +\end{docCommand} +\begin{dispExample} +\begin{mysolution*} + \msub{u}{\mu} &= \mivector{\ezero,\eone,\etwo,\ethree} \\ + \msub{u}{\mu} &= \mivector[\quad]{\ezero,\eone,\etwo,\ethree} \\ + \vect{v} &= \mivector{1,3,5}[\velocityonlyaltnunit] \\ + \vect{E} &= \mivector{\oofpezmathsymbol \frac{Q}{x^2},0,0} \\ + \vect{E} &= \mivector[\quad]{\oofpezmathsymbol \frac{Q}{x^2},0,0} +\end{mysolution*} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magvectncomps}{\marg{listofcomps}\oarg{unit}} +Expression for a vector's magnitude with numerical components and an optional +unit. The first example is the preferred and recommended way to handle units when +they are needed. The second example requires explicitly picking out the desired +unit form. The third example demonstrates components of a unit vector. +\end{docCommand} +\begin{dispExample} +\magvectncomps{\velocity{3.12},\velocity{4.04},\velocity{6.73}} \\ +\magvectncomps{3.12,4.04,6.73}[\velocityonlyaltnunit] \\ +\magvectncomps{\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsvect}{\marg{kernel}} +Expression for a vector's symbolic components. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scompsvect{E} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compvect}{\marg{kernel}\marg{component}} +Isolates one of a vector's symbolic components. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\compvect{E}{y} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsdirvect}{\marg{kernel}} +Expression for a direction's symbolic components. The hats are necessary to +denote a direction. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scompsdirvect{r} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compdirvect}{\marg{kernel}\marg{component}} +Isolates one of a direction's symbolic components. The hat is necessary to +denote a direction. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\compdirvect{r}{z} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magvectscomps}{\marg{kernel}} +Expression for a vector's magnitude in terms of its symbolic components. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magvectscomps{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Differentials and Derivatives of Vectors} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dvect}{\marg{kernel}} +Symbol for the differential of a vector. +\end{docCommand} +\begin{docCommand}{Dvect}{\marg{kernel}} +Identical to \refCom{dvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +a change \dvect{E} in electric field \\ +a change \Dvect{E} in electric field +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dirdvect}{\marg{kernel}} +Symbol for the direction of a vector's differential. +\end{docCommand} +\begin{docCommand}{dirDvect}{\marg{kernel}} +Identical to \refCom{dirdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the direction \dirdvect{E} of the change \\ +the direction \dirDvect{E} of the change +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ddirvect}{\marg{kernel}} +Symbol for the differential of a vector's direction. +\end{docCommand} +\begin{docCommand}{Ddirvect}{\marg{kernel}} +Identical to \refCom{ddirvect} but uses \(\Delta\). +\end{docCommand} +\begin{docCommand}{ddirection}{\marg{kernel}} +Alias for \refCom{ddirvect}. +\end{docCommand} +\begin{docCommand}{Ddirection}{\marg{kernel}} +Alias for \refCom{Ddirvect}. +\end{docCommand} +\begin{dispExample} +the change \ddirvect{E} or \ddirection{E} in the direction of \vect{E} \\ +the change \Ddirvect{E} or \Ddirection{E} in the direction of \vect{E} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magdvect}{\marg{kernel}} +Symbol for the magnitude of a vector's differential. +\end{docCommand} +\begin{docCommand}{magDvect}{\marg{kernel}} +Identical to \refCom{magdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the magnitude \magdvect{E} of the change \\ +the magnitude \magDvect{E} of the change +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dmagvect}{\marg{kernel}} +Symbol for the differential of a vector's magnitude. +\end{docCommand} +\begin{docCommand}{Dmagvect}{\marg{kernel}} +Identical to \refCom{dmagvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the change \dmagvect{E} in the magnitude \\ +the change \Dmagvect{E} in the magnitude +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsdvect}{\marg{kernel}} +Symbolic components of a vector. +\end{docCommand} +\begin{docCommand}{scompsDvect}{\marg{kernel}} +Identical to \refCom{scompsdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the vector \scompsdvect{E} \\ +the vector \scompsDvect{E} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compdvect}{\marg{kernel}\marg{component}} +Isolates one symbolic component of a vector's differential. +\end{docCommand} +\begin{docCommand}{compDvect}{\marg{kernel}\marg{component}} +Identical to \refCom{compdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the \compdvect{E}{y} component of the change \\ +the \compDvect{E}{y} component of the change +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervect}{\marg{kernel}\marg{indvar}} +Symbol for a vector's derivative with respect to an independent variable. +\end{docCommand} +\begin{docCommand}{Dervect}{\marg{kernel}\marg{indvar}} +Identical to \refCom{dervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the derivative \dervect{E}{t} \\ +the derivative \Dervect{E}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dermagvect}{\marg{kernel}\marg{indvar}} +Symbol for the derivative of a vector's magnitude with respect to an +independent variable. +\end{docCommand} +\begin{docCommand}{Dermagvect}{\marg{kernel}\marg{indvar}} +Identical to \refCom{dermagvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the derivative \dermagvect{E}{t} \\ +the derivative \Dermagvect{E}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{derdirvect}{\marg{kernel}\marg{indvar}} +Symbol for the derivative of a vector's direction with respect to an +independent variable. +\end{docCommand} +\begin{docCommand}{derdirection}{\marg{kernel}\marg{indvar}} +Alias for \refCom{derdirvect}. +\end{docCommand} +\begin{docCommand}{Derdirvect}{\marg{kernel}\marg{indvar}} +Identical to \refCom{derdirvect} but uses \(\Delta\). +\end{docCommand} +\begin{docCommand}{Derdirection}{\marg{kernel}\marg{indvar}} +Alias for \refCom{Derdirvect}. +\end{docCommand} +\begin{dispExample} +the derivative \derdirvect{E}{t} or \derdirection{E}{t} \\ +the derivative \Derdirvect{E}{t} or \Derdirection{E}{t} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsdervect}{\marg{kernel}\marg{indvar}} +Symbolic components of a vector's derivative with respect to an independent +variable. +\end{docCommand} +\begin{docCommand}{scompsDervect}{\marg{kernel}\marg{indvar}} +Identical to \refCom{scompsdervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the derivative \scompsdervect{E}{t} \\ +the derivative \scompsdervect{E}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compdervect}{\marg{kernel}\marg{component}\marg{indvar}} +Isolates one component of a vector's derivative with respect to an +independent variable. +\end{docCommand} +\begin{docCommand}{compDervect}{\marg{kernel}\marg{component}\marg{indvar}} +Identical to \refCom{compdervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the derivative \compdervect{E}{y}{t} \\ +the derivative \compDervect{E}{y}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magdervect}{\marg{kernel}\marg{indvar}} +Symbol for the magnitude of a vector's derivative with respect to an +independent variable. +\end{docCommand} +\begin{docCommand}{magDervect}{\marg{kernel}\marg{indvar}} +Identical to \refCom{magdervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +the derivative \magdervect{E}{t} \\ +the derivative \magDervect{E}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Naming Conventions You Have Seen} +% By now you probably understand that commands are named as closely as +% possible to the way you would say or write what you want. Every time you +% see |comp| you should think of a single component. Every time you see +% |scomps| you should think of a set of symbolic components. Every time you +% see |der| you should think derivative. Every time you see |dir| you should +% think direction. I have tried to make the names simple both logically and +% lexically. +% +% \subsubsection{Subscripted or Indexed Vectors} +% Now we have commands for vectors that carry subscripts or indices, usually +% to identify an object or something similar. Basically, \refCom{vect} becomes +% \refCom{vectsub}. Ideally, a subscript should not contain mathematical symbols. +% However, if you wish to do so, just wrap the symbol with |\(|\(\ldots \)|\)| +% as you normally would. All of the commands for non-subscripted vectors are +% available for subscripted vectors. +% +% As a matter of convention, when the initial and final values of a quantity +% are referenced, they should be labeled with subscripts |i| and |f| respectively +% using the commands in this section and similarly named commands in other +% sections. If the quantity also refers to a particular entity (e.g.\ a ball), +% specify the |i| or |f| with a comma after the label +% (e.g.\ |\vectsub{r}{ball,f}|). +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsub}{\marg{kernel}\marg{sub}} +Symbol for a subscripted vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +the vector \vectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magvectsub}{\marg{kernel}\marg{sub}} +Symbol for a subscripted vector's magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magsquaredvectsub}{\marg{kernel}\marg{sub}} +Symbol for a subscripted vector's squared magnitude. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magsquaredvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magnvectsub}{\marg{kernel}\marg{sub}\marg{exponent}} +Symbol for a subscripted vector's magnitude to an arbitrary power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magnvectsub{r}{dipole}{5} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dirvectsub}{\marg{kernel}\marg{sub}} +Symbol for a subscripted vector's direction. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dirvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsvectsub}{\marg{kernel}\marg{sub}} +Symbolic components of a subscripted vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scompsvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compvectsub}{\marg{kernel}\marg{sub}\marg{component}} +Isolates one component of a subscripted vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\compvectsub{p}{ball}{z} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magvectsubscomps}{\marg{kernel}\marg{sub}} +Expression for a subscripted vector's magnitude in terms of symbolic +components. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magvectsubscomps{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dvectsub}{\marg{kernel}\marg{sub}} +Differential of a subscripted vector. +\end{docCommand} +\begin{docCommand}{Dvectsub}{\marg{kernel}\marg{sub}} +Identical to \refCom{dvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dvectsub{p}{ball} \\ +\Dvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsdvectsub}{\marg{kernel}\marg{sub}} +Symbolic components of a subscripted vector's differential. +\end{docCommand} +\begin{docCommand}{scompsDvectsub}{\marg{kernel}\marg{sub}} +Identical to \refCom{scompsdvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scompsdvectsub{p}{ball} \\ +\scompsDvectsub{p}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compdvectsub}{\marg{kernel}\marg{sub}\marg{component}} +Isolates one component of a subscripted vector's differential. +\end{docCommand} +\begin{docCommand}{compDvectsub}{\marg{kernel}\marg{sub}\marg{component}} +Identical to \refCom{compdvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\compdvectsub{p}{ball}{y} \\ +\compDvectsub{p}{ball}{y} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Symbol for derivative of a subscripted vector with respect to an +independent variable. +\end{docCommand} +\begin{docCommand}{Dervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Identical to \refCom{dervectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dervectsub{p}{ball}{t} \\ +\Dervectsub{p}{ball}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dermagvectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Symbol for the derivative of a subscripted vector's magnitude with respect +to an independent variable. +\end{docCommand} +\begin{docCommand}{Dermagvectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Identical to \refCom{dermagvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dermagvectsub{E}{ball}{t} \\ +\Dermagvectsub{E}{ball}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsdervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Symbolic components of a subscripted vector's derivative with respect to +an independent variable. +\end{docCommand} +\begin{docCommand}{scompsDervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Identical to \refCom{scompsdervectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scompsdervectsub{p}{ball}{t} \\ +\scompsDervectsub{p}{ball}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{compdervectsub}{\marg{kernel}\marg{sub}\marg{component} +\marg{indvar}} +Isolates one component of a subscripted vector's derivative with respect +to an independent variable. +\end{docCommand} +\begin{docCommand}{compDervectsub}{\marg{kernel}\marg{sub}\marg{component} +\marg{indvar}} +Identical to \refCom{compdervectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\compdervectsub{p}{ball}{y}{t} \\ +\compDervectsub{p}{ball}{y}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magdervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Symbol for magnitude of a subscripted vector's derivative with respect +to an independent variable. +\end{docCommand} +\begin{docCommand}{magDervectsub}{\marg{kernel}\marg{sub}\marg{indvar}} +Identical to \refCom{magdervectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magdervectsub{p}{ball}{t} \\ +\magDervectsub{p}{ball}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Expressions Containing Dots} +% Now we get to commands that will save you many, many keystrokes. All of +% the naming conventions documented in earlier commands still apply. There +% are some new ones though. Every time you see |dot| you should think +% \emph{dot product}. When you see |dots| you should think \emph{dot +% product in terms of symbolic components}. When you see |dote| you should +% think \emph{dot product expanded as a sum}. These, along with the previous +% naming conventions, handle many dot product expressions. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotvect}{\marg{kernel1}\marg{kernel2}} +Symbol for dot of two vectors as a single symbol. +\end{docCommand} +\begin{docCommand}{vectDotvect}{\marg{kernel1}\marg{kernel2}} +Same as \cs{vectdotvect} but uses \cs{bullet}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotvect{\vect{F}}{\vect{v}} \\ +\vectDotvect{\vect{F}}{\vect{v}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotsvect}{\marg{kernel1}\marg{kernel2}} +Symbol for dot of two vectors with symbolic components. +\end{docCommand} +\begin{docCommand}{vectDotsvect}{\marg{kernel1}\marg{kernel2}} +Same as \cs{vectdotsvect} but uses \cs{bullet}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotsvect{F}{v} \\ +\vectDotsvect{F}{v} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotevect}{\marg{kernel1}\marg{kernel2}} +Symbol for dot of two vectors as an expanded sum. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotevect{F}{v} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotsdvect}{\marg{kernel1}\marg{kernel2}} +Dot of a vector a vector's differential with symbolic components. +\end{docCommand} +\begin{docCommand}{vectdotsDvect}{\marg{kernel1}\marg{kernel2}} +Identical to \refCom{vectdotsdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotsdvect{F}{r} \\ +\vectdotsDvect{F}{r} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotedvect}{\marg{kernel1}\marg{kernel2}} +Dot of a vector a vector's differential as an expanded sum. +\end{docCommand} +\begin{docCommand}{vectdoteDvect}{\marg{kernel1}\marg{kernel2}} +Identical to \refCom{vectdotedvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotedvect{F}{r} \\ +\vectdoteDvect{F}{r} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotsvectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Dot of two subscripted vectors with symbolic components. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotsvectsub{F}{grav}{r}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotevectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Dot of two subscripted vectors as an expanded sum. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotevectsub{F}{grav}{r}{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotsdvectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Dot of a subscripted vector and a subscripted vector's differential with +symbolic components. +\end{docCommand} +\begin{docCommand}{vectsubdotsDvectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Identical to \refCom{vectsubdotsdvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotsdvectsub{A}{ball}{B}{car} \\ +\vectsubdotsDvectsub{A}{ball}{B}{car} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotedvectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Dot of a subscripted vector and a subscripted vector's differential +as an expanded sum. +\end{docCommand} +\begin{docCommand}{vectsubdoteDvectsub} +{\marg{kernel1}\marg{sub1}\marg{kernel2}\marg{sub2}} +Identical to \refCom{vectsubdotedvectsub} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotedvectsub{A}{ball}{B}{car} \\ +\vectsubdoteDvectsub{A}{ball}{B}{car} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotsdvect}{\marg{kernel1}\marg{sub1}\marg{kernel2}} +Dot of a subscripted vector and a vector's differential with symbolic +components. +\end{docCommand} +\begin{docCommand}{vectsubdotsDvect}{\marg{kernel1}\marg{sub1}\marg{kernel2}} +Identical to \refCom{vectsubdotsdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotsdvect{A}{ball}{B} \\ +\vectsubdotsDvect{A}{ball}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectsubdotedvect}{\marg{kernel1}\marg{sub1}\marg{kernel2}} +Dot of a subscripted vector and a vector's differential as an expanded sum. +\end{docCommand} +\begin{docCommand}{vectsubdoteDvect}{\marg{kernel1}\marg{sub1}\marg{kernel2}} +Identical to \refCom{vectsubdotedvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\vectsubdotedvect{A}{ball}{B} \\ +\vectsubdoteDvect{A}{ball}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervectdotsvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Dot of a vector's derivative and a vector with symbolic components. +\end{docCommand} +\begin{docCommand}{Dervectdotsvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Identical to \refCom{dervectdotsvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dervectdotsvect{A}{t}{B} \\ +\Dervectdotsvect{A}{t}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervectdotevect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Dot of a vector's derivative and a vector as an expanded sum. +\end{docCommand} +\begin{docCommand}{Dervectdotevect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Identical to \refCom{dervectdotevect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dervectdotevect{A}{t}{B} \\ +\Dervectdotevect{A}{t}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotsdervect}{\marg{kernel1}\marg{kernel2}\marg{indvar}} +Dot of a vector and a vector's derivative with symbolic components. +\end{docCommand} +\begin{docCommand}{vectdotsDervect}{\marg{kernel1}\marg{kernel2}\marg{indvar}} +Identical to \refCom{vectdotsdervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotsdervect{A}{B}{t} \\ +\vectdotsDervect{A}{B}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectdotedervect}{\marg{kernel1}\marg{kernel2}\marg{indvar}} +Dot of a vector and a vector's derivative as an expanded sum. +\end{docCommand} +\begin{docCommand}{vectdoteDervect}{\marg{kernel1}\marg{kernel2}\marg{indvar}} +Identical to \cs{vectdotedervect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectdotedervect{A}{B}{t} \\ +\vectdoteDervect{A}{B}{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervectdotsdvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Dot of a vector's derivative and a vector's differential with symbolic +components. +\end{docCommand} +\begin{docCommand}{DervectdotsDvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Identical to \refCom{dervectdotsdvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\dervectdotsdvect{A}{t}{B} \\ +\DervectdotsDvect{A}{t}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dervectdotedvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Dot of a vector's derivative and a vector's differential as an expanded sum. +\end{docCommand} +\begin{docCommand}{DervectdoteDvect}{\marg{kernel1}\marg{indvar}\marg{kernel2}} +Identical to \refCom{dervectdotedvect} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dervectdotedvect{A}{t}{B} \\ +\DervectdoteDvect{A}{t}{B} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Expressions Containing Crosses} +% All of the naming conventions documented in earlier commands still apply. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vectcrossvect}{\marg{kernel1}\marg{kernel2}} +Cross of two vectors. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vectcrossvect{\vect{r}}{\vect{p}} +\end{dispExample*} +%\iffalse +% +%\fi +% +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ltriplecross}{\marg{kernel1}\marg{kernel2}\marg{kernel3}} +Symbol for left associated triple cross product. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ltriplecross{\vect{A}}{\vect{B}}{\vect{C}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{rtriplecross}{\marg{kernel1}\marg{kernel2}\marg{kernel3}} +Symbol for right associated triple cross product. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\rtriplecross{\vect{A}}{\vect{B}}{\vect{C}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ltriplescalar}{\marg{kernel1}\marg{kernel2}\marg{kernel3}} +Symbol for left associated triple scalar product. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ltriplescalar{\vect{A}}{\vect{B}}{\vect{C}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{rtriplescalar}{\marg{kernel1}\marg{kernel2}\marg{kernel3}} +Symbol for right associated triple scalar product. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\rtriplescalar{\vect{A}}{\vect{B}}{\vect{C}} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Basis Vectors and Bivectors} +% If you use geometric algebra or tensors, eventually you will need +% symbols for basis vectors and basis bivectors. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ezero}{} +Symbols for basis vectors with lower indices up to 4. +\end{docCommand} +\begin{docCommand}{eone}{} +\end{docCommand} +\begin{docCommand}{etwo}{} +\end{docCommand} +\begin{docCommand}{ethree}{} +\end{docCommand} +\begin{docCommand}{efour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ezero, \eone, \etwo, \ethree, \efour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{uezero}{} +Symbols for normalized basis vectors with lower indices up to 4. +\end{docCommand} +\begin{docCommand}{ueone}{} +\end{docCommand} +\begin{docCommand}{uetwo}{} +\end{docCommand} +\begin{docCommand}{uethree}{} +\end{docCommand} +\begin{docCommand}{uefour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\uezero, \ueone, \uetwo, \uethree, \uefour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ezerozero}{} +Symbols for basis bivectors with lower indices up to 4. +\end{docCommand} +\begin{docCommand}{ezeroone}{} +\end{docCommand} +\begin{docCommand}{ezerotwo}{} +\end{docCommand} +\begin{docCommand}{ezerothree}{} +\end{docCommand} +\begin{docCommand}{ezerofour}{} +\end{docCommand} +\begin{docCommand}{eoneone}{} +\end{docCommand} +\begin{docCommand}{eonetwo}{} +\end{docCommand} +\begin{docCommand}{eonethree}{} +\end{docCommand} +\begin{docCommand}{eonefour}{} +\end{docCommand} +\begin{docCommand}{etwoeone}{} +\end{docCommand} +\begin{docCommand}{etwotwo}{} +\end{docCommand} +\begin{docCommand}{etwothree}{} +\end{docCommand} +\begin{docCommand}{etwofour}{} +\end{docCommand} +\begin{docCommand}{ethreeeone}{} +\end{docCommand} +\begin{docCommand}{ethreetwo}{} +\end{docCommand} +\begin{docCommand}{ethreethree}{} +\end{docCommand} +\begin{docCommand}{ethreefour}{} +\end{docCommand} +\begin{docCommand}{efoureone}{} +\end{docCommand} +\begin{docCommand}{efourtwo}{} +\end{docCommand} +\begin{docCommand}{efourthree}{} +\end{docCommand} +\begin{docCommand}{efourfour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ezerozero, \ezeroone, \ezerotwo, \ezerothree, \ezerofour, \\ +\eoneone, \eonetwo, \eonethree, \eonefour, \etwoone, \\ +\etwotwo, \etwothree, \etwofour, \ethreeone, \ethreetwo, \\ +\ethreethree, \ethreefour, \efourone, \efourtwo, \efourthree, \\ +\efourfour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{euzero}{} +Symbols for basis vectors with upper indices up to 4. +\end{docCommand} +\begin{docCommand}{euone}{} +\end{docCommand} +\begin{docCommand}{eutwo}{} +\end{docCommand} +\begin{docCommand}{euthree}{} +\end{docCommand} +\begin{docCommand}{eufour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\euzero, \euone, \eutwo, \euthree, \eufour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ueuzero}{} +Symbols for normalized basis vectors with upper indices up to 4. +\end{docCommand} +\begin{docCommand}{ueuone}{} +\end{docCommand} +\begin{docCommand}{ueutwo}{} +\end{docCommand} +\begin{docCommand}{ueuthree}{} +\end{docCommand} +\begin{docCommand}{ueufour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ueuzero, \ueuone, \ueutwo, \ueuthree, \ueufour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{euzerozero}{} +Symbols for basis bivectors with upper indices up to 4. +\end{docCommand} +\begin{docCommand}{euzeroone}{} +\end{docCommand} +\begin{docCommand}{euzerotwo}{} +\end{docCommand} +\begin{docCommand}{euzerothree}{} +\end{docCommand} +\begin{docCommand}{euzerofour}{} +\end{docCommand} +\begin{docCommand}{euoneone}{} +\end{docCommand} +\begin{docCommand}{euonetwo}{} +\end{docCommand} +\begin{docCommand}{euonethree}{} +\end{docCommand} +\begin{docCommand}{euonefour}{} +\end{docCommand} +\begin{docCommand}{eutwoeone}{} +\end{docCommand} +\begin{docCommand}{eutwotwo}{} +\end{docCommand} +\begin{docCommand}{eutwothree}{} +\end{docCommand} +\begin{docCommand}{eutwofour}{} +\end{docCommand} +\begin{docCommand}{euthreeeone}{} +\end{docCommand} +\begin{docCommand}{euthreetwo}{} +\end{docCommand} +\begin{docCommand}{euthreethree}{} +\end{docCommand} +\begin{docCommand}{euthreefour}{} +\end{docCommand} +\begin{docCommand}{eufoureone}{} +\end{docCommand} +\begin{docCommand}{eufourtwo}{} +\end{docCommand} +\begin{docCommand}{eufourthree}{} +\end{docCommand} +\begin{docCommand}{eufourfour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\euzerozero, \euzeroone, \euzerotwo, \euzerothree, \euzerofour, \\ +\euoneone, \euonetwo, \euonethree, \euonefour, \eutwoone, \\ +\eutwotwo, \eutwothree, \eutwofour, \euthreeone, \euthreetwo, \\ +\euthreethree, \euthreefour, \eufourone, \eufourtwo, \eufourthree, \\ +\eufourfour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gzero}{} +Symbols for basis vectors, with \(\gamma\) as the kernel, with lower indices +up to 4. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\gzero, \gone, \gtwo, \gthree, \gfour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{guzero}{} +Symbols for basis vectors, with \(\gamma\) as the kernel, with upper indices +up to 4. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\guzero, \guone, \gutwo, \guthree, \gufour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gzerozero}{} +Symbols for basis bivectors, with \(\gamma\) as the kernel, with lower indices +up to 4. +\end{docCommand} +\begin{docCommand}{gzeroone}{} +\end{docCommand} +\begin{docCommand}{gzerotwo}{} +\end{docCommand} +\begin{docCommand}{gzerothree}{} +\end{docCommand} +\begin{docCommand}{gzerofour}{} +\end{docCommand} +\begin{docCommand}{goneone}{} +\end{docCommand} +\begin{docCommand}{gonetwo}{} +\end{docCommand} +\begin{docCommand}{gonethree}{} +\end{docCommand} +\begin{docCommand}{gonefour}{} +\end{docCommand} +\begin{docCommand}{gtwoeone}{} +\end{docCommand} +\begin{docCommand}{gtwotwo}{} +\end{docCommand} +\begin{docCommand}{gtwothree}{} +\end{docCommand} +\begin{docCommand}{gtwofour}{} +\end{docCommand} +\begin{docCommand}{gthreeeone}{} +\end{docCommand} +\begin{docCommand}{gthreetwo}{} +\end{docCommand} +\begin{docCommand}{gthreethree}{} +\end{docCommand} +\begin{docCommand}{gthreefour}{} +\end{docCommand} +\begin{docCommand}{gfoureone}{} +\end{docCommand} +\begin{docCommand}{gfourtwo}{} +\end{docCommand} +\begin{docCommand}{gfourthree}{} +\end{docCommand} +\begin{docCommand}{gfourfour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\gzerozero, \gzeroone, \gzerotwo, \gzerothree, \gzerofour, \\ +\goneone, \gonetwo, \gonethree, \gonefour, \gtwoone, \\ +\gtwotwo, \gtwothree, \gtwofour, \gthreeone, \gthreetwo, \\ +\gthreethree, \gthreefour, \gfourone, \gfourtwo, \gfourthree, \\ +\gfourfour +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{guzerozero}{} +Symbols for basis bivectors, with \(\gamma\) as the kernel, with upper indices +up to 4. +\end{docCommand} +\begin{docCommand}{guzeroone}{} +\end{docCommand} +\begin{docCommand}{guzerotwo}{} +\end{docCommand} +\begin{docCommand}{guzerothree}{} +\end{docCommand} +\begin{docCommand}{guzerofour}{} +\end{docCommand} +\begin{docCommand}{guoneone}{} +\end{docCommand} +\begin{docCommand}{guonetwo}{} +\end{docCommand} +\begin{docCommand}{guonethree}{} +\end{docCommand} +\begin{docCommand}{guonefour}{} +\end{docCommand} +\begin{docCommand}{gutwoeone}{} +\end{docCommand} +\begin{docCommand}{gutwotwo}{} +\end{docCommand} +\begin{docCommand}{gutwothree}{} +\end{docCommand} +\begin{docCommand}{gutwofour}{} +\end{docCommand} +\begin{docCommand}{guthreeeone}{} +\end{docCommand} +\begin{docCommand}{guthreetwo}{} +\end{docCommand} +\begin{docCommand}{guthreethree}{} +\end{docCommand} +\begin{docCommand}{guthreefour}{} +\end{docCommand} +\begin{docCommand}{gufoureone}{} +\end{docCommand} +\begin{docCommand}{gufourtwo}{} +\end{docCommand} +\begin{docCommand}{gufourthree}{} +\end{docCommand} +\begin{docCommand}{gufourfour}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\guzerozero, \guzeroone, \guzerotwo, \guzerothree, \guzerofour, \\ +\guoneone, \guonetwo, \guonethree, \guonefour, \gutwoone, \\ +\gutwotwo, \gutwothree, \gutwofour, \guthreeone, \guthreetwo, \\ +\guthreethree, \guthreefour, \gufourone, \gufourtwo, \gufourthree, \\ +\gufourfour +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsubsection{Other Vector Related} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{colvector}{\marg{commadelimitedlistofcomps}} +Typesets column vectors. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\colvector{x^0,x^1,x^2,x^3} \\ +\colvector{x_0,x_1,x_2,x_3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{rowvector}{\marg{commadelimitedlistofcomps}} +Typesets row vectors. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\rowvector{x^0,x^1,x^2,x^3} \\ +\rowvector{x_0,x_1,x_2,x_3} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompscvect}{\oarg{anynonzero}\marg{kernel}} +Typesets subscripted symbolic components of column 3- or 4-vectors +(use any nonzero value for the optional argument to typeset a 4-vector). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\begin{mysolution*} + \vect{p} &= \scompscvect{p} \\ + \vect{p} &= \scompscvect[4]{p} +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsCvect}{\oarg{anynonzero}\marg{kernel}} +Typesets superscripted symbolic components of column 3- or 4-vectors +(use any nonzero value for the optional argument to typeset a 4-vector). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\begin{mysolution*} + \vect{p} &= \scompsCvect{p} \\ + \vect{p} &= \scompsCvect[4]{p} +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsrvect}{\oarg{anynonzero}\marg{kernel}} +Typesets subscripted symbolic components of row 3- or 4-vectors +(use any nonzero value for the optional argument to typeset a 4-vector). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\begin{mysolution*} + \vect{p} &= \scompsrvect{p} \\ + \vect{p} &= \scompsrvect[4]{p} +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scompsRvect}{\oarg{anynonzero}\marg{kernel}} +Typesets superscripted symbolic components of row 3- or 4-vectors +(use any nonzero value for the optional argument to typeset a 4-vector). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\begin{mysolution*} + \vect{p} &= \scompsRvect{p} \\ + \vect{p} &= \scompsRvect[4]{p} +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{anglebetween}{\marg{kernal}\marg{kernel}} +Typesets the symbol for the angle between two vectors. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\anglebetween{a}{b} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{parallelto}{\marg{thing}} +A better looking parallel symbol whose height is the same as the perpendicular +symbol's height. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\vect{A}_{\parallelto\vect{B}}\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{perpendicularto}{\marg{thing}} +An alias for the perpendicular symbol. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\vect{A}_{\perpendicularto\vect{B}}\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{bra}{\marg{bra}} +Typesets a Dirac bra. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\bra{\Psi^*} or \bra{\frac{1}{a}\Psi^*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ket}{\marg{ket}} +Typesets a Dirac ket. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ket{\Psi} or \ket{\frac{1}{b}\Psi^*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{bracket}{\marg{bra}\marg{ket}} +Typesets a Dirac bracket. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\bracket{\Psi^*}{\Psi} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{Frequently Used Fractions} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{onehalf}{} +Small fractions with numerator 1 and denominators up to 10. +\end{docCommand} +\begin{docCommand}{onethird}{} +\end{docCommand} +\begin{docCommand}{onefourth}{} +\end{docCommand} +\begin{docCommand}{onefifth}{} +\end{docCommand} +\begin{docCommand}{onesixth}{} +\end{docCommand} +\begin{docCommand}{oneseventh}{} +\end{docCommand} +\begin{docCommand}{oneeighth}{} +\end{docCommand} +\begin{docCommand}{onenineth}{} +\end{docCommand} +\begin{docCommand}{onetenth}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\onehalf, \onethird, \onefourth, \onefifth, \onesixth, \\ +\oneseventh, \oneeighth, \oneninth, \onetenth\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{twooneths}{} +Small fractions with numerator 2 and denominators up to 10. +\end{docCommand} +\begin{docCommand}{twohalves}{} +\end{docCommand} +\begin{docCommand}{twothirds}{} +\end{docCommand} +\begin{docCommand}{twofourths}{} +\end{docCommand} +\begin{docCommand}{twofifths}{} +\end{docCommand} +\begin{docCommand}{twosixths}{} +\end{docCommand} +\begin{docCommand}{twosevenths}{} +\end{docCommand} +\begin{docCommand}{twoeighths}{} +\end{docCommand} +\begin{docCommand}{twonineths}{} +\end{docCommand} +\begin{docCommand}{twotenths}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\twooneths, \twohalves, \twothirds, \twofourths, \twofifths, \\ +\twosixths, \twosevenths, \twoeighths, \twoninths, \twotenths\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{threeoneths}{} +Small fractions with numerator 3 and denominators up to 10. +\end{docCommand} +\begin{docCommand}{threehalves}{} +\end{docCommand} +\begin{docCommand}{threethirds}{} +\end{docCommand} +\begin{docCommand}{threefourths}{} +\end{docCommand} +\begin{docCommand}{threefifths}{} +\end{docCommand} +\begin{docCommand}{threesixths}{} +\end{docCommand} +\begin{docCommand}{threesevenths}{} +\end{docCommand} +\begin{docCommand}{threeeighths}{} +\end{docCommand} +\begin{docCommand}{threenineths}{} +\end{docCommand} +\begin{docCommand}{threetenths}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\threeoneths, \threehalves, \threethirds, \threefourths, \threefifths, \\ +\threesixths, \threesevenths, \threeeighths, \threeninths, \threetenths\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fouroneths}{\marg{magnitude}} +Small fractions with numerator 4 and denominators up to 10. +\end{docCommand} +\begin{docCommand}{fourhalves}{} +\end{docCommand} +\begin{docCommand}{fourthirds}{} +\end{docCommand} +\begin{docCommand}{fourfourths}{} +\end{docCommand} +\begin{docCommand}{fourfifths}{} +\end{docCommand} +\begin{docCommand}{foursixths}{} +\end{docCommand} +\begin{docCommand}{foursevenths}{} +\end{docCommand} +\begin{docCommand}{foureighths}{} +\end{docCommand} +\begin{docCommand}{fournineths}{} +\end{docCommand} +\begin{docCommand}{fourtenths}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\fouroneths, \fourhalves, \fourthirds, \fourfourths, \fourfifths, \\ +\foursixths, \foursevenths, \foureighths, \fourninths, \fourtenths\) +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{Calculus} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{sumoverall}{\marg{variable}} +Properly typesets summation over all of some user specified entities. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \sumoverall{particles} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dx}{\marg{variable}} +Properly typesets variables of integration (the d should not be in +italics and should be properly spaced relative to the integrand). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \dx{y} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dslashx}{\marg{variable}} +Symbol indicating an inexact differential. Frequently used in physics. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \dslashx{Q} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{evaluatedfromto}{\marg{lower}\oarg{upper}} +Properly typesets the evaluation of definite integrals. Note that the upper +limit is optional. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( {\onethird y^3}\evaluatedfromto{0}[3] \) \\ +\( {\onethird y^3}\evaluatedfromto{0} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{evaluatedat}{\marg{evaluationpoint}} +Properly indicates evaluation at a particular point or value without +specifying the quantity. This is really just an alias for \cs{evaluatedfromto} +with no optional upper limit. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \text{LMST}\evaluatedat{\longitude{0}} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{integral}{\oarg{lower}\oarg{upper}\marg{integrand}\marg{var}} +Typesets indefinite and definite integrals. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \integral{y^2}{y} \] +\[ \integral[0][3]{y^2}{y} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{opensurfaceintegral}{\marg{surfacename}\marg{vectorname}} +Integral over an open surface of the normal component of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \opensurfaceintegral{S}{\vect{E}} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{closedsurfaceintegral}{\marg{surfacename}\marg{vectorname}} +Integral over a closed surface of the normal component of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \closedsurfaceintegral{S}{\vect{E}} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{openlineintegral}{\marg{pathname}\marg{vectorname}} +Integral over an open path of the tangential component of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \openlineintegral{C}{\vect{E}} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{closedlineintegral}{\marg{pathname}\marg{vectorname}} +Integral over a closed path of the tangential component of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \closedlineintegral{C}{\vect{E}} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +% For line integrals, I have not employed the common \dx{\vect{\ell}} symbol. +% Instead, I use \(\hat{t}\dx{\ell}\) for two main reason. The first is that +% line integrals require the component of a vector that is tangent to a curve, +% and I use \(\hat{t}\) to denote a unit tangent. The second is that the new +% notation looks more like that for surface integrals. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{volumeintegral}{\marg{volumename}\marg{integrand}} +Integral over a volume. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\[ \volumeintegral{V}{\rho} \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dbydt}{\oarg{operand}} +First time derivative operator. +\end{docCommand} +\begin{docCommand}{DbyDt}{\oarg{operand}} +Identical to \refCom{dbydt} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \dbydt \) or \( \dbydt x \) or \dbydt[x] \\ +\( \DbyDt \) or \( \DbyDt x \) or \DbyDt[x] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ddbydt}{\oarg{operand}} +Second time derivative operator. +\end{docCommand} +\begin{docCommand}{DDbyDt}{\oarg{operand}} +Identical to \cs{ddbydt} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \ddbydt \) or \( \ddbydt x \) or \ddbydt[x] \\ +\( \DDbyDt \) or \( \DDbyDt x \) or \DDbyDt[x] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{pbypt}{\oarg{operand}} +First partial time derivative operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \pbypt \) or \( \pbypt x \) or \pbypt[x] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ppbypt}{\oarg{operand}} +Second partial time derivative operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \ppbypt \) or \( \ppbypt x \) or \ppbypt[x] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dbyd}{\marg{dependentvariable}\marg{indvar}} +Generic first derivative operator. +\end{docCommand} +\begin{docCommand}{DbyD}{\marg{dependentvariable}\marg{indvar}} +Identical to \refCom{dbyd} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \dbyd{f}{y} \) \\ +\( \DbyD{f}{y} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ddbyd}{\marg{dependentvariable}\marg{indvar}} +Generic second derivative operator. +\end{docCommand} +\begin{docCommand}{DDbyD}{\marg{dependentvariable}\marg{indvar}} +Identical to \refCom{ddbyd} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \ddbyd{f}{y} \) \\ +\( \DDbyD{f}{y} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{pbyp}{\marg{dependentvariable}\marg{indvar}} +Generic first partial derivative operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \pbyp{f}{y} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ppbyp}{\marg{dependentvariable}\marg{indvar}} +Generic second partial derivative operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \ppbyp{f}{y} \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gradient}{} +Gibbs' gradient operator. It's just an alias for \cs{nabla}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\gradient +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{divergence}{} +Gibbs' divergence operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\divergence +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{curl}{} +Gibbs' curl operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\curl +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{taigrad}{} +Tai's gradient operator. It's just an alias for \cs{nabla}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\taigrad +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{taisvec}{} +Tai's symbol for symbolic vector. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\taisvec +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{taidivg}{} +Tai's symbol for divergence operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\taidivg +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{taicurl}{} +Tai's symbol for curl operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\taicurl +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{laplacian}{} +Laplacian operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\laplacian +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dalembertian}{} +D'Alembertian operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dalembertian +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriesfofx}{} +Series expansion of \(f(x)\) around \(x=a\). +\end{docCommand} +\begin{dispExample} +\seriesfofx \\ +\seriesfofx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriesexpx}{} +Series expansion of \(e^x\). +\end{docCommand} +\begin{dispExample} +\seriesexpx \\ +\seriesexpx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriessinx}{} +Series expansion of \(\sin x\). +\end{docCommand} +\begin{dispExample} +\seriessinx \\ +\seriessinx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriescosx}{} +Series expansion of \(\cos x\). +\end{docCommand} +\begin{dispExample} +\seriescosx \\ +\seriescosx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriestanx}{} +Series expansion of \(\tan x\). +\end{docCommand} +\begin{dispExample} +\seriestanx \\ +\seriestanx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{seriesatox}{} +Series expansion of \(a^x\). +\end{docCommand} +\begin{dispExample} +\seriesatox \\ +\seriesatox[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{serieslnoneplusx}{} +Series expansion of \(\ln(1+x)\). +\end{docCommand} +\begin{dispExample} +\serieslnoneplusx \\ +\serieslnoneplusx[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{binomialseries}{} +Series expansion of \((1+x)^n\). +\end{docCommand} +\begin{dispExample} +\binomialseries \\ +\binomialseries[z] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{diracdelta}{\marg{arg}} +Dirac delta function. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\diracdelta{x} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{orderof}{\marg{arg}} +Order of indicator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\orderof{x^2} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{eulerlagrange}{\oarg{operand}} +Euler-Lagrange equation. +\end{docCommand} +\begin{docCommand}{Eulerlagrange}{\oarg{operand}} +Like \refCom{eulerlagrange} but uses \(\Delta\). +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\( \eulerlagrange \) or \( \eulerlagrange[x] \) \\ +\( \Eulerlagrange \) or \( \Eulerlagrange[x] \) +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{Other Useful Commands} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{asin}{} +Symbol for inverse sine and other inverse circular trig functions. +\end{docCommand} +\begin{docCommand}{acos}{} +\end{docCommand} +\begin{docCommand}{atan}{} +\end{docCommand} +\begin{docCommand}{asec}{} +\end{docCommand} +\begin{docCommand}{acsc}{} +\end{docCommand} +\begin{docCommand}{acot}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \asin, \acos, \atan, \asec, \acsc, \acot \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{sech}{} +Hyperbolic and inverse hyperbolic functions not defined in \LaTeX. +\end{docCommand} +\begin{docCommand}{csch}{} +\end{docCommand} +\begin{docCommand}{asinh}{} +\end{docCommand} +\begin{docCommand}{acosh}{} +\end{docCommand} +\begin{docCommand}{atanh}{} +\end{docCommand} +\begin{docCommand}{asech}{} +\end{docCommand} +\begin{docCommand}{acsch}{} +\end{docCommand} +\begin{docCommand}{acoth}{} +\end{docCommand} +\begin{dispExample} +\( \sech, \csch, \asinh, \acosh, \atanh, \asech, \acsch, \acoth \) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{sgn}{\marg{arg}} +Signum function. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \sgn \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dex}{} +Decimal exponentiation function (used in astrophysics). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\( \dex \) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{logb}{\oarg{base}} +Logarithm to an arbitrary base. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\logb 8, \logb[2] 8 +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{cB}{} +Alternate symbol for magnetic field inspired by Tom Moore. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\cB, \vect{\cB} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{newpi}{} +Bob Palais' symbol for \(2\pi\). +\end{docCommand} +\begin{dispExample*}{sidebyside} +\newpi +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{scripty}{\marg{kernel}} +Command to get fonts in Griffiths' electrodynamics textbook. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\scripty{r} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Lagr}{} +Command to get symbol for Lagrangian. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Lagr +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{flux}{\oarg{label}} +Symbol for flux of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\flux, \flux[E] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{circulation}{\oarg{label}} +Symbol for circulation of a vector field. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\circulation, \circulation[E] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inparens}{\marg{arg}} +Surrounds with argument with parentneses. A blank argument generates a +placeholder. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\inparens{\onehalf}, \inparens{-3}, \inparens{} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{absof}{\marg{arg}} +Absolute value function. A blank argument generates a placeholder. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\absof{-4}, \absof{} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{magof}{\marg{arg}} +Magnitude of a quantity (lets you selectively use double bars even +when the \opt{singlemagbars} option is use when loading the package). +A blank argument generates a placeholder. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\magof{\vect{E}}, \magof{} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dimsof}{\marg{arg}} +Notation for showing the dimensions of a quantity. A blank argument +generates a placeholder. +\end{docCommand} +\begin{dispExample} +\( \dimsof{\vect{v}} = L \cdot T^{-1} \), \dimsof{} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{unitsof}{\marg{arg}} +Notation for showing the units of a quantity. I propose this notation and +hope to propagate it because I could not find any standard notation for +this same idea in other sources. A blank argument generates a placeholder. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\unitsof{\vect{v}} = \velocityonlyaltnunit, \unitsof{} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Changein}{\marg{arg}} +Notation for \emph{the change in a quantity}. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\Changein{\vect{E}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{xtento}{\marg{exponent}\oarg{unit}} +Command for scientific notation with an optional unit. +\end{docCommand} +\begin{docCommand}{timestento}{\marg{exponent}\oarg{unit}} +Another command for scientific notation with an optional unit. +\end{docCommand} +\begin{dispExample*}{sidebyside} +2.99\xtento{8}[\velocityonlyaltnunit] \\ +2.99\timestento{-4} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ee}{\marg{mantissa}\marg{exponent}} +Command for scientific notation for computer code. Units are not used in computer +code. +\end{docCommand} +\begin{docCommand}{EE}{\marg{mantissa}\marg{exponent}} +Identical to \refCom{ee} but gives capital letters. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ee{2.99}{8} \\ +\EE{2.99}{8} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{dms}{\marg{deg}\marg{min}\marg{sec}} +Command for formatting angles and time. Note that other packages may do +this better. +\end{docCommand} +\begin{docCommand}{hms}{\marg{deg}\marg{min}\marg{sec}} +Like \refCom{dms} but formats time. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\dms{23}{34}{10.27} \\ +\hms{23}{34}{10.27} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{clockreading}{\marg{hrs}\marg{min}\marg{sec}} +Command for formatting a clock reading. Really an alias for \refCom{hms}, +but conceptually a very different idea that introductory textbooks don't +do a good enough job at articulating. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\clockreading{23}{34}{10.27} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{latitude}{\marg{arg}} +Command for formatting latitude, useful in astronomy. +\end{docCommand} +\begin{docCommand}{latitudeN}{\marg{arg}} +Command for formatting latitude with an N for north. +\end{docCommand} +\begin{docCommand}{latitudeS}{\marg{arg}} +Command for formatting latitude with an S for north. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\latitude{+35}, \latitudeN{35}, \latitudeS{35} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{longitude}{\marg{arg}} +Command for formatting longitude, useful in astronomy. +Use \refCom{longitudeE} or \refCom{longitudeW} to include a letter. +\end{docCommand} +\begin{docCommand}{longitudeE}{\marg{arg}} +Command for formatting longitude with an E for east. +\end{docCommand} +\begin{docCommand}{longitudeW}{\marg{arg}} +Command for formatting longitude with an W for east. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\longitude{-81}, \longitudeE{81}, \longitudeW{81} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ssup}{\marg{kernel}\marg{sup}} +Command for typesetting text superscripts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ssup{N}{contact} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ssub}{\marg{kernel}\marg{sub}} +Command for typesetting text subscripts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ssub{N}{AB} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ssud}{\marg{sup}\marg{sub}} +Command for typesetting text superscripts and subscripts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\ssud{N}{contact}{AB} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{msub}{\marg{kernel}\marg{sub}} +Command for typesetting mathematical subscripts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\msub{R}{\alpha\beta} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{msud}{\marg{kernel}\marg{sup}\marg{sub}} +Command for typesetting mathematical superscripts and subscripts. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\msud{\Gamma}{\gamma}{\alpha\beta} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{levicivita}{\marg{indices}} +Command for Levi-Civita symbol. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\levicivita{ijk} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{kronecker}{\marg{indices}} +Command for Kronecker delta symbol. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\kronecker{ij} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{xaxis}{} +Command for coordinate axes. +\end{docCommand} +\begin{docCommand}{yaxis}{} +\end{docCommand} +\begin{docCommand}{zaxis}{} +\end{docCommand} +\begin{dispExample*}{sidebyside} + \xaxis, \yaxis, \zaxis +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{naxis}{\oarg{axis}} +Command for custom naming a coordinate axis. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\naxis{t} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{axis}{} +Suffix command for custom naming a coordinate axis. You are responsible +for using math mode if necessary for the thing to which you apply the +suffix. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(t\axis\) +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{xyplane}{} +Commands for naming coordinate planes. All combinations are defined. +\end{docCommand} +\begin{docCommand}{yzplane}{} +\end{docCommand} +\begin{docCommand}{zxplane}{} +\end{docCommand} +\begin{docCommand}{yxplane}{} +\end{docCommand} +\begin{docCommand}{zyplane}{} +\end{docCommand} +\begin{docCommand}{xzplane}{} +\end{docCommand} +\begin{dispExample} +\xyplane, \yzplane, \zxplane, \yxplane, \zyplane, \xzplane +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{plane}{} +Suffix command for custom naming a coordinate plane. You are responsible +for using math mode if necessary for the thing to which you apply the suffix. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(xt\)\plane +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fsqrt}{\marg{arg}} +Command for square root as a fractional exponent. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\fsqrt{x} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{cuberoot}{\marg{arg}} +Command for cube root of an argument. +\end{docCommand} +\begin{docCommand}{fcuberoot}{\marg{arg}} +Command for cube root of an argument as a fractional power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\cuberoot{x} \\ +\fcuberoot{x} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fourthroot}{\marg{arg}} +Command for fourth root of an argument. +\end{docCommand} +\begin{docCommand}{ffourthroot}{\marg{arg}} +Command for fourth root of an argument as a fractional power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\fourthroot{x} \\ +\ffourthroot{x} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fifthroot}{\marg{arg}} +Command for fifth root of an argument. +\end{docCommand} +\begin{docCommand}{ffifthroot}{\marg{arg}} +Command for fifth root of an argument as a fractional power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\fifthroot{x} \\ +\ffifthroot{x} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{relgamma}{\marg{arg}} +Expression for Lorentz factor. +\end{docCommand} +\begin{docCommand}{frelgamma}{\marg{arg}} +Expression for Lorentz factor with a fractional power. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\begin{mysolution*} + \gamma &= \relgamma{\magvect{v}} \\ + \gamma &= \frelgamma{\magvect{v}} +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{oosqrtomxs}{\marg{arg}} +Commands for \textbf{o}ne \textbf{o}ver \textbf{s}quare root \textbf{o}f +\textbf{o}ne \textbf{m}inus \textbf{x} \textbf{s}quared. Say that out loud and +you will see where the name comes from. +\end{docCommand} +\begin{docCommand}{oosqrtomx}{\marg{arg}} +Commands for \textbf{o}ne \textbf{o}ver \textbf{s}quare root \textbf{o}f +\textbf{o}ne \textbf{m}inus \textbf{x}. Say that out loud and +you will see where the name comes from. +\end{docCommand} +\begin{docCommand}{oomx}{\marg{arg}} +Commands for \textbf{o}ne \textbf{o}ver \textbf{s}quare root \textbf{o}f +\textbf{o}ne \textbf{m}inus \textbf{x}. Say that out loud and +you will see where the name comes from. +\end{docCommand} +\begin{docCommand}{oopx}{\marg{arg}} +Commands for \textbf{o}ne \textbf{o}ver \textbf{s}quare root \textbf{o}f +\textbf{o}ne \textbf{p}lus \textbf{x}. Say that out loud and +you will see where the name comes from. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\oosqrtomxs{0.22} \\ +\oosqrtomx{0.22} \\ +\ooomx{0.22} \\ +\ooopx{0.11} +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{Custom Operators} +% The \(=\) operator is frequently misused. We need other operators +% for other cases to express conceptual relationships other than, say, +% mathematical equality. Some of these may seem strange to you but I have +% found them helpful. +%\iffalse +%<*example> +%\fi +\begin{docCommand}{isequals}{} +Command for \emph{test-for-equality} operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +5 \isequals 3 +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{wordoperator}{\marg{firstline}\marg{secondline}} +Command for two lines of tiny text to be use as an operator without using +mathematical symbols. +\end{docCommand} +\begin{docCommand}{pwordoperator}{\marg{firstline}\marg{secondline}} +Like \refCom{wordoperator} but puts parentheses around the operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\wordoperator{added}{to} \\ +\pwordoperator{added}{to} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{definedas}{} +Operator representing a definition. +\end{docCommand} +\begin{docCommand}{pdefinedas}{} +Same as \refCom{definedas} but puts parentheses around the operator. +\end{docCommand} +\begin{docCommand}{earlierthan}{} +Operator useful for comparing times and clock readings. +\end{docCommand} +\begin{docCommand}{pearlierthan}{} +Same as \refCom{earlierthan} but puts parentheses around the operator. +\end{docCommand} +\begin{docCommand}{laterthan}{} +Operator useful for comparing times and clock readings. +\end{docCommand} +\begin{docCommand}{platerthan}{} +Same as \refCom{laterthan} but puts parentheses around the operator. +\end{docCommand} +\begin{docCommand}{adjustedby}{} +Operator useful for comparing times and clock readings. +\end{docCommand} +\begin{docCommand}{padjustedby}{} +Same as \refCom{adjustedby} but puts parentheses around the operator. +\end{docCommand} +\begin{docCommand}{forevery}{} +Operator for conveying the idea of for every. +\end{docCommand} +\begin{docCommand}{pforevery}{} +Same as \refCom{forevery} but puts parentheses around the operator. +\end{docCommand} +\begin{docCommand}{associated}{} +Operator representing a conceptual association. +\end{docCommand} +\begin{docCommand}{passociated}{} +Same as \refCom{associated} but puts parentheses around the operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\definedas \\ +\pdefinedas \\ +\earlierthan \\ +\pearlierthan \\ +\laterthan \\ +\platerthan \\ +\adjustedby \\ +\padjustedby \\ +\forevery \\ +\pforevery \\ +\associated \\ +\passociated +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{defines}{} +Command for \emph{defines} or \emph{defined by} operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\vect{p} \defines \(\gamma m\)\vect{v} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{inframe}{\oarg{frame}} +Command for operator indicating the coordinate representation of a vector +in a particular reference frame denoted by a capital letter. +\end{docCommand} +\begin{dispExample} +\vect{p} \inframe[S] \momentum{\mivector{1,2,3}} \\ +\vect{p} \inframe[S'] \momentum{\mivector{\sqrt{14},0,0}} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{associates}{} +Command for \emph{associated with} or \emph{associates with} operator +(for verbal concepts). This is conceptually different from the +\refCom{associated} or \refCom{passociated} operators. +\end{docCommand} +\begin{dispExample*}{sidebyside} +kinetic energy \associates velocity +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{becomes}{} +Command for \emph{becomes} operator. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\(\gamma m\)\vect{v} \becomes \(m\)\vect{v} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{rrelatedto}{\marg{leftoperation}} +Command for left-to-right relationship. +\end{docCommand} +\begin{dispExample} +(flux ratio) \rrelatedto{taking logarithm} (mag diff) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{lrelatedto}{\marg{roperation}} +Command for right-to-left relationship. +\end{docCommand} +\begin{dispExample} +(flux ratio) \lrelatedto{exponentiation} (mag diff) +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{brelatedto}{\marg{leftoperation}\marg{roperation}} +Command for bidirectional relationship. +\end{docCommand} +\begin{dispExample} +(mag diff) \brelatedto{taking logarithm}{exponentiation}(flux ratio) +\end{dispExample} +%\iffalse +% +%\fi +% +% \subsection{Commands Specific to \mi} +% While these commands were inspired by \mi, they can certainly be used in +% any introductory physics course. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{momentumprinciple}{} +Expression for the momentum principle. +\end{docCommand} +\begin{docCommand}{LHSmomentumprinciple}{} +Just the left hand side. +\end{docCommand} +\begin{docCommand}{RHSmomentumprinciple}{} +Just the right hand side. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\momentumprinciple \\ +\LHSmomentumprinciple \\ +\RHSmomentumprinciple +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{momentumprinciplediff}{} +Expression for the momentum principle in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\momentumprinciplediff +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{energyprinciple}{} +Expression for the energy principle. Processes other than work and +thermal energy transfer (e.g.\ radiation) are neglected. +\end{docCommand} +\begin{docCommand}{LHSenergyprinciple}{} +Just the left hand side. +\end{docCommand} +\begin{docCommand}{RHSenergyprinciple}{} +Just the right hand side. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\energyprinciple \\ +\LHSenergyprinciple \\ +\RHSenergyprinciple +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{energyprinciplediff}{} +Expression for the energy principle in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\energyprinciplediff +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularmomentumprinciple}{} +Expression for the angular momentum principle. +\end{docCommand} +\begin{docCommand}{LHSangularmomentumprinciple}{} +Just the left hand side. +\end{docCommand} +\begin{docCommand}{RHSangularmomentumprinciple}{} +Just the right hand side. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\angularmomentumprinciple \\ +\LHSangularmomentumprinciple \\ +\RHSangularmomentumprinciple +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{angularmomentumprinciplediff}{} +Expression for the angular momentum principle in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\angularmomentumprinciplediff +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalinteraction}{} +Expression for gravitational interaction. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\gravitationalinteraction +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricinteraction}{} +Expression for electric interaction. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\electricinteraction +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springinteraction}{} +Expression for spring interaction. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\springinteraction +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gfieldofparticle}{} +Expression for a particle's gravitational field. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\gfieldofparticle +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Efieldofparticle}{} +Expression for a particle's electric field. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Efieldofparticle +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Bfieldofparticle}{} +Expression for a particle's magnetic field. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Bfieldofparticle +\end{dispExample*} +%\iffalse +% +%\fi +% +% In the commands that take an optional label, note how to specify +% initial and final values of quantities. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Esys}{\oarg{label}} +Symbol for system energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Esys, \Esys[final], \Esys[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Us}{\oarg{label}} +Symbol for spring potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Us, \Us[final], \Us[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ug}{\oarg{label}} +Symbol for gravitational potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Ug, \Ug[final], \Ug[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ue}{\oarg{label}} +Symbol for electric potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Ue, \Ue[final], \Ue[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ktrans}{\oarg{label}} +Symbol for translational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Ktrans, \Ktrans[final], \Ktrans[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Krot}{\oarg{label}} +Symbol for rotational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Krot, \Krot[final], \Krot[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Kvib}{\oarg{label}} +Symbol for vibrational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Kvib, \Evib[final], \Evib[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Eparticle}{\oarg{label}} +Symbol for particle energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Eparticle, \Eparticle[final], \Eparticle[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Einternal}{\oarg{label}} +Symbol for internal energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Einternal, \Einternal[final], \Einternal[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Erest}{\oarg{label}} +Symbol for rest energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Erest, \Erest[final], \Erest[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Echem}{\oarg{label}} +Symbol for chemical energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Echem, \Echem[final], \Echem[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Etherm}{\oarg{label}} +Symbol for thermal energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Etherm, \Etherm[final], \Etherm[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Evib}{\oarg{label}} +Symbol for vibrational energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Evib, \Evib[final], \Evib[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ephoton}{\oarg{label}} +Symbol for photon energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Ephoton, \Ephoton[final], \Ephoton[initial] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEsys}{} +Symbol for change in system energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEsys +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DUs}{} +Symbol for change in spring potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DUs +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DUg}{} +Symbol for change in gravitational potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DUg +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DUe}{} +Symbol for change in electric potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DUe +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DKtrans}{} +Symbol for change in translational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DKtrans +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DKrot}{} +Symbol for change in rotational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DKrot +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DKvib}{} +Symbol for change in vibrational kinetic energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DKvib +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEparticle}{} +Symbol for change in particle energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEparticle +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEinternal}{} +Symbol for change in internal energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEinternal +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DErest}{} +Symbol for change in rest energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DErest +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEchem}{} +Symbol for change in chemical energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEchem +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEtherm}{} +Symbol for change in thermal energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEtherm +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEvib}{} +Symbol for change in vibrational energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEvib +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{DEphoton}{} +Symbol for change in photon energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\DEphoton +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{springpotentialenergy}{} +Expression for spring potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\springpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{finalspringpotentnialenergy}{} +Expression for final spring potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\finalspringpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{initialspringpotentialenergy}{} +Expression for initial spring potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\initialspringpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{electricpotentialenergy}{} +Expression for electric potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\electricpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{finalelectricpotentialenergy}{} +Expression for final electric potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\finalelectricpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{initialelectricpotentialenergy}{} +Expression for initial electric potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\initialelectricpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{gravitationalpotentialenergy}{} +Expression for gravitational potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\gravitationalpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{finalgravitationalpotentialenergy}{} +Expression for final gravitational potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\finalgravitationalpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{initialgravitationalpotentialenergy}{} +Expression for initial gravitational potential energy. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\initialgravitationalpotentialenergy +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{ks}{} +Symbol for spring stiffness. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\ks +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Fnet}{} +Various symbols for net force. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Fnet, \Fnetext, \Fnetsys, \Fsub{ball,bat} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Tnet}{} +Various symbols for net torque. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Tnet, \Tnetext, \Tnetsys, \Tsub{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{Ltotal}{} +Various symbols for total angular momentum. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\Ltotal, \Lsys, \Lsub{ball} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwelliint}{\oarg{surfacename}} +Left hand side of Maxwell's first equation in integral form. Note the +default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\LHSmaxwelliint \\ + &\LHSmaxwelliint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliint}{} +Right hand side of Maxwell's first equation in integral form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliint \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliinta}{\oarg{volumename}} +Alternate form of right hand side of Maxwell's first equation in +integral form. Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliinta \\ + &\RHSmaxwelliinta[\upsilon] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliintfree}{} +Right hand side of Maxwell's first equation in integral form in +free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliintfree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliint}{\oarg{surfacename}} +Maxwell's first equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliint \\ + &\maxwelliint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliinta}{\oarg{surfacename}\oarg{volumename}} +Alternate form of Maxwell's first equation in integral form. +Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliinta \\ + &\maxwelliinta[S][\upsilon] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliintfree}{\oarg{surfacename}} +Maxwell's first equation in integral form in free space. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliintfree \\ + &\maxwelliintfree[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwelliiint}{\oarg{surfacename}} +Left hand side of Maxwell's second equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\LHSmaxwelliiint \\ + &\LHSmaxwelliiint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiint}{} +Right hand side of Maxwell's second equation in integral form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiint \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiintm}{} +Right hand side of Maxwell's second equation in integral form +with magnetic monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiintm \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiintma}{\oarg{volumename}} +Alternate form of right hand side of Maxwell's second equation in +integral form with magnetic monopoles. Note the default value of +the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliiintma \\ + &\RHSmaxwelliiintma[\upsilon] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiintfree}{} +Right hand side of Maxwell's second equation in integral form in +free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiintfree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiint}{\oarg{surfacename}} +Maxwell's second equation in integral form. Note the default value +of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiint \\ + &\maxwelliiint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiintm}{\oarg{surfacename}} +Maxwell's second equation in integral form with magnetic monopoles. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiintm \\ + &\maxwelliiintm[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiintma}{\oarg{surfacename}\oarg{volumename}} +Alternate form of Maxwell's second equation in integral form with +magnetic monopoles. Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiintma \\ + &\maxwelliiintma[S][\upsilon] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiintfree}{\oarg{surfacename}} +Maxwell's second equation in integral form in free space. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiintfree \\ + &\maxwelliiintfree[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwelliiiint}{\oarg{boundaryname}} +Left hand side of Maxwell's third equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\LHSmaxwelliiiint \\ + &\LHSmaxwelliiiint[C] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiiint}{\oarg{surfacename}} +Right hand side of Maxwell's third equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliiiint \\ + &\RHSmaxwelliiiint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiiintm}{\oarg{surfacename}} +Right hand side of Maxwell's third equation in integral form with +magnetic monopoles. Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliiiintm \\ + &\RHSmaxwelliiiintm[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiiintma}{\oarg{surfacename}} +Alternate form of right hand side of Maxwell's third equation in +integral form with magnetic monopoles. Note the default value of +the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliiiintma \\ + &\RHSmaxwelliiiintma[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiiintfree}{\oarg{surfacename}} +Right hand side of Maxwell's third equation in integral form in +free space. Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwelliiiintfree \\ + &\RHSmaxwelliiiintfree[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiiint}{\oarg{boundaryname}\oarg{surfacename}} +Maxwell's third equation in integral form. Note the default values of +the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiiint \\ + &\maxwelliiiint[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiiintm}{\oarg{boundaryname}\oarg{surfacename}} +Maxwell's third equation in integral form with magnetic monopoles. +Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiiintm \\ + &\maxwelliiiintm[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiiintma}{\oarg{boundaryname}\oarg{surfacename}} +Alternate form of Maxwell's third equation in integral form with magnetic +monopoles. Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiiintma \\ + &\maxwelliiiintma[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiiintfree}{\oarg{boundaryname}\oarg{surfacename}} +Maxwell's third equation in integral form in free space. Note the default +values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwelliiiintfree \\ + &\maxwelliiiintfree[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwellivint}{\oarg{boundaryname}} +Left hand side of Maxwell's fourth equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\LHSmaxwellivint \\ + &\LHSmaxwellivint[C] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellivint}{\oarg{surfacename}} +Right hand side of Maxwell's fourth equation in integral form. +Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwellivint \\ + &\RHSmaxwellivint[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellivinta}{\oarg{surfacename}} +Alternate form of right hand side of Maxwell's fourth equation in +integral form. Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwellivinta \\ + &\RHSmaxwellivinta[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellivintfree}{\oarg{surfacename}} +Right hand side of Maxwell's fourth equation in integral form in +free space. Note the default value of the optional argument. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\RHSmaxwellivintfree \\ + &\RHSmaxwellivintfree[S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellivint}{\oarg{boundaryname}\oarg{surfacename}} +Maxwell's fourth equation in integral form. Note the default values of +the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwellivint \\ + &\maxwellivint[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellivinta}{\oarg{boundaryname}\oarg{surfacename}} +Alternate form of Maxwell's fourth equation in integral form. +Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwellivinta \\ + &\maxwellivinta[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellivintfree}{\oarg{boundaryname}\oarg{surfacename}} +Maxwell's fourth equation in integral form in free space. +Note the default values of the optional arguments. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{mysolution*} + &\maxwellivintfree \\ + &\maxwellivintfree[C][S] +\end{mysolution*} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwellidif}{} +Left hand side of Maxwell's first equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \LHSmaxwellidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellidif}{} +Right hand side of Maxwell's first equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwellidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellidiffree}{} +Right hand side of Maxwell's first equation in differential form +in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwellidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellidif}{} +Maxwell's first equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwellidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellidiffree}{} +Maxwell's first equation in differential form in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwellidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwelliidif}{} +Left hand side of Maxwell's second equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \LHSmaxwelliidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliidif}{} +Right hand side of Maxwell's second equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliidifm}{} +Right hand side of Maxwell's second equation in differential +form with magnetic monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliidifm \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliidiffree}{} +Right hand side of Maxwell's second equation in differential +form in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliidif}{} +Maxwell's second equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliidifm}{} +Maxwell's second equation in differential form with magnetic +monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliidifm \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellidiiffree}{} +Maxwell's second equation in differential form in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwelliiidif}{} +Left hand side of Maxwell's third equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \LHSmaxwelliiidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiidif}{} +Right hand side of Maxwell's third equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiidifm}{} +Right hand side of Maxwell's third equation in differential form +with magnetic monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiidifm \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwelliiidiffree}{} +Right hand side of Maxwell's third equation in differential form +in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwelliiidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiidif}{} +Maxwell's third equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliiidif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiidifm}{} +Maxwell's third equation in differential form with magnetic +monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliiidifm \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwelliiidiffree}{} +Maxwell's third equation in differential form in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwelliiidiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{LHSmaxwellivdif}{} +Left hand side of Maxwell's fourth equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \LHSmaxwellivdif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellivdif}{} +Right hand side of Maxwell's fourth equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwellivdif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSmaxwellivdiffree}{} +Right hand side of Maxwell's fourth equation in differential form +in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSmaxwellivdiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellivdif}{} +Maxwell's fourth equation in differential form. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwellivdif \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{maxwellivdiffree}{} +Maxwell's fourth equation in differential form in free space. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \maxwellivdiffree \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSlorentzforce}{} +Right hand side of Lorentz force. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSlorentzforce \] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{RHSlorentzforcem}{} +Right hand side of Lorentz force with magnetic monopoles. +\end{docCommand} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\[ \RHSlorentzforcem \] +\end{dispExample*} +%\iffalse +% +%\fi +% +% \subsection{VPython and GlowScript Code} +% There are three ways to deal with VPython\footnote{See the VPython home page at +% \url{https://vpython.org/} for more information.} and GlowScript\footnote{See the +% GlowScript home page at \url{https://glowscript.org/} for more information.} code. +% With very few exceptions, VPython code and GlowScript code are identical. The +% commands with |vpython| in their names can handle both, but for semantic +% completeness there are corresponding commands with |glowscript| in their names. +% Because Classic VPython will no longer be developed, the first line of all +% VPython programs not used in GlowScript will conform to Jupyter syntax. +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vpythonline}{\marg{vpythoncode}} +Command for a single line of VPython or GlowScript code used inline. +\end{docCommand} +\begin{dispExample} +\vpythonline{from vpython import *} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{glowscriptline}{\marg{glowscriptcode}} +Command for a single line of GlowScript code used inline. Note that with very +few exceptions, GlowScript code is identical to VPython code. +\end{docCommand} +\begin{dispExample} +\glowscriptline{xyplane = box(pos=vector(0,0,0),length=10,width=10,height=0.05)} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{vpythonblock}{\marg{caption}\marg{label}} +Environment for a block of VPython code. A caption and label are +required. The label can be used by \cs{ref} or \cs{hyperref}. +\end{docEnvironment} +\begin{docEnvironment}{glowscriptblock}{\marg{caption}\marg{label}} +Functionally identical to \refEnv{vpythonblock}. +\end{docEnvironment} +\begin{dispExample} +\begin{vpythonblock}{Example VPython Listing}{listing1} + from vpython import * + + sphere(pos=vector(1,2,3),color=color.green) + # create a named arrow + MyArrow=arrow(pos=earth.pos,axis=fscale*Fnet,color=color.green) + print ("arrow.pos = "), arrow.pos +\end{vpythonblock} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{vpythonfile}{\marg{caption}\marg{label}\meta{filename}} +Typesets a file in the current directory containing VPython code. A caption and +label are required. The label can be used by \cs{ref} and \cs{hyperref}. +The listing will begin on a new page. +\end{docCommand} +\begin{docCommand}{glowscriptfile}{\marg{caption}\marg{label}\meta{filename}} +Functionally identical to \refCom{vpythonfile}. +\end{docCommand} +\begin{dispExample} +\vpythonfile{Program vdemo.py}{vlisting1}{vdemo.py} +\end{dispExample} +%\iffalse +% +%\fi +% +% \subsection{Boxes and Environments} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{emptyanswer}{\oarg{wdth}\oarg{hght}} +Typesets empty space for filling answer boxes, so there is nothing to see. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\emptyanswer[0.75][0.2] +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{activityanswer} + {\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Main environment for typesetting boxed answers. +\end{docEnvironment} +\begin{dispExample} +\begin{activityanswer} + Lorem ipsum dolor sit amet, consectetuer adipiscing elit. + Morbi commodo, ipsum sed pharetra gravida, orci magna + rhoncus neque, id pulvinar odio lorem non turpis. Nullam + sit amet enim. +\end{activityanswer} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{adjactivityanswer} + {\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Like \refEnv{activityanswer} but adjusts vertically to tightly surround text. +\end{docEnvironment} +\begin{dispExample} +\begin{adjactivityanswer} + Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Morbi + commodo, ipsum sed pharetra gravida, orci magna rhoncus neque, + id pulvinar odio lorem non turpis. Nullam sit amet enim. + Suspendisse id velit vitae ligula volutpat condimentum. Aliquam + erat volutpat. Sed quis velit. Nulla facilisi. Nulla libero. + Vivamus pharetra posuere sapien. Nam consectetuer. Sed aliquam, + nunc eget euismod ullamcorper, lectus nunc ullamcorper orci, + fermentum bibendum enim nibh eget ipsum. Donec porttitor ligula + eu dolor. Maecenas vitae nulla consequat libero cursus venenatis. + Nam magna enim, accumsan eu, blandit sed, blandit a, eros. +\end{adjactivityanswer} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{emptybox} + {\oarg{txt}\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Provides a fixed-size box with optional text. +\end{docCommand} +\begin{dispExample} +\emptybox[Lorem ipsum dolor sit amet, consectetuer adipiscing elit. +Morbi commodo, ipsum sed pharetra gravida, orci magna rhoncus neque, +id pulvinar odio lorem non turpis. Nullam sit amet enim.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{adjemptybox} + {\oarg{txt}\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Like \refCom{emptybox} but adjusts vertically to tightly surround text. +\end{docCommand} +\begin{dispExample} +\adjemptybox[Lorem ipsum dolor sit amet, consectetuer adipiscing +elit. Morbi commodo, ipsum sed pharetra gravida, orci magna rhoncus +neque, id pulvinar odio lorem non turpis. Nullam sit amet enim.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{answerbox} + {\oarg{txt}\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Wrapper for \refCom{emptybox}. +\end{docCommand} +\begin{dispExample} +\answerbox[Lorem ipsum dolor sit amet, consectetuer adipiscing elit. +Morbi commodo, ipsum sed pharetra gravida, orci magna rhoncus neque, +id pulvinar odio lorem non turpis. Nullam sit amet enim.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{adjanswerbox} + {\oarg{txt}\oarg{bgclr}\oarg{frmclr}\oarg{txtclr}\oarg{wdth}\oarg{hght}} +Wrapper for \refCom{adjemptybox}. +\end{docCommand} +\begin{dispExample} +\adjanswerbox[Lorem ipsum dolor sit amet, consectetuer adipiscing +elit. Morbi commodo, ipsum sed pharetra gravida, orci magna rhoncus +neque, id pulvinar odio lorem non turpis. Nullam sit amet enim.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{smallanswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.10 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth}. +\end{docCommand} +\begin{dispExample} +\smallanswerbox[][red] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mediumanswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.20 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth}. +\end{docCommand} +\begin{dispExample} +\mediumanswerbox[][lightgray] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{largeanswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.25 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\largeanswerbox[][lightgray] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{largeranswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.33 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\largeranswerbox[][lightgray] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hugeanswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.50 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\hugeanswerbox[][lightgray] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hugeranswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 0.75 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\hugeranswerbox[][lightgray] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fullpageanswerbox}{\oarg{txt}\oarg{bgclr}} +Answer box with height 1.00 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\fullpageanswerbox[][lightgray] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{smallanswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.10 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth}. The first argument isn't +really optional, and \emph{must} be different for each form used. +Content can be typed in the box and saved with a PDF editor or viewer +that supports PDF forms. +\end{docCommand} +\begin{dispExample} +\smallanswerform[a1][Type your response here.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{mediumanswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.20 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth}. The first argument isn't +really optional, and \textbf{must} be different for each form used. +Content can be typed in the box and saved with a PDF editor or viewer +that supports PDF forms. +\end{docCommand} +\begin{dispExample} +\mediumanswerform[a1][Type your response here.] +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{largeanswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.25 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\largeanswerform[a1][Type your response here.] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{largeranswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.33 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\largeranswerform[a1][Type your response here.] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hugeanswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.50 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\hugeanswerform[a1][Type your response here.] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{hugeranswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 0.75 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\hugeranswerform[a1][Type your response here.] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{fullpageanswerform}{\oarg{name}\oarg{prompt}} +Editable answer form with height 1.00 that of current \cs{textheight} +and width 0.90 that of current \cs{linewidth} (too large to show here). +\end{docCommand} +\begin{dispListing} +\fullpageanswerform[a1][Type your response here.] +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{miinstructornote}{} +Environment for highlighting notes to instructors. +\end{docEnvironment} +\begin{dispExample} +\begin{miinstructornote} + Nunc auctor bibendum eros. Maecenas porta accumsan mauris. Etiam + enim enim, elementum sed, bibendum quis, rhoncus non, metus. Fusce + neque dolor, adipiscing sed, consectetuer et, lacinia sit amet, + quam. Suspendisse wisi quam, consectetuer in, blandit sed, + suscipit eu, eros. Etiam ligula enim, tempor ut, blandit nec, + mollis eu, lectus. Nam cursus. Vivamus iaculis. Aenean risus + purus, pharetra in, blandit quis, gravida a, turpis. Donec nisl. + Aenean eget mi. Fusce mattis est id diam. Phasellus faucibus + interdum sapien. +\end{miinstructornote} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{mistudentnote}{} +Environment for highlighting notes to students. +\end{docEnvironment} +\begin{dispExample} +\begin{mistudentnote} + Nunc auctor bibendum eros. Maecenas porta accumsan mauris. Etiam + enim enim, elementum sed, bibendum quis, rhoncus non, metus. Fusce + neque dolor, adipiscing sed, consectetuer et, lacinia sit amet, + quam. Suspendisse wisi quam, consectetuer in, blandit sed, + suscipit eu, eros. Etiam ligula enim, tempor ut, blandit nec, + mollis eu, lectus. Nam cursus. Vivamus iaculis. Aenean risus + purus, pharetra in, blandit quis, gravida a, turpis. Donec nisl. + Aenean eget mi. Fusce mattis est id diam. Phasellus faucibus + interdum sapien. +\end{mistudentnote} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{miderivation}{} +Environment for mathematical derivations based on the |align| environment. +See \refEnv{mysolution} for how to handle long lines in this environment. +Note that using this environment resets the counter for equation numbering. +If you want continuous numbering throughout your document, use the |align| +environment. +\end{docEnvironment} +\begin{docEnvironment}{miderivation*}{} +Like \refEnv{miderivation} but suppresses line numbers. +\end{docEnvironment} +\begin{dispExample} +\begin{miderivation} + \gamma &= \relgamma{\magvect{v}} && \text{given} \\ + \gamma\squared &= \ooomx{\inparens{\frac{\magvect{v}}{c}}\squared} + &&\text{square both sides} \\ + \frac{1}{\gamma\squared} &= 1-\inparens{\frac{\magvect{v}}{c}}\squared + &&\text{reciprocal of both sides} \\ + \inparens{\frac{\magvect{v}}{c}}\squared &= 1-\frac{1}{\gamma\squared} + &&\text{rearrange} \\ + \frac{\magvect{v}}{c} &= \sqrt{1-\frac{1}{\gamma\squared}} + &&\text{square root of both sides} +\end{miderivation} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{mistandard}{} +Environment for standards for standards-based grading. +\end{docEnvironment} +\begin{dispExample} +\begin{mistandard} + I can create a standard which reflects deep student learning. +\end{mistandard} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{bwinstructornote}{} +Like \refEnv{miinstructornote} but in black and grey. +\end{docEnvironment} +\begin{dispExample} +\begin{bwinstructornote} + Nunc auctor bibendum eros. Maecenas porta accumsan mauris. Etiam + enim enim, elementum sed, bibendum quis, rhoncus non, metus. Fusce + neque dolor, adipiscing sed, consectetuer et, lacinia sit amet, + quam. Suspendisse wisi quam, consectetuer in, blandit sed, + suscipit eu, eros. Etiam ligula enim, tempor ut, blandit nec, + mollis eu, lectus. Nam cursus. Vivamus iaculis. Aenean risus + purus, pharetra in, blandit quis, gravida a, turpis. Donec nisl. + Aenean eget mi. Fusce mattis est id diam. Phasellus faucibus + interdum sapien. +\end{bwinstructornote} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{bwstudentnote}{} +Like \refEnv{mistudentnote} but in black and grey. +\end{docEnvironment} +\begin{dispExample} +\begin{bwstudentnote} + Nunc auctor bibendum eros. Maecenas porta accumsan mauris. Etiam + enim enim, elementum sed, bibendum quis, rhoncus non, metus. Fusce + neque dolor, adipiscing sed, consectetuer et, lacinia sit amet, + quam. Suspendisse wisi quam, consectetuer in, blandit sed, + suscipit eu, eros. Etiam ligula enim, tempor ut, blandit nec, + mollis eu, lectus. Nam cursus. Vivamus iaculis. Aenean risus + purus, pharetra in, blandit quis, gravida a, turpis. Donec nisl. + Aenean eget mi. Fusce mattis est id diam. Phasellus faucibus + interdum sapien. +\end{bwstudentnote} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{bwderivation}{} +Like \refEnv{miderivation} but in black and grey. See \refEnv{mysolution} for +how to handle long lines in this environment. +\end{docEnvironment} +\begin{docEnvironment}{bwderivation*}{} +Like \refEnv{bwderivation} but suppresses line numbers. +\end{docEnvironment} +\begin{dispExample} +\begin{bwderivation} + \gamma &= \relgamma{\magvect{v}} && \text{given} \\ + \gamma\squared &= \ooomx{\inparens{\frac{\magvect{v}}{c}}\squared} + &&\text{square both sides} \\ + \frac{1}{\gamma\squared} &= 1-\inparens{\frac{\magvect{v}}{c}}\squared + &&\text{reciprocal of both sides} \\ + \inparens{\frac{\magvect{v}}{c}}\squared &= 1-\frac{1}{\gamma\squared} + &&\text{rearrange} \\ + \frac{\magvect{v}}{c}&=\sqrt{1-\frac{1}{\gamma\squared}} + &&\text{square root of both sides} +\end{bwderivation} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{bwstandard}{} +Like \refEnv{mistandard} but in black and grey. +\end{docEnvironment} +\begin{dispExample} +\begin{bwstandard} + I can create a standard which reflects deep student learning. +\end{bwstandard} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{mysolution}{} +Alias for simple environment for mathematical derivations based on the +|align| environment. The second example shows how to handle long lines +for this and the derivation environments. +\end{docEnvironment} +\begin{docEnvironment}{mysolution*}{} +Like \refEnv{mysolution} but suppresses line numbers. +\end{docEnvironment} +\begin{dispExample} +\begin{mysolution} + \gamma &= \relgamma{\magvect{v}} + && \text{given} \\ + \gamma\squared &= \ooomx{\inparens{\frac{\magvect{v}}{c}}\squared} + &&\text{square both sides} \\ + \frac{1}{\gamma\squared} &= 1-\inparens{\frac{\magvect{v}}{c}}\squared + &&\text{reciprocal of both sides} \\ + \inparens{\frac{\magvect{v}}{c}}\squared &= 1-\frac{1}{\gamma\squared} + &&\text{rearrange} \\ + \frac{\magvect{v}}{c} &= \sqrt{1-\frac{1}{\gamma\squared}} + &&\text{square root of both sides} +\end{mysolution} +\begin{mysolution*} + \vect{E} &= \electricfield{\mivector{1,2,3}} + \electricfield{\mivector{2,4,6}} + \nonumber \\ + &\hphantom{{}=\electricfield{\mivector{1,1,1}}}+\electricfield{\mivector{3,5,6}} + &&\text{superposition} \\ + \vect{E} &= \electricfield{\mivector{2,3,4}} + \electricfield{\mivector{2,4,6}} + \nonumber \\ + &+ \electricfield{\mivector{1,1,1}} +\electricfield{\mivector{3,5,6}} + &&\text{superposition again} \\ + \vect{E} &= \electricfield{\mivector{2,3,4}} + \electricfield{\mivector{2,4,6}} + \nonumber \\ + &\quad + \electricfield{\mivector{1,1,1}} +\electricfield{\mivector{3,5,6}} + && \text{more superposition} +\end{mysolution*} +\end{dispExample} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docEnvironment}{problem}{\marg{problemname}} +Creates a simple environment for problem solutions. This +environment is mainly for students. Each new problem starts on a new page in an +effort to force organization upon students. The environment also creates a new +|enumerate| environment called |parts| for which labels are alphabetic, +reflecting the organization of multipart textbook problems. The \cs{item} command +is renamed \cs{problempart} to, again, help with organization for newcomers to +\LaTeX. A typical example would be structured as follows. +\end{docEnvironment} +\begin{dispExample*}{sidebyside, lefthand ratio=0.50} +\begin{problem}{Chapter 2 Problem 1} +This problem has two parts. +\begin{parts} + \problempart + This is the first part + \problempart + This is the second part +\end{parts} +\end{problem} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{reason}{\marg{text}} +In a \refEnv{mysolution} environment, this aligns the text arguments with the +end of the longest line and nicely handles line wrapping. Make sure your margins +are narrow enough. You may need to experiment. +\end{docCommand} +\begin{dispExample} +\begin{mysolution} + c^2 &= a^2 + b^2 && \reason{given} \\ + a^2 &= c^2 - b^2 && \reason{Rearrange, and add some extra text just for fun.} \\ + a &= \sqrt{c^2 - b^2} && \reason{Take square root of both sides.} +\end{mysolution} +\end{dispExample} +%\iffalse +% +%\fi +% +% \newpage +% \subsection{Miscellaneous Commands} +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{checkpoint}{} +Centered checkpoint for student discussion. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\checkpoint +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{image}{\oarg{scalesize}\marg{filename}\marg{caption}\marg{label}} +Centered figure displayed actual size with caption. The optional argument can be +a scale factor (with 1 being the original image size), explicit \texttt{width} +and/or \texttt{height} parameters, or even an \texttt{angle} for rotating the +image. Be sure to give each image a unique label. This allows you to refer back +to the image subsequently just by using the label. +\end{docCommand} +\begin{dispListing} + \image{sampleimage.pdf}{An image shown actual size.}{img-label1} + \image[scale=1.5]{sampleimage.pdf}{An image scaled by 1.5 times.}{img-label2} + \image[height=1cm,width=2cm]{sampleimage.pdf}{An image resized.}{img-label3} + \image[width=0.8\textwidth]{sampleimage.pdf}{An image 80 percent the text width.} + {img-label4} + \image[angle=45]{sampleimage.pdf}{An image actual size, rotated.}{img-label5} +\end{dispListing} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{sneakyone}{\marg{thing}} +Shows argument as a sneaky one. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\sneakyone{\frac{\m}{\m}} +\end{dispExample*} +%\iffalse +% +%\fi +% +%\iffalse +%<*example> +%\fi +\begin{docCommand}{qed}{} +Command for QED symbol. +\end{docCommand} +\begin{dispExample*}{sidebyside} +\qed +\end{dispExample*} +%\iffalse +% +%\fi +% \StopEventually{} +% +% \newpage +% \section{Source Code} +% +% \iffalse +%<*package> +% \fi +% Note the packages that must be present. +% \begin{macrocode} +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage{array} +\RequirePackage{cancel} +\RequirePackage[dvipsnames]{xcolor} +\RequirePackage{enumitem} +\RequirePackage{environ} +\RequirePackage{esint} +\RequirePackage[g]{esvect} +\RequirePackage{etoolbox} +\RequirePackage{filehook} +\RequirePackage{extarrows} +\RequirePackage{float} +\RequirePackage[T1]{fontenc} +\RequirePackage{graphicx} +\RequirePackage{epstopdf} +\RequirePackage{textcomp} +\RequirePackage{letltxmacro} +\RequirePackage{listings} +\RequirePackage{mathtools} +\RequirePackage[framemethod=TikZ]{mdframed} +\RequirePackage{stackengine} +\RequirePackage{suffix} +\RequirePackage{tensor} +\RequirePackage{xargs} +\RequirePackage{xparse} +\RequirePackage{xspace} +\RequirePackage{ifthen} +\RequirePackage{calligra} +\RequirePackage[hypertexnames=false]{hyperref} +\hypersetup{colorlinks=true,urlcolor=blue} +\DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n} +\DeclareFontShape{T1}{calligra}{m}{n}{<->s*[2.2]callig15}{} +\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `basename #1 .tif`.png} +\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} +\usetikzlibrary{shadows} +\definecolor{vbgcolor}{rgb}{1,1,1} % background for code listings +\definecolor{vshadowcolor}{rgb}{0.5,0.5,0.5} % shadow for code listings +\lstdefinestyle{vpython}{% % style for code listings + language=Python,% % select language + morekeywords={__future__,division,append, % VPython/GlowScript specific keywords + arange,arrow,astuple,axis,background,black,blue,cyan,green,% + magenta,orange,red,white,yellow,border,box,color,comp,% + cone,convex,cross,curve,cylinder,degrees,diff_angle,dot,ellipsoid,extrusion,faces,% + font,frame,graphs,headlength,height,headwidth,helix,index,interval,label,length,% + line,linecolor,mag,mag2,make_trail,material,norm,normal,objects,opacity,points,pos,% + print,print_function,proj,pyramid,radians,radius,rate,retain,ring,rotate,scene,% + shaftwidth,shape,sign,size,space,sphere,text,trail_object,trail_type,True,twist,up,% + vector,visual,width,offset,yoffset,GlowScript,VPython,vpython,trail_color,% + trail_radius,pps,clear,False,CoffeeScript,graph,gdisplay,canvas,pause,vec,clone,% + compound,vertex,triangle,quad,attach_trail,attach_arrow,textures,bumpmaps,% + print_options,get_library,read_local_file},% + captionpos=b,% % position caption + frame=shadowbox,% % shadowbox around listing + rulesepcolor=\color{vshadowcolor},% % shadow color + basicstyle=\footnotesize,% % basic font for code listings + commentstyle=\bfseries\color{red}, % font for comments + keywordstyle=\bfseries\color{blue},% % font for keywords + showstringspaces=true,% % show spaces in strings + stringstyle=\bfseries\color{green},% % color for strings + numbers=left,% % where to put line numbers + numberstyle=\tiny,% % set to 'none' for no line numbers + xleftmargin=20pt,% % extra left margin + backgroundcolor=\color{vbgcolor},% % some people find this annoying + upquote=true,% % how to typeset quotes + breaklines=true}% % break long lines +\definecolor{formcolor}{gray}{0.90} % color for form background +\newcolumntype{C}[1]{>{\centering}m{#1}} +\newboolean{@optromanvectors} +\newboolean{@optboldvectors} +\newboolean{@optsinglemagbars} +\newboolean{@optbaseunits} +\newboolean{@optdrvdunits} +\newboolean{@optaltnunits} +\newboolean{@optapproxconsts} +\newboolean{@optuseradians} +\setboolean{@optromanvectors}{false} % this is where you set the default option +\setboolean{@optboldvectors}{false} % this is where you set the default option +\setboolean{@optsinglemagbars}{false} % this is where you set the default option +\setboolean{@optbaseunits}{false} % this is where you set the default option +\setboolean{@optdrvdunits}{true} % this is where you set the default option +\setboolean{@optaltnunits}{false} % this is where you set the default option +\setboolean{@optapproxconsts}{false} % this is where you set the default option +\setboolean{@optuseradians}{false} % this is where you set the default option +\DeclareOption{romanvectors}{\setboolean{@optromanvectors}{true}} +\DeclareOption{boldvectors}{\setboolean{@optboldvectors}{true}} +\DeclareOption{singlemagbars}{\setboolean{@optsinglemagbars}{true}} +\DeclareOption{baseunits}{\setboolean{@optbaseunits}{true}} +\DeclareOption{drvdunits}{\setboolean{@optdrvdunits}{true}} +\DeclareOption{approxconsts}{\setboolean{@optapproxconsts}{true}} +\DeclareOption{useradians}{\setboolean{@optuseradians}{true}} +\ProcessOptions\relax +% \end{macrocode} +% +% \begin{macrocode} +\newcommand*{\mandiversion}{\ifmmode% + 2.7.5\mbox{ dated }2019/01/12% + \else% + 2.7.5 dated 2019/01/12% + \fi + }% +\typeout{ } +\typeout{mandi: You're using mandi version \mandiversion.} +% \end{macrocode} +% +% \noindent This block of code fixes a conflict with the amssymb package. +% \begin{macrocode} +\@ifpackageloaded{amssymb}{% + \csundef{square} + \typeout{mandi: Package amssymb detected. Its \protect\square\space + has been redefined.} +}{% + \typeout{mandi: Package amssymb not detected.} +}% +% \end{macrocode} +% +% \noindent This block of code defines unit names and symbols. +% \begin{macrocode} +\newcommand*{\per}{\ensuremath{/}} +\newcommand*{\usk}{\ensuremath{\cdot}} +\newcommand*{\unit}[2]{\ensuremath{{#1}\;{#2}}} +\newcommand*{\ampere}{\ensuremath{\mathrm{A}}} +\newcommand*{\arcminute}{\ensuremath{'}} +\newcommand*{\arcsecond}{\ensuremath{''}} +\newcommand*{\atomicmassunit}{\ensuremath{\mathrm{u}}} +\newcommand*{\candela}{\ensuremath{\mathrm{cd}}} +\newcommand*{\coulomb}{\ensuremath{\mathrm{C}}} +\newcommand*{\degree}{\ensuremath{^{\circ}}} +\newcommand*{\electronvolt}{\ensuremath{\mathrm{eV}}} +\newcommand*{\eV}{\electronvolt} +\newcommand*{\farad}{\ensuremath{\mathrm{F}}} +\newcommand*{\henry}{\ensuremath{\mathrm{H}}} +\newcommand*{\hertz}{\ensuremath{\mathrm{Hz}}} +\newcommand*{\hour}{\ensuremath{\mathrm{h}}} +\newcommand*{\joule}{\ensuremath{\mathrm{J}}} +\newcommand*{\kelvin}{\ensuremath{\mathrm{K}}} +\newcommand*{\kilogram}{\ensuremath{\mathrm{kg}}} +\newcommand*{\metre}{\ensuremath{\mathrm{m}}} +\newcommand*{\minute}{\ensuremath{\mathrm{min}}} +\newcommand*{\mole}{\ensuremath{\mathrm{mol}}} +\newcommand*{\newton}{\ensuremath{\mathrm{N}}} +\newcommand*{\ohm}{\ensuremath{\Omega}} +\newcommand*{\pascal}{\ensuremath{\mathrm{Pa}}} +\newcommand*{\radian}{\ensuremath{\mathrm{rad}}} +\newcommand*{\second}{\ensuremath{\mathrm{s}}} +\newcommand*{\siemens}{\ensuremath{\mathrm{S}}} +\newcommand*{\steradian}{\ensuremath{\mathrm{sr}}} +\newcommand*{\tesla}{\ensuremath{\mathrm{T}}} +\newcommand*{\volt}{\ensuremath{\mathrm{V}}} +\newcommand*{\watt}{\ensuremath{\mathrm{W}}} +\newcommand*{\weber}{\ensuremath{\mathrm{Wb}}} +\newcommand*{\C}{\coulomb} +\newcommand*{\F}{\farad} +%\H is already defined as a LaTeX accent +\newcommand*{\J}{\joule} +\newcommand*{\N}{\newton} +\newcommand*{\Pa}{\pascal} +\newcommand*{\rad}{\radian} +\newcommand*{\sr}{\steradian} +%\S is already defined as a LaTeX symbol +\newcommand*{\T}{\tesla} +\newcommand*{\V}{\volt} +\newcommand*{\W}{\watt} +\newcommand*{\Wb}{\weber} +\newcommand*{\square}[1]{\ensuremath{{#1}^2}} % prefix 2 +\newcommand*{\cubic}[1]{\ensuremath{{#1}^3}} % prefix 3 +\newcommand*{\quartic}[1]{\ensuremath{{#1}^4}} % prefix 4 +\newcommand*{\reciprocal}[1]{\ensuremath{{#1}^{-1}}} % prefix -1 +\newcommand*{\reciprocalsquare}[1]{\ensuremath{{#1}^{-2}}} % prefix -2 +\newcommand*{\reciprocalcubic}[1]{\ensuremath{{#1}^{-3}}} % prefix -3 +\newcommand*{\reciprocalquartic}[1]{\ensuremath{{#1}^{-4}}} % prefix -4 +\newcommand*{\squared}{\ensuremath{^2}} % postfix 2 +\newcommand*{\cubed}{\ensuremath{^3}} % postfix 3 +\newcommand*{\quarted}{\ensuremath{^4}} % postfix 4 +\newcommand*{\reciprocaled}{\ensuremath{^{-1}}} % postfix -1 +\newcommand*{\reciprocalsquared}{\ensuremath{^{-2}}} % postfix -2 +\newcommand*{\reciprocalcubed}{\ensuremath{^{-3}}} % postfix -3 +\newcommand*{\reciprocalquarted}{\ensuremath{^{-4}}} % postfix -4 +\newcommand*{\emptyunit}{\ensuremath{\Box}} +% \end{macrocode} +% +% \noindent Define a new named physics quantity or physical constant and +% commands for selecting units. My thanks to Ulrich Diez for contributing +% this code. +% \begin{macrocode} +\newcommand*\mi@exchangeargs[2]{#2#1}% +\newcommand*\mi@name{}% +\long\def\mi@name#1#{\romannumeral0\mi@innername{#1}}% +\newcommand*\mi@innername[2]{% + \expandafter\mi@exchangeargs\expandafter{\csname#2\endcsname}{#1}}% +\begingroup +\@firstofone{% + \endgroup + \newcommand*\mi@forkifnull[3]{% + \romannumeral\iffalse{\fi\expandafter\@secondoftwo\expandafter% + {\expandafter{\string#1}\expandafter\@secondoftwo\string}% + \expandafter\@firstoftwo\expandafter{\iffalse}\fi0 #3}{0 #2}}}% +\newcommand*\selectbaseunit[3]{#1} +\newcommand*\selectdrvdunit[3]{#2} +\newcommand*\selectaltnunit[3]{#3} +\newcommand*\selectunit{} +\newcommand*\perpusebaseunit{\let\selectunit=\selectbaseunit} +\newcommand*\perpusedrvdunit{\let\selectunit=\selectdrvdunit} +\newcommand*\perpusealtnunit{\let\selectunit=\selectaltnunit} +\newcommand*\hereusebaseunit[1]{% + \begingroup\perpusebaseunit#1\endgroup}% +\newcommand*\hereusedrvdunit[1]{% + \begingroup\perpusedrvdunit#1\endgroup}% +\newcommand*\hereusealtnunit[1]{% + \begingroup\perpusealtnunit#1\endgroup}% +\newenvironment{usebaseunit}{\perpusebaseunit}{}% +\newenvironment{usedrvdunit}{\perpusedrvdunit}{}% +\newenvironment{usealtnunit}{\perpusealtnunit}{}% +\newcommand*\newphysicsquantity{\definephysicsquantity{\newcommand}} +\newcommand*\redefinephysicsquantity{\definephysicsquantity{\renewcommand}} +\newcommandx*\definephysicsquantity[5][4=,5=]{% + \innerdefinewhatsoeverquantityfork{#3}{#4}{#5}{#1}{#2}{}{[1]}{##1}}% +\newcommand*\newphysicsconstant{\definephysicsconstant{\newcommand}} +\newcommand*\redefinephysicsconstant{\definephysicsconstant{\renewcommand}} +\newcommandx*\definephysicsconstant[7][6=,7=]{% + \innerdefinewhatsoeverquantityfork{#5}{#6}{#7}{#1}{#2}{#3}{}{#4}}% +\newcommand*\innerdefinewhatsoeverquantityfork[3]{% + \expandafter\innerdefinewhatsoeverquantity\romannumeral0% + \mi@forkifnull{#3}{\mi@forkifnull{#2}{{#1}}{{#2}}{#1}}% + {\mi@forkifnull{#2}{{#1}}{{#2}}{#3}}{#1}}% +\newcommand*\innerdefinewhatsoeverquantity[8]{% + \mi@name#4{#5}#7{\unit{#8}{\selectunit{#3}{#1}{#2}}}% + \mi@name#4{#5baseunit}#7{\unit{#8}{#3}}% + \mi@name#4{#5drvdunit}#7{\unit{#8}{#1}}% + \mi@name#4{#5altnunit}#7{\unit{#8}{#2}}% + \mi@name#4{#5onlyunit}{\selectunit{#3}{#1}{#2}}% + \mi@name#4{#5onlybaseunit}{\ensuremath{#3}}% + \mi@name#4{#5onlydrvdunit}{\ensuremath{#1}}% + \mi@name#4{#5onlyaltnunit}{\ensuremath{#2}}% + \mi@name#4{#5value}#7{\ensuremath{#8}}% + \mi@forkifnull{#7}{% + \ifx#4\renewcommand\mi@name\let{#5mathsymbol}=\relax\fi + \mi@name\newcommand*{#5mathsymbol}{\ensuremath{#6}}}{}}% +% \end{macrocode} +% +% \noindent This block of code processes the options. +% \begin{macrocode} +\ifthenelse{\boolean{@optboldvectors}} + {\typeout{mandi: You'll get bold vectors.}} + {\ifthenelse{\boolean{@optromanvectors}} + {\typeout{mandi: You'll get Roman vectors.}} + {\typeout{mandi: You'll get italic vectors.}}} +\ifthenelse{\boolean{@optsinglemagbars}} + {\typeout{mandi: You'll get single magnitude bars.}} + {\typeout{mandi: You'll get double magnitude bars.}} +\ifthenelse{\boolean{@optbaseunits}} + {\perpusebaseunit % + \typeout{mandi: You'll get base units.}} + {\ifthenelse{\boolean{@optdrvdunits}} + {\perpusedrvdunit % + \typeout{mandi: You'll get derived units.}} + {\perpusealtnunit % + \typeout{mandi: You'll get alternate units.}}} +\ifthenelse{\boolean{@optapproxconsts}} + {\typeout{mandi: You'll get approximate constants.}} + {\typeout{mandi: You'll get precise constants.}} +\ifthenelse{\boolean{@optuseradians}} + {\typeout{mandi: You'll get radians in ang mom, ang impulse, and torque.}} + {\typeout{mandi: You won't get radians in ang mom, ang impulse, and torque.}} +\typeout{ } +% \end{macrocode} +% +% \noindent This is a utility command for picking constants. Do not use this +% command manually. +% \begin{macrocode} +\ifthenelse{\boolean{@optapproxconsts}} + {\newcommand*{\mi@p}[2]{#1}} % approximate value + {\newcommand*{\mi@p}[2]{#2}} % precise value +% \end{macrocode} +% +% \noindent SI base unit of length or spatial displacement +% \begin{macrocode} +\newcommand*{\m}{\metre} +% \end{macrocode} +% +% \noindent SI base unit of mass +% \begin{macrocode} +\newcommand*{\kg}{\kilogram} +% \end{macrocode} +% +% \noindent SI base unit of time or temporal displacement +% \begin{macrocode} +\newcommand*{\s}{\second} +% \end{macrocode} +% +% \noindent SI base unit of electric current +% \begin{macrocode} +\newcommand*{\A}{\ampere} +% \end{macrocode} +% +% \noindent SI base unit of thermodynamic temperature +% \begin{macrocode} +\newcommand*{\K}{\kelvin} +% \end{macrocode} +% +% \noindent SI base unit of amount +% \begin{macrocode} +\newcommand*{\mol}{\mole} +% \end{macrocode} +% +% \noindent SI base unit of luminous intensity +% \begin{macrocode} +\newcommand*{\cd}{\candela} +% \end{macrocode} +% +% \begin{macrocode} +\newcommand*{\dimdisplacement}{\ensuremath{\mathrm{L}}} +\newcommand*{\dimmass}{\ensuremath{\mathrm{M}}} +\newcommand*{\dimduration}{\ensuremath{\mathrm{T}}} +\newcommand*{\dimcurrent}{\ensuremath{\mathrm{I}}} +\newcommand*{\dimtemperature}{\ensuremath{\mathrm{\Theta}}} +\newcommand*{\dimamount}{\ensuremath{\mathrm{N}}} +\newcommand*{\dimluminous}{\ensuremath{\mathrm{J}}} +\newcommand*{\infeet}[1]{\unit{#1}{\mathrm{ft}}} +\newcommand*{\infeetpersecond}[1]{\unit{#1}{\mathrm{ft}\per\s}} +\newcommand*{\infeetpersecondsquared}[1]{\unit{#1}{\mathrm{ft}\per\s\squared}} +\newcommand*{\indegrees}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} +\newcommand*{\inFarenheit}[1]{\unit{#1}{\mkern-\thickmuskip\degree\mathrm{F}}} +\newcommand*{\inCelsius}[1]{\unit{#1}{\mkern-\thickmuskip\degree\mathrm{C}}} +\newcommand*{\inarcminutes}[1]{\unit{#1}{\mkern-\thickmuskip\arcminute}} +\newcommand*{\inarcseconds}[1]{\unit{#1}{\mkern-\thickmuskip\arcsecond}} +\newcommand*{\ineV}[1]{\unit{#1}{\electronvolt}} +\newcommand*{\ineVocs}[1]{\unit{#1}{\mathrm{eV}\per c^2}} +\newcommand*{\ineVoc}[1]{\unit{#1}{\mathrm{eV}\per c}} +\newcommand*{\inMeV}[1]{\unit{#1}{\mathrm{MeV}}} +\newcommand*{\inMeVocs}[1]{\unit{#1}{\mathrm{MeV}\per c^2}} +\newcommand*{\inMeVoc}[1]{\unit{#1}{\mathrm{MeV}\per c}} +\newcommand*{\inGeV}[1]{\unit{#1}{\mathrm{GeV}}} +\newcommand*{\inGeVocs}[1]{\unit{#1}{\mathrm{GeV}\per c^2}} +\newcommand*{\inGeVoc}[1]{\unit{#1}{\mathrm{GeV}\per c}} +\newcommand*{\inamu}[1]{\unit{#1}{\mathrm{u}}} +\newcommand*{\ingram}[1]{\unit{#1}{\mathrm{g}}} +\newcommand*{\ingrampercubiccm}[1]{\unit{#1}{\mathrm{g}\per\cubic\mathrm{cm}}} +\newcommand*{\inAU}[1]{\unit{#1}{\mathrm{AU}}} +\newcommand*{\inly}[1]{\unit{#1}{\mathrm{ly}}} +\newcommand*{\incyr}[1]{\unit{#1}{c\usk\mathrm{year}}} +\newcommand*{\inpc}[1]{\unit{#1}{\mathrm{pc}}} +\newcommand*{\insolarL}[1]{\unit{#1}{\Lsolar}} +\newcommand*{\insolarT}[1]{\unit{#1}{\Tsolar}} +\newcommand*{\insolarR}[1]{\unit{#1}{\Rsolar}} +\newcommand*{\insolarM}[1]{\unit{#1}{\Msolar}} +\newcommand*{\insolarF}[1]{\unit{#1}{\Fsolar}} +\newcommand*{\insolarf}[1]{\unit{#1}{\fsolar}} +\newcommand*{\insolarMag}[1]{\unit{#1}{\Magsolar}} +\newcommand*{\insolarmag}[1]{\unit{#1}{\magsolar}} +\newcommand*{\insolarD}[1]{\unit{#1}{\Dsolar}} +\newcommand*{\insolard}[1]{\unit{#1}{\dsolar}} +\newcommand*{\velocityc}[1]{\ensuremath{#1c}} +\newcommand*{\lorentzfactor}[1]{\ensuremath{#1}} +\newcommand*{\speed}{\velocity} +\newphysicsquantity{displacement}% + {\m}% + [\m]% + [\m] +\newphysicsquantity{mass}% + {\kg}% + [\kg]% + [\kg] +\newphysicsquantity{duration}% + {\s}% + [\s]% + [\s] +\newphysicsquantity{current}% + {\A}% + [\A]% + [\A] +\newphysicsquantity{temperature}% + {\K}% + [\K]% + [\K] +\newphysicsquantity{amount}% + {\mol}% + [\mol]% + [\mol] +\newphysicsquantity{luminous}% + {\cd}% + [\cd]% + [\cd] +\newphysicsquantity{planeangle}% + {\m\usk\reciprocal\m}% + [\rad]% + [\rad] +\newphysicsquantity{solidangle}% + {\m\squared\usk\reciprocalsquare\m}% + [\sr]% + [\sr] +\newphysicsquantity{velocity}% + {\m\usk\reciprocal\s}% + [\m\usk\reciprocal\s]% + [\m\per\s] +\newphysicsquantity{acceleration}% + {\m\usk\s\reciprocalsquared}% + [\N\per\kg]% + [\m\per\s\squared] +\newphysicsquantity{gravitationalfield}% + {\m\usk\s\reciprocalsquared}% + [\N\per\kg]% + [\N\per\kg] +\newphysicsquantity{gravitationalpotential}% + {\square\m\usk\reciprocalsquare\s}% + [\J\per\kg]% + [\J\per\kg] +\newphysicsquantity{momentum}% + {\m\usk\kg\usk\reciprocal\s}% + [\N\usk\s]% + [\kg\usk\m\per\s] +\newphysicsquantity{impulse}% + {\m\usk\kg\usk\reciprocal\s}% + [\N\usk\s]% + [\N\usk\s] +\newphysicsquantity{force}% + {\m\usk\kg\usk\s\reciprocalsquared}% + [\N]% + [\N] +\newphysicsquantity{springstiffness}% + {\kg\usk\s\reciprocalsquared}% + [\N\per\m]% + [\N\per\m] +\newphysicsquantity{springstretch}% + {\m}% + []% + [] +\newphysicsquantity{area}% + {\m\squared}% + []% + [] +\newphysicsquantity{volume}% + {\cubic\m}% + []% + [] +\newphysicsquantity{linearmassdensity}% + {\reciprocal\m\usk\kg}% + [\kg\per\m]% + [\kg\per\m] +\newphysicsquantity{areamassdensity}% + {\m\reciprocalsquared\usk\kg}% + [\kg\per\m\squared]% + [\kg\per\m\squared] +\newphysicsquantity{volumemassdensity}% + {\m\reciprocalcubed\usk\kg}% + [\kg\per\m\cubed]% + [\kg\per\m\cubed] +\newphysicsquantity{youngsmodulus}% + {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% + [\N\per\m\squared]% + [\Pa] +\newphysicsquantity{stress}% + {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% + [\N\per\m\squared]% + [\Pa] +\newphysicsquantity{pressure}% + {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% + [\N\per\m\squared]% + [\Pa] +\newphysicsquantity{strain}% + {}% + []% + [] +\newphysicsquantity{work}% + {\m\squared\usk\kg\usk\s\reciprocalsquared}% + [\J]% + [\N\usk\m] +\newphysicsquantity{energy}% + {\m\squared\usk\kg\usk\s\reciprocalsquared}% + [\J]% + [\N\usk\m] +\newphysicsquantity{power}% + {\m\squared\usk\kg\usk\s\reciprocalcubed}% + [\W]% + [\J\per\s] +\newphysicsquantity{specificheatcapacity}% + {\J\per\K\usk\kg}% + [\J\per\K\usk\kg]% + [\J\per\K\usk\kg] +\newphysicsquantity{angularvelocity}% + {\rad\usk\reciprocal\s}% + [\rad\per\s]% + [\rad\per\s] +\newphysicsquantity{angularacceleration}% + {\rad\usk\s\reciprocalsquared}% + [\rad\per\s\squared]% + [\rad\per\s\squared] +\newphysicsquantity{momentofinertia}% + {\m\squared\usk\kg}% + [\m\squared\usk\kg]% + [\J\usk\s\squared] +\ifthenelse{\boolean{@optuseradians}} + {% + \newphysicsquantity{angularmomentum}% + {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% + [\kg\usk\m\squared\per(\s\usk\rad)]% + [\N\usk\m\usk\s\per\rad] + \newphysicsquantity{angularimpulse}% + {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% + [\J\usk\s\per\rad]% + [\N\usk\m\usk\s\per\rad] + \newphysicsquantity{torque}% + {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\rad}% + [\N\usk\m\per\rad]% + [\J\per\rad] + }% + {% + \newphysicsquantity{angularmomentum}% + {\m\squared\usk\kg\usk\reciprocal\s}% + [\kg\usk\m\squared\per\s]% + [\N\usk\m\usk\s] + \newphysicsquantity{angularimpulse}% + {\m\squared\usk\kg\usk\reciprocal\s}% + [\J\usk\s]% + [\N\usk\m\usk\s] + \newphysicsquantity{torque}% + {\m\squared\usk\kg\usk\s\reciprocalsquared}% + [\N\usk\m]% + [\J] + }% +\newphysicsquantity{entropy}% + {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\K}% + [\J\per\K]% + [\J\per\K] +\newphysicsquantity{wavelength}% + {\m}% + [\m]% + [\m] +\newphysicsquantity{wavenumber}% + {\reciprocal\m}% + [\per\m]% + [\per\m] +\newphysicsquantity{frequency}% + {\reciprocal\s}% + [\hertz]% + [\hertz] +\newphysicsquantity{angularfrequency}% + {\rad\usk\reciprocal\s}% + [\rad\per\s]% + [\rad\per\s] +\newphysicsquantity{charge}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsquantity{permittivity}% + {\m\reciprocalcubed\usk\reciprocal\kg\usk\s\reciprocalquarted\usk\A\squared}% + [\C\squared\per\N\usk\m\squared]% + [\F\per\m] +\newphysicsquantity{permeability}% + {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% + [\T\usk\m\per\A]% + [\henry\per\m] +\newphysicsquantity{electricfield}% + {\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\N\per\C]% + [\V\per\m] +\newphysicsquantity{electricdipolemoment}% + {\m\usk\s\usk\A}% + [\C\usk\m]% + [\C\usk\m] +\newphysicsquantity{electricflux}% + {\m\cubed\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\N\usk\m\squared\per\C]% + [\V\usk\m] +\newphysicsquantity{magneticfield}% + {\kg\usk\s\reciprocalsquared\usk\reciprocal\A}% + [\T]% + [\N\per\C\usk(\m\per\s)] % also \Wb\per\m\squared +\newphysicsquantity{magneticflux}% + {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\A}% + [\T\usk\m\squared]% + [\volt\usk\s] % also \Wb and \J\per\A +\newphysicsquantity{cmagneticfield}% + {\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\N\per\C]% + [\V\per\m] +\newphysicsquantity{linearchargedensity}% + {\reciprocal\m\usk\s\usk\A}% + [\C\per\m]% + [\C\per\m] +\newphysicsquantity{areachargedensity}% + {\reciprocalsquare\m\usk\s\usk\A}% + [\C\per\square\m]% + [\C\per\square\m] +\newphysicsquantity{volumechargedensity}% + {\reciprocalcubic\m\usk\s\usk\A}% + [\C\per\cubic\m]% + [\C\per\cubic\m] +\newphysicsquantity{mobility}% + {\m\squared\usk\kg\usk\s\reciprocalquarted\usk\reciprocal\A}% + [\m\squared\per\volt\usk\s]% + [(\m\per\s)\per(\N\per\C)] +\newphysicsquantity{numberdensity}% + {\reciprocalcubic\m}% + [\per\cubic\m]% + [\per\cubic\m] +\newphysicsquantity{polarizability}% + {\reciprocal\kg\usk\s\quarted\usk\square\A}% + [\C\usk\square\m\per\V]% + [\C\usk\m\per(\N\per\C)] +\newphysicsquantity{electricpotential}% + {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A}% + [\V]% + [\J\per\C] +\newphysicsquantity{emf}% + {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A}% + [\V]% + [\J\per\C] +\newphysicsquantity{dielectricconstant}% + {}% + []% + [] +\newphysicsquantity{indexofrefraction}% + {}% + []% + [] +\newphysicsquantity{relativepermittivity}% + {}% + []% + [] +\newphysicsquantity{relativepermeability} + {}% + []% + [] +\newphysicsquantity{energydensity}% + {\m\reciprocaled\usk\kg\usk\reciprocalsquare\s}% + [\J\per\cubic\m]% + [\J\per\cubic\m] +\newphysicsquantity{energyflux}% + {\kg\usk\s\reciprocalcubed}% + [\W\per\m\squared]% + [\W\per\m\squared] +\newphysicsquantity{momentumflux}% + {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% + [\N\per\m\squared]% + [\N\per\m\squared] +\newphysicsquantity{electroncurrent}% + {\reciprocal\s}% + [\ensuremath{\mathrm{e}}\per\s]% + [\ensuremath{\mathrm{e}}\per\s] +\newphysicsquantity{conventionalcurrent}% + {\A}% + [\A]% + [\C\per\s] +\newphysicsquantity{magneticdipolemoment}% + {\square\m\usk\A}% + [\A\usk\square\m]% + [\J\per\T] +\newphysicsquantity{currentdensity}% + {\reciprocalsquare\m\usk\A}% + [\A\per\square\m]% + [\C\usk\s\per\square\m] +\newphysicsquantity{capacitance}% + {\reciprocalsquare\m\usk\reciprocal\kg\usk\quartic\s\usk\square\A}% + [\F]% + [\C\per\V] % also \C\squared\per\N\usk\m, \s\per\ohm +\newphysicsquantity{inductance}% + {\square\m\usk\kg\usk\reciprocalsquare\s\usk\reciprocalsquare\A}% + [\henry]% + [\volt\usk\s\per\A] % also \square\m\usk\kg\per\C\squared, \Wb\per\A +\newphysicsquantity{conductivity}% + {\reciprocalcubic\m\usk\reciprocal\kg\usk\cubic\s\usk\square\A}% + [(\A\per\square\m)\per(\V\per\m)]% + [\siemens\per\m] +\newphysicsquantity{resistivity}% + {\cubic\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocalsquare\A}% + [\ohm\usk\m]% + [(\V\per\m)\per(\A\per\square\m)] +\newphysicsquantity{resistance}% + {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocalsquare\A}% + [\ohm]% + [\V\per\A] +\newphysicsquantity{conductance}% + {\reciprocalsquare\m\usk\reciprocal\kg\usk\cubic\s\usk\square\A}% + [\A\per\V]% + [\siemens] +\newphysicsquantity{magneticcharge}% + {\m\usk\A}% + [\m\usk\A]% + [\m\usk\A] +\newcommand*{\vectordisplacement}[1]{\ensuremath{\displacement{\mivector{#1}}}} +\newcommand*{\vectorvelocity}[1]{\ensuremath{\velocity{\mivector{#1}}}} +\newcommand*{\vectorvelocityc}[1]{\ensuremath{\velocityc{\mivector{#1}}}} +\newcommand*{\vectoracceleration}[1]{\ensuremath{\acceleration{\mivector{#1}}}} +\newcommand*{\vectormomentum}[1]{\ensuremath{\momentum{\mivector{#1}}}} +\newcommand*{\vectorforce}[1]{\ensuremath{\force{\mivector{#1}}}} +\newcommand*{\vectorgravitationalfield}[1] + {\ensuremath{\gravitationalfield{\mivector{#1}}}} +\newcommand*{\vectorimpulse}[1]{\ensuremath{\impulse{\mivector{#1}}}} +\newcommand*{\vectorangularvelocity}[1]{\ensuremath{\angularvelocity{\mivector{#1}}}} +\newcommand*{\vectorangularacceleration}[1] + {\ensuremath{\angularacceleration{\mivector{#1}}}} 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+\newcommand*{\dervectdotedvect}[3]{\ensuremath{% + \compdervect{#1}{x}{#2}\compdvect{#3}{x}+% + \compdervect{#1}{y}{#2}\compdvect{#3}{y}+% + \compdervect{#1}{z}{#2}\compdvect{#3}{z}}} +\newcommand*{\DervectdoteDvect}[3]{\ensuremath{% + \compDervect{#1}{x}{#2}\compDvect{#3}{x}+% + \compDervect{#1}{y}{#2}\compDvect{#3}{y}+% + \compDervect{#1}{z}{#2}\compDvect{#3}{z}}} +\newcommand*{\vectcrossvect}[2]{\ensuremath{% + {#1}\boldsymbol{\times}{#2}}} +\newcommand*{\ltriplecross}[3]{\ensuremath{% + \inparens{{#1}\boldsymbol{\times}{#2}}\boldsymbol{\times}{#3}}} +\newcommand*{\rtriplecross}[3]{\ensuremath{{#1}\boldsymbol{\times}% + \inparens{{#2}\boldsymbol{\times}{#3}}}} +\newcommand*{\ltriplescalar}[3]{\ensuremath{% + {#1}\boldsymbol{\times}{#2}\cdot{#3}}} +\newcommand*{\ltripleScalar}[3]{\ensuremath{% + {#1}\boldsymbol{\times}{#2}\bullet{#3}}} +\newcommand*{\rtriplescalar}[3]{\ensuremath{% + {#1}\cdot{#2}\boldsymbol{\times}{#3}}} +\newcommand*{\rtripleScalar}[3]{\ensuremath{% + {#1}\bullet{#2}\boldsymbol{\times}{#3}}} +\newcommand*{\ezero}{\ensuremath{\boldsymbol{e}_0}} +\newcommand*{\eone}{\ensuremath{\boldsymbol{e}_1}} +\newcommand*{\etwo}{\ensuremath{\boldsymbol{e}_2}} +\newcommand*{\ethree}{\ensuremath{\boldsymbol{e}_3}} +\newcommand*{\efour}{\ensuremath{\boldsymbol{e}_4}} +\newcommand*{\ek}[1]{\ensuremath{\boldsymbol{e}_{#1}}} +\newcommand*{\e}{\ek} +\newcommand*{\uezero}{\ensuremath{\widehat{\boldsymbol{e}}_0}} +\newcommand*{\ueone}{\ensuremath{\widehat{\boldsymbol{e}}_1}} +\newcommand*{\uetwo}{\ensuremath{\widehat{\boldsymbol{e}}_2}} +\newcommand*{\uethree}{\ensuremath{\widehat{\boldsymbol{e}}_3}} +\newcommand*{\uefour}{\ensuremath{\widehat{\boldsymbol{e}}_4}} +\newcommand*{\uek}[1]{\ensuremath{\widehat{\boldsymbol{e}}_{#1}}} +\newcommand*{\ue}{\uek} +\newcommand*{\ezerozero}{\ek{00}} +\newcommand*{\ezeroone}{\ek{01}} +\newcommand*{\ezerotwo}{\ek{02}} +\newcommand*{\ezerothree}{\ek{03}} +\newcommand*{\ezerofour}{\ek{04}} +\newcommand*{\eoneone}{\ek{11}} +\newcommand*{\eonetwo}{\ek{12}} +\newcommand*{\eonethree}{\ek{13}} +\newcommand*{\eonefour}{\ek{14}} +\newcommand*{\etwoone}{\ek{21}} +\newcommand*{\etwotwo}{\ek{22}} +\newcommand*{\etwothree}{\ek{23}} +\newcommand*{\etwofour}{\ek{24}} +\newcommand*{\ethreeone}{\ek{31}} +\newcommand*{\ethreetwo}{\ek{32}} +\newcommand*{\ethreethree}{\ek{33}} +\newcommand*{\ethreefour}{\ek{34}} +\newcommand*{\efourone}{\ek{41}} +\newcommand*{\efourtwo}{\ek{42}} +\newcommand*{\efourthree}{\ek{43}} +\newcommand*{\efourfour}{\ek{44}} +\newcommand*{\euzero}{\ensuremath{\boldsymbol{e}^0}} +\newcommand*{\euone}{\ensuremath{\boldsymbol{e}^1}} +\newcommand*{\eutwo}{\ensuremath{\boldsymbol{e}^2}} +\newcommand*{\euthree}{\ensuremath{\boldsymbol{e}^3}} +\newcommand*{\eufour}{\ensuremath{\boldsymbol{e}^4}} +\newcommand*{\euk}[1]{\ensuremath{\boldsymbol{e}^{#1}}} +\newcommand*{\eu}{\euk} +\newcommand*{\ueuzero}{\ensuremath{\widehat{\boldsymbol{e}}^0}} +\newcommand*{\ueuone}{\ensuremath{\widehat{\boldsymbol{e}}^1}} +\newcommand*{\ueutwo}{\ensuremath{\widehat{\boldsymbol{e}}^2}} +\newcommand*{\ueuthree}{\ensuremath{\widehat{\boldsymbol{e}}^3}} +\newcommand*{\ueufour}{\ensuremath{\widehat{\boldsymbol{e}}^4}} +\newcommand*{\ueuk}[1]{\ensuremath{\widehat{\boldsymbol{e}}^{#1}}} +\newcommand*{\ueu}{\ueuk} +\newcommand*{\euzerozero}{\euk{00}} +\newcommand*{\euzeroone}{\euk{01}} +\newcommand*{\euzerotwo}{\euk{02}} +\newcommand*{\euzerothree}{\euk{03}} +\newcommand*{\euzerofour}{\euk{04}} +\newcommand*{\euoneone}{\euk{11}} +\newcommand*{\euonetwo}{\euk{12}} +\newcommand*{\euonethree}{\euk{13}} +\newcommand*{\euonefour}{\euk{14}} +\newcommand*{\eutwoone}{\euk{21}} +\newcommand*{\eutwotwo}{\euk{22}} +\newcommand*{\eutwothree}{\euk{23}} +\newcommand*{\eutwofour}{\euk{24}} +\newcommand*{\euthreeone}{\euk{31}} +\newcommand*{\euthreetwo}{\euk{32}} +\newcommand*{\euthreethree}{\euk{33}} +\newcommand*{\euthreefour}{\euk{34}} +\newcommand*{\eufourone}{\euk{41}} +\newcommand*{\eufourtwo}{\euk{42}} +\newcommand*{\eufourthree}{\euk{43}} +\newcommand*{\eufourfour}{\euk{44}} +\newcommand*{\gzero}{\ensuremath{\boldsymbol{\gamma}_0}} +\newcommand*{\gone}{\ensuremath{\boldsymbol{\gamma}_1}} +\newcommand*{\gtwo}{\ensuremath{\boldsymbol{\gamma}_2}} +\newcommand*{\gthree}{\ensuremath{\boldsymbol{\gamma}_3}} +\newcommand*{\gfour}{\ensuremath{\boldsymbol{\gamma}_4}} +\newcommand*{\gk}[1]{\ensuremath{\boldsymbol{\gamma}_{#1}}} +\newcommand*{\g}{\gk} +\newcommand*{\gzerozero}{\gk{00}} +\newcommand*{\gzeroone}{\gk{01}} +\newcommand*{\gzerotwo}{\gk{02}} +\newcommand*{\gzerothree}{\gk{03}} +\newcommand*{\gzerofour}{\gk{04}} +\newcommand*{\goneone}{\gk{11}} +\newcommand*{\gonetwo}{\gk{12}} +\newcommand*{\gonethree}{\gk{13}} +\newcommand*{\gonefour}{\gk{14}} +\newcommand*{\gtwoone}{\gk{21}} +\newcommand*{\gtwotwo}{\gk{22}} +\newcommand*{\gtwothree}{\gk{23}} +\newcommand*{\gtwofour}{\gk{24}} +\newcommand*{\gthreeone}{\gk{31}} +\newcommand*{\gthreetwo}{\gk{32}} +\newcommand*{\gthreethree}{\gk{33}} +\newcommand*{\gthreefour}{\gk{34}} +\newcommand*{\gfourone}{\gk{41}} +\newcommand*{\gfourtwo}{\gk{42}} +\newcommand*{\gfourthree}{\gk{43}} +\newcommand*{\gfourfour}{\gk{44}} +\newcommand*{\guzero}{\ensuremath{\boldsymbol{\gamma}^0}} +\newcommand*{\guone}{\ensuremath{\boldsymbol{\gamma}^1}} +\newcommand*{\gutwo}{\ensuremath{\boldsymbol{\gamma}^2}} +\newcommand*{\guthree}{\ensuremath{\boldsymbol{\gamma}^3}} +\newcommand*{\gufour}{\ensuremath{\boldsymbol{\gamma}^4}} +\newcommand*{\guk}[1]{\ensuremath{\boldsymbol{\gamma}^{#1}}} +\newcommand*{\gu}{\guk} +\newcommand*{\guzerozero}{\guk{00}} +\newcommand*{\guzeroone}{\guk{01}} +\newcommand*{\guzerotwo}{\guk{02}} +\newcommand*{\guzerothree}{\guk{03}} +\newcommand*{\guzerofour}{\guk{04}} +\newcommand*{\guoneone}{\guk{11}} +\newcommand*{\guonetwo}{\guk{12}} +\newcommand*{\guonethree}{\guk{13}} +\newcommand*{\guonefour}{\guk{14}} +\newcommand*{\gutwoone}{\guk{21}} +\newcommand*{\gutwotwo}{\guk{22}} +\newcommand*{\gutwothree}{\guk{23}} +\newcommand*{\gutwofour}{\guk{24}} +\newcommand*{\guthreeone}{\guk{31}} +\newcommand*{\guthreetwo}{\guk{32}} +\newcommand*{\guthreethree}{\guk{33}} +\newcommand*{\guthreefour}{\guk{34}} +\newcommand*{\gufourone}{\guk{41}} +\newcommand*{\gufourtwo}{\guk{42}} +\newcommand*{\gufourthree}{\guk{43}} +\newcommand*{\gufourfour}{\guk{44}} +\ExplSyntaxOn % Vectors formated as in M\&I, written in LaTeX3 +\NewDocumentCommand{\mivector}{ O{,} m o }% + {% + \mi_vector:nn { #1 } { #2 } + \IfValueT{#3}{\;{#3}} + }% +\seq_new:N \l__mi_list_seq +\cs_new_protected:Npn \mi_vector:nn #1 #2 +{% + \ensuremath{% + \seq_set_split:Nnn \l__mi_list_seq { , } { #2 } + \int_compare:nF { \seq_count:N \l__mi_list_seq = 1 } { \left\langle } + \seq_use:Nnnn \l__mi_list_seq { #1 } { #1 } { #1 } + \int_compare:nF { \seq_count:N \l__mi_list_seq = 1 } { \right\rangle } + }% +}% +\ExplSyntaxOff +\ExplSyntaxOn % Column and row vectors, written in LaTeX3 +\seq_new:N \l__vector_arg_seq +\cs_new_protected:Npn \vector_main:nnnn #1 #2 #3 #4 + {% + \seq_set_split:Nnn \l__vector_arg_seq { #3 } { #4 } + \begin{#1matrix} + \seq_use:Nnnn \l__vector_arg_seq { #2 } { #2 } { #2 } + \end{#1matrix} + }% +\NewDocumentCommand{\rowvector}{ O{,} m } + {% + \ensuremath{ + \vector_main:nnnn { p } { \,\, } { #1 } { #2 } + }% + }% +\NewDocumentCommand{\colvector}{ O{,} m } + {% + \ensuremath{ + \vector_main:nnnn { p } { \\ } { #1 } { #2 } + }% + }% +\ExplSyntaxOff +\newcommandx{\scompscvect}[2][1,usedefault]{% + \ifthenelse{\equal{#1}{}}% + {% + \colvector{\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% + }% + {% + \colvector{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% + }% +}% +\newcommandx{\scompsCvect}[2][1,usedefault]{% + \ifthenelse{\equal{#1}{}}% + {% + \colvector{\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% + }% + {% + \colvector{\msup{#2}{0},\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% + }% +}% +\newcommandx{\scompsrvect}[2][1,usedefault]{% + \ifthenelse{\equal{#1}{}}% + {% + \rowvector[,]{\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% + }% + {% + \rowvector[,]{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% + }% +}% +\newcommandx{\scompsRvect}[2][1,usedefault]{% + \ifthenelse{\equal{#1}{}}% + {% + \rowvector[,]{\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% + }% + {% + \rowvector[,]{\msup{#2}{0},\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% + }% +}% +\newcommand*{\anglebetween}[2]{\ensuremath{\theta_{\vect{#1},\vect{#2}}}} +\newcommand*{\bra}[1]{\ensuremath{\left\langle{#1}\right\lvert}} +\newcommand*{\ket}[1]{\ensuremath{\left\lvert{#1}\right\rangle}} +\newcommand*{\bracket}[2]{\ensuremath{\left\langle{#1}\!\!\right.% + \left\lvert{#2}\right\rangle}} +\newphysicsconstant{oofpez}% + {\ensuremath{\frac{1}{\phantom{_o}4\pi\epsilon_0}}}% + {\mi@p{9}{8.9875517873681764}\timestento{9}}% + {\m\cubed\usk\kg\usk\reciprocalquartic\s\usk\A\reciprocalsquared}% + [\newton\usk\m\squared\per\coulomb\squared]% + [\m\per\farad] +\newphysicsconstant{oofpezcs}% + {\ensuremath{\frac{1}{\phantom{_o}4\pi\epsilon_0 c^2\phantom{_o}}}}% + {\tento{-7}}% + {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% + [\N\usk\s\squared\per\C\squared]% + [\T\usk\m\squared] +\newphysicsconstant{vacuumpermittivity}% + {\ensuremath{\epsilon_0}}% + {\mi@p{9.0}{8.854187817}\timestento{-12}}% + {\m\reciprocalcubed\usk\reciprocal\kg\usk\s\quarted\usk\A\squared}% + [\C\squared\per\N\usk\m\squared]% + [\F\per\m] +\newphysicsconstant{mzofp}% + {\ensuremath{\frac{\phantom{_oo}\mu_0\phantom{_o}}{4\pi}}}% + {\tento{-7}}% + {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% + [\tesla\usk\m\per\A]% + [\henry\per\m] +\newphysicsconstant{vacuumpermeability}% + {\ensuremath{\mu_0}}% + {4\pi\timestento{-7}}% + {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% + [\T\usk\m\per\A]% + [\henry\per\m] +\newphysicsconstant{boltzmann}% + {\ensuremath{k_B}}% + {\mi@p{1.4}{1.38064852}\timestento{-23}}% + {\m\squared\usk\kg\usk\reciprocalsquare\s\usk\reciprocal\K}% + [\J\per\K]% + [\J\per\K] +\newphysicsconstant{boltzmannineV}% + {\ensuremath{k_B}}% + {\mi@p{8.6}{8.6173303}\timestento{-5}}% + {\eV\usk\reciprocal\K}% + [\eV\per\K]% + [\eV\per\K] +\newphysicsconstant{stefanboltzmann}% + {\ensuremath{\sigma}}% + {\mi@p{5.7}{5.670367}\timestento{-8}}% + {\kg\usk\s\reciprocalcubed\usk\K\reciprocalquarted}% + [\W\per\m\squared\usk\K\quarted]% + [\W\per\m\squared\usk\K\quarted] +\newphysicsconstant{planck}% + {\ensuremath{h}}% + {\mi@p{6.6}{6.626070040}\timestento{-34}}% + {\m\squared\usk\kg\usk\reciprocal\s}% + [\J\usk\s]% + [\J\usk\s] +\newphysicsconstant{planckineV}% + {\ensuremath{h}}% + {\mi@p{4.1}{4.135667662}\timestento{-15}}% + {\eV\usk\s}% + [\eV\usk\s]% + [\eV\usk\s] +\newphysicsconstant{planckbar}% + {\ensuremath{\hslash}}% + {\mi@p{1.1}{1.054571800}\timestento{-34}}% + {\m\squared\usk\kg\usk\reciprocal\s}% + [\J\usk\s]% + [\J\usk\s] +\newphysicsconstant{planckbarineV}% + {\ensuremath{\hslash}}% + {\mi@p{6.6}{6.582119514}\timestento{-16}}% + {\eV\usk\s}% + [\eV\usk\s]% + [\eV\usk\s] +\newphysicsconstant{planckc}% + {\ensuremath{hc}}% + {\mi@p{2.0}{1.98644568}\timestento{-25}}% + {\m\cubed\usk\kg\usk\reciprocalsquare\s}% + [\J\usk\m]% + [\J\usk\m] +\newphysicsconstant{planckcineV}% + {\ensuremath{hc}}% + {\mi@p{1240}{1.23984193}\timestento{3}}% + {\eV\usk\text{n}\m}% + [\eV\usk\text{n}\m]% + [\eV\usk\text{n}\m] +\newphysicsconstant{rydberg}% + {\ensuremath{\msub{R}{\infty}}}% + {\mi@p{1.1}{1.0973731568508}\timestento{7}}% + {\reciprocal\m}% + [\reciprocal\m]% + [\reciprocal\m] +\newphysicsconstant{bohrradius}% + {\ensuremath{a_0}}% + {\mi@p{5.3}{5.2917721067}\timestento{-11}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{finestructure}% + {\ensuremath{\alpha}}% + {\mi@p{\frac{1}{137}}{7.2973525664\timestento{-3}}}% + {}% + []% + [] +\newphysicsconstant{avogadro}% + {\ensuremath{N_A}}% + {\mi@p{6.0}{6.022140857}\timestento{23}}% + {\reciprocal\mol}% + [\reciprocal\mol]% + [\reciprocal\mol] +\newphysicsconstant{universalgrav}% + {\ensuremath{G}}% + {\mi@p{6.7}{6.67408}\timestento{-11}}% + {\m\cubed\usk\reciprocal\kg\usk\s\reciprocalsquared}% + [\N\usk\m\squared\per\kg\squared]% + [\J\usk\m\per\kg\squared] +\newphysicsconstant{surfacegravfield}% + {\ensuremath{g}}% + {\mi@p{9.8}{9.807}}% + {\m\usk\s\reciprocalsquared}% + [\N\per\kg]% + [\N\per\kg] +\newphysicsconstant{clight}% + {\ensuremath{c}}% + {\mi@p{3}{2.99792458}\timestento{8}}% + {\m\usk\reciprocal\s}% + [\m\per\s]% + [\m\per\s] +\newphysicsconstant{clightinfeet}% + {\ensuremath{c}}% + {\mi@p{1}{0.983571}}% + {\text{ft}\usk\reciprocal{\text{n}\s}}% + [\text{ft}\per\text{n}\s]% + [\text{ft}\per\mathrm{n}\s] +\newphysicsconstant{Ratom}% + {\ensuremath{r_{\text{atom}}}}% + {\tento{-10}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{Mproton}% + {\ensuremath{m_p}}% + {\mi@p{1.7}{1.672621898}\timestento{-27}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{Mneutron}% + {\ensuremath{m_n}}% + {\mi@p{1.7}{1.674927471}\timestento{-27}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{Mhydrogen}% + {\ensuremath{m_H}}% + {\mi@p{1.7}{1.6737236}\timestento{-27}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{Melectron}% + {\ensuremath{m_e}}% + {\mi@p{9.1}{9.10938356}\timestento{-31}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{echarge}% + {\ensuremath{e}}% + {\mi@p{1.6}{1.6021766208}\timestento{-19}}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsconstant{Qelectron}% + {\ensuremath{Q_e}}% + {-\echargevalue}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsconstant{qelectron}% + {\ensuremath{q_e}}% + {-\echargevalue}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsconstant{Qproton}% + {\ensuremath{Q_p}}% + {+\echargevalue}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsconstant{qproton}% + {\ensuremath{q_p}}% + {+\echargevalue}% + {\A\usk\s}% + [\C]% + [\C] +\newphysicsconstant{MEarth}% + {\ensuremath{M_{\text{Earth}}}}% + {\mi@p{6.0}{5.97237}\timestento{24}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{MMoon}% + {\ensuremath{M_{\text{Moon}}}}% + {\mi@p{7.3}{7.342}\timestento{22}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{MSun}% + {\ensuremath{M_{\text{Sun}}}}% + {\mi@p{2.0}{1.98855}\timestento{30}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{REarth}% + {\ensuremath{R_{\text{Earth}}}}% + {\mi@p{6.4}{6.371}\timestento{6}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{RMoon}% + {\ensuremath{R_{\text{Moon}}}}% + {\mi@p{1.7}{1.7371}\timestento{6}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{RSun}% + {\ensuremath{R_{\text{Sun}}}}% + {\mi@p{7.0}{6.957}\timestento{8}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{ESdist}% + {\magvectsub{r}{ES}}% + {\mi@p{1.5}{1.496}\timestento{11}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{SEdist}% + {\magvectsub{r}{SE}}% + {\mi@p{1.5}{1.496}\timestento{11}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{EMdist}% + {\magvectsub{r}{EM}}% + {\mi@p{3.8}{3.81550}\timestento{8}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{MEdist}% + {\magvectsub{r}{ME}}% + {\mi@p{3.8}{3.81550}\timestento{8}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{LSun}% + {\ensuremath{L_{\text{Sun}}}}% + {\mi@p{3.8}{3.8460}\timestento{26}}% + {\m\squared\usk\kg\usk\s\reciprocalcubed}% + [\W] + [\J\per\s] +\newphysicsconstant{TSun}% + {\ensuremath{T_{\text{Sun}}}}% + {\mi@p{5800}{5778}}% + {\K}% + [\K]% + [\K] +\newphysicsconstant{MagSun}% + {\ensuremath{M_{\text{Sun}}}}% + {+4.83}% + {}% + []% + [] +\newphysicsconstant{magSun}% + {\ensuremath{m_{\text{Sun}}}}% + {-26.74}% + {}% + []% + [] +\newcommand*{\coulombconstant}{\oofpez} +\newcommand*{\altcoulombconstant}{\oofpezcs} +\newcommand*{\biotsavartconstant}{\mzofp} +\newcommand*{\boltzmannconstant}{\boltzmann} +\newcommand*{\stefanboltzmannconstant}{\stefanboltzmann} +\newcommand*{\planckconstant}{\planck} +\newcommand*{\reducedplanckconstant}{\planckbar} +\newcommand*{\planckconstanttimesc}{\planckc} +\newcommand*{\rydbergconstant}{\rydberg} +\newcommand*{\finestructureconstant}{\finestructure} +\newcommand*{\avogadroconstant}{\avogadro} +\newcommand*{\universalgravitationalconstant}{\universalgrav} +\newcommand*{\earthssurfacegravitationalfield}{\surfacegravfield} +\newcommand*{\photonconstant}{\clight} +\newcommand*{\elementarycharge}{\echarge} +\newcommand*{\EarthSundistance}{\ESdist} +\newcommand*{\SunEarthdistance}{\SEdist} +\newcommand*{\EarthMoondistance}{\ESdist} +\newcommand*{\MoonEarthdistance}{\SEdist} +\newcommand*{\Lstar}[1][\(\star\)]{\ensuremath{L_{\text{#1}}}\xspace} +\newcommand*{\Lsolar}{\ensuremath{\Lstar[\(\odot\)]}\xspace} +\newcommand*{\Tstar}[1][\(\star\)]{\ensuremath{T_{\text{#1}}}\xspace} +\newcommand*{\Tsolar}{\ensuremath{\Tstar[\(\odot\)]}\xspace} +\newcommand*{\Rstar}[1][\(\star\)]{\ensuremath{R_{\text{#1}}}\xspace} +\newcommand*{\Rsolar}{\ensuremath{\Rstar[\(\odot\)]}\xspace} +\newcommand*{\Mstar}[1][\(\star\)]{\ensuremath{M_{\text{#1}}}\xspace} +\newcommand*{\Msolar}{\ensuremath{\Mstar[\(\odot\)]}\xspace} +\newcommand*{\Fstar}[1][\(\star\)]{\ensuremath{F_{\text{#1}}}\xspace} +\newcommand*{\fstar}[1][\(\star\)]{\ensuremath{f_{\text{#1}}}\xspace} +\newcommand*{\Fsolar}{\ensuremath{\Fstar[\(\odot\)]}\xspace} +\newcommand*{\fsolar}{\ensuremath{\fstar[\(\odot\)]}\xspace} +\newcommand*{\Magstar}[1][\(\star\)]{\ensuremath{M_{\text{#1}}}\xspace} +\newcommand*{\magstar}[1][\(\star\)]{\ensuremath{m_{\text{#1}}}\xspace} +\newcommand*{\Magsolar}{\ensuremath{\Magstar[\(\odot\)]}\xspace} +\newcommand*{\magsolar}{\ensuremath{\magstar[\(\odot\)]}\xspace} +\newcommand*{\Dstar}[1][\(\star\)]{\ensuremath{D_{\text{#1}}}\xspace} +\newcommand*{\dstar}[1][\(\star\)]{\ensuremath{d_{\text{#1}}}\xspace} +\newcommand*{\Dsolar}{\ensuremath{\Dstar[\(\odot\)]}\xspace} +\newcommand*{\dsolar}{\ensuremath{\dstar[\(\odot\)]}\xspace} +\newcommand*{\onehalf}{\ensuremath{\frac{1}{2}}\xspace} +\newcommand*{\onethird}{\ensuremath{\frac{1}{3}}\xspace} +\newcommand*{\onefourth}{\ensuremath{\frac{1}{4}}\xspace} +\newcommand*{\onefifth}{\ensuremath{\frac{1}{5}}\xspace} +\newcommand*{\onesixth}{\ensuremath{\frac{1}{6}}\xspace} +\newcommand*{\oneseventh}{\ensuremath{\frac{1}{7}}\xspace} +\newcommand*{\oneeighth}{\ensuremath{\frac{1}{8}}\xspace} +\newcommand*{\oneninth}{\ensuremath{\frac{1}{9}}\xspace} +\newcommand*{\onetenth}{\ensuremath{\frac{1}{10}}\xspace} +\newcommand*{\twooneths}{\ensuremath{\frac{2}{1}}\xspace} +\newcommand*{\twohalves}{\ensuremath{\frac{2}{2}}\xspace} +\newcommand*{\twothirds}{\ensuremath{\frac{2}{3}}\xspace} +\newcommand*{\twofourths}{\ensuremath{\frac{2}{4}}\xspace} +\newcommand*{\twofifths}{\ensuremath{\frac{2}{5}}\xspace} +\newcommand*{\twosixths}{\ensuremath{\frac{2}{6}}\xspace} +\newcommand*{\twosevenths}{\ensuremath{\frac{2}{7}}\xspace} +\newcommand*{\twoeighths}{\ensuremath{\frac{2}{8}}\xspace} +\newcommand*{\twoninths}{\ensuremath{\frac{2}{9}}\xspace} +\newcommand*{\twotenths}{\ensuremath{\frac{2}{10}}\xspace} +\newcommand*{\threeoneths}{\ensuremath{\frac{3}{1}}\xspace} +\newcommand*{\threehalves}{\ensuremath{\frac{3}{2}}\xspace} +\newcommand*{\threethirds}{\ensuremath{\frac{3}{3}}\xspace} +\newcommand*{\threefourths}{\ensuremath{\frac{3}{4}}\xspace} +\newcommand*{\threefifths}{\ensuremath{\frac{3}{5}}\xspace} +\newcommand*{\threesixths}{\ensuremath{\frac{3}{6}}\xspace} +\newcommand*{\threesevenths}{\ensuremath{\frac{3}{7}}\xspace} +\newcommand*{\threeeighths}{\ensuremath{\frac{3}{8}}\xspace} +\newcommand*{\threeninths}{\ensuremath{\frac{3}{9}}\xspace} +\newcommand*{\threetenths}{\ensuremath{\frac{3}{10}}\xspace} +\newcommand*{\fouroneths}{\ensuremath{\frac{4}{1}}\xspace} +\newcommand*{\fourhalves}{\ensuremath{\frac{4}{2}}\xspace} +\newcommand*{\fourthirds}{\ensuremath{\frac{4}{3}}\xspace} +\newcommand*{\fourfourths}{\ensuremath{\frac{4}{4}}\xspace} +\newcommand*{\fourfifths}{\ensuremath{\frac{4}{5}}\xspace} +\newcommand*{\foursixths}{\ensuremath{\frac{4}{6}}\xspace} +\newcommand*{\foursevenths}{\ensuremath{\frac{4}{7}}\xspace} +\newcommand*{\foureighths}{\ensuremath{\frac{4}{8}}\xspace} +\newcommand*{\fourninths}{\ensuremath{\frac{4}{9}}\xspace} +\newcommand*{\fourtenths}{\ensuremath{\frac{4}{10}}\xspace} +\newcommand*{\sumoverall}[1]{\ensuremath{\displaystyle + \sum_{\substack{\text{\tiny{all }}\text{\tiny{{#1}}}}}}} +\newcommand*{\dx}[1]{\ensuremath{\,\mathrm{d}{#1}}} +\newcommand*{\dslashx}[1]{\ensuremath{\,\mathchar'26\mkern-12mu \mathrm{d}{#1}}} +\newcommandx{\evaluatedfromto}[2][2,usedefault]{\ensuremath{% + \Bigg.\Bigg\rvert_{#1}^{#2}}} +\newcommand*{\evaluatedat}{\evaluatedfromto} +\newcommandx{\integral}[4][1,2,usedefault]{\ensuremath{% + \int_{\ifthenelse{\equal{#1}{}}{}{#4=#1}}^{\ifthenelse{% + \equal{#2}{}}{}{#4=#2}}}{#3}\dx{#4}} +\newcommand*{\opensurfaceintegral}[2]{\ensuremath{% + \iint\nolimits_{#1}\vectdotvect{#2}{\dirvect{n}}\dx{A}}} +\newcommand*{\closedsurfaceintegral}[2]{\ensuremath{% + \varoiint\nolimits_{#1}\vectdotvect{#2}{\dirvect{n}}\dx{A}}} +\newcommand*{\openlineintegral}[2]{\ensuremath{% + \int\nolimits_{#1}\vectdotvect{#2}{\dirvect{t}}\dx{\ell}}} +\newcommand*{\closedlineintegral}[2]{\ensuremath{% + \oint\nolimits_{#1}\vectdotvect{#2}{\dirvect{t}}\dx{\ell}}} +\newcommand*{\volumeintegral}[2]{\ensuremath{% + \iiint\nolimits_{#1}{#2}\dx{V}}} +\newcommandx{\dbydt}[1][1]{\ensuremath{% + \frac{\mathrm{d}{#1}}{\mathrm{d}t}}} +\newcommandx{\DbyDt}[1][1]{\ensuremath{% + \frac{\Delta{#1}}{\Delta t}}} +\newcommandx{\ddbydt}[1][1]{\ensuremath{% + \frac{\mathrm{d}^{2}{#1}}{\mathrm{d}t^{2}}}} +\newcommandx{\DDbyDt}[1][1]{\ensuremath{% + \frac{\Delta^{2}{#1}}{\Delta t^{2}}}} +\newcommandx{\pbypt}[1][1]{\ensuremath{% + \frac{\partial{#1}}{\partial t}}} +\newcommandx{\ppbypt}[1][1]{\ensuremath{% + \frac{\partial^{2}{#1}}{\partial t^{2}}}} +\newcommand*{\dbyd}[2]{\ensuremath{\frac{% + \mathrm{d}{#1}}{\mathrm{d}{#2}}}} +\newcommand*{\DbyD}[2]{\ensuremath{\frac{% + \Delta{#1}}{\Delta{#2}}}} +\newcommand*{\ddbyd}[2]{\ensuremath{% + \frac{\mathrm{d}^{2}{#1}}{\mathrm{d}{#2}^{2}}}} +\newcommand*{\DDbyD}[2]{\ensuremath{% + \frac{\Delta^{2}{#1}}{\Delta{#2}^{2}}}} +\newcommand*{\pbyp}[2]{\ensuremath{% + \frac{\partial{#1}}{\partial{#2}}}} +\newcommand*{\ppbyp}[2]{\ensuremath{% + \frac{\partial^{2}{#1}}{\partial{#2}^{2}}}} +\newcommandx{\seriesfofx}[1][1=x,usedefault]{\ensuremath{% + f({#1}) \approx f(a) + \frac{f^\prime (a)}{1!}({#1}-a) + + \frac{f^{\prime\prime}(a)}{2!}({#1}-a)^2 + + \frac{f^{\prime\prime\prime}(a)}{3!}({#1}-a)^3 + \ldots}\xspace} +\newcommandx{\seriesexpx}[1][1=x,usedefault]{\ensuremath{% + e^{#1} \approx 1 + {#1} + \frac{{#1}^2}{2!} + \frac{{#1}^3}{3!} + \ldots}\xspace} +\newcommandx{\seriessinx}[1][1=x,usedefault]{\ensuremath{% + \sin {#1} \approx {#1} - \frac{{#1}^3}{3!} + \frac{{#1}^5}{5!} - \ldots}\xspace} +\newcommandx{\seriescosx}[1][1=x,usedefault]{\ensuremath{% + \cos {#1} \approx 1 - \frac{{#1}^2}{2!} + \frac{{#1}^4}{4!} - \ldots}\xspace} +\newcommandx{\seriestanx}[1][1=x,usedefault]{\ensuremath{% + \tan {#1} \approx {#1} + \frac{{#1}^3}{3} + \frac{2{#1}^5}{15} + \ldots}\xspace} +\newcommandx{\seriesatox}[1][1=x,usedefault]{\ensuremath{% + a^{#1} \approx 1 + {#1} \ln{a} + \frac{({#1} \ln a)^2}{2!} + + \frac{({#1} \ln a)^3}{3!} + \ldots}\xspace} +\newcommandx{\serieslnoneplusx}[1][1=x,usedefault]{\ensuremath{% + \ln(1 \pm {#1}) \approx \pm\; {#1} - \frac{{#1}^2}{2} \pm \frac{{#1}^3}{3} - % + \frac{{#1}^4}{4} \pm \ldots}\xspace} +\newcommandx{\binomialseries}[1][1=x,usedefault]{\ensuremath{% + (1 + {#1})^n \approx 1 + n{#1} + \frac{n(n-1)}{2!}{#1}^2 + \ldots}\xspace} +\newcommand*{\gradient}{\ensuremath{\boldsymbol{\nabla}}} +\newcommand*{\divergence}{\ensuremath{\boldsymbol{\nabla}\bullet}} +\newcommand*{\curl}{\ensuremath{\boldsymbol{\nabla\times}}} +\newcommand{\taigrad}{\ensuremath{\nabla}}% +\newcommand{\taisvec}{\ensuremath{% + \stackinset{c}{0.07ex}{c}{0.1ex}{\tiny$-$}{$\nabla$}} +}% +\newcommand{\taidivg}{\ensuremath{% + \stackinset{c}{0.07ex}{c}{0.1ex}{$\cdot$}{$\nabla$}} +}% +\newcommand{\taicurl}{\ensuremath{% + \stackinset{c}{0.04ex}{c}{0.32ex}{\tiny$\times$}{$\nabla$}} +}% +\newcommand*{\laplacian}{\ensuremath{\boldsymbol{\nabla}^2}} +\newcommand*{\dalembertian}{\ensuremath{\boldsymbol{\Box}}} +\newcommand*{\diracdelta}[1]{\ensuremath{\delta}(#1)} +\newcommand*{\orderof}[1]{\ensuremath{\mathcal{O}(#1)}} +\DeclareMathOperator{\asin}{\sin^{-1}} +\DeclareMathOperator{\acos}{\cos^{-1}} +\DeclareMathOperator{\atan}{\tan^{-1}} +\DeclareMathOperator{\asec}{\sec^{-1}} +\DeclareMathOperator{\acsc}{\csc^{-1}} +\DeclareMathOperator{\acot}{\cot^{-1}} +\DeclareMathOperator{\sech}{sech} +\DeclareMathOperator{\csch}{csch} +\DeclareMathOperator{\asinh}{\sinh^{-1}} +\DeclareMathOperator{\acosh}{\cosh^{-1}} +\DeclareMathOperator{\atanh}{\tanh^{-1}} +\DeclareMathOperator{\asech}{\sech^{-1}} +\DeclareMathOperator{\acsch}{\csch^{-1}} +\DeclareMathOperator{\acoth}{\coth^{-1}} +\DeclareMathOperator{\sgn}{sgn} +\DeclareMathOperator{\dex}{dex} +\newcommand*{\logb}[1][\relax]{\ensuremath{\log_{#1}}} +\ifthenelse{\boolean{@optboldvectors}} + {\newcommand*{\cB}{\ensuremath{\boldsymbol{c\mskip -3.00mu B}}}} + {\ifthenelse{\boolean{@optromanvectors}} + {\newcommand*{\cB}{\ensuremath{\textsf{c}\mskip -3.00mu\mathrm{B}}}} + {\newcommand*{\cB}{\ensuremath{c\mskip -3.00mu B}}}} +\newcommand*{\newpi}{\ensuremath{\pi\mskip -7.8mu\pi}} +\newcommand*{\scripty}[1]{\ensuremath{\mathcalligra{#1}}} +\newcommand*{\Lagr}{\ensuremath{\mathcal{L}}} +\newcommandx{\flux}[1][1]{\ensuremath{\ssub{\Phi}{#1}}} +\newcommandx{\circulation}[1][1]{\ensuremath{\ssub{\Gamma}{#1}}} +\newcommand*{\absof}[1]{\ensuremath{% + \left\lvert{\ifblank{#1}{\:\_\:}{#1}}\right\rvert}} +\newcommand*{\inparens}[1]{\ensuremath{% + \left({\ifblank{#1}{\:\_\:}{#1}}\right)}} +\newcommand*{\magof}[1]{\ensuremath{% + \left\lVert{\ifblank{#1}{\:\_\:}{#1}}\right\rVert}} +\newcommand*{\dimsof}[1]{\ensuremath{% + \left[{\ifblank{#1}{\:\_\:}{#1}}\right]}} +\newcommand*{\unitsof}[1]{\ensuremath{% + \left[{\ifblank{#1}{\:\_\:}{#1}}\right]_u}} +\newcommand*{\changein}[1]{\ensuremath{\delta{#1}}} +\newcommand*{\Changein}[1]{\ensuremath{\Delta{#1}}} +\newcommandx{\timestento}[2][2=\!\!,usedefault]{\ensuremath{% + \ifthenelse{\equal{#2}{}} + {\unit{\;\times\;10^{#1}}{}} + {\unit{\;\times\;10^{#1}}{#2}}}} +\newcommand*{\xtento}{\timestento} +\newcommandx{\tento}[2][2=\!\!,usedefault]{\ensuremath{% + \ifthenelse{\equal{#2}{}} + {\unit{10^{#1}}{}} + {\unit{10^{#1}}{#2}}}} +\newcommand*{\ee}[2]{\texttt{{#1}e{#2}}} +\newcommand*{\EE}[2]{\texttt{{#1}E{#2}}} +\newcommand*{\dms}[3]{\ensuremath{% + \indegrees{#1}\inarcminutes{#2}\inarcseconds{#3}}} +\newcommand*{\hms}[3]{\ensuremath{% + {#1}^{\hour}{#2}^{\mathrm{m}}{#3}^{\s}}} +\newcommand*{\clockreading}{\hms} +\newcommand*{\latitude}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} +\newcommand*{\latitudeN}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{N}}} +\newcommand*{\latitudeS}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{S}}} +\newcommand*{\longitude}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} +\newcommand*{\longitudeE}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{E}}} +\newcommand*{\longitudeW}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{W}}} +\newcommand*{\ssub}[2]{\ensuremath{#1_{\text{#2}}}} +\newcommand*{\ssup}[2]{\ensuremath{#1^{\text{#2}}}} +\newcommand*{\ssud}[3]{\ensuremath{#1^{\text{#2}}_{\text{#3}}}} +\newcommand*{\msub}[2]{\ensuremath{#1_{#2}}} +\newcommand*{\msup}[2]{\ensuremath{#1^{#2}}} +\newcommand*{\msud}[3]{\ensuremath{#1^{#2}_{#3}}} +\newcommand*{\levicivita}[1]{\ensuremath{% + \varepsilon_{\scriptscriptstyle{#1}}}} +\newcommand*{\kronecker}[1]{\ensuremath{% + \delta_{\scriptscriptstyle{#1}}}} +\newcommand*{\xaxis}{\ensuremath{x\text{-axis}}\xspace} +\newcommand*{\yaxis}{\ensuremath{y\text{-axis}}\xspace} +\newcommand*{\zaxis}{\ensuremath{z\text{-axis}}\xspace} +\newcommand*{\naxis}[1]{\ensuremath{{#1}\text{-axis}}\xspace} +\newcommand*{\axis}{\ensuremath{\text{-axis}}\xspace} +\newcommand*{\xyplane}{\ensuremath{xy\text{-plane}}\xspace} +\newcommand*{\yzplane}{\ensuremath{yz\text{-plane}}\xspace} +\newcommand*{\zxplane}{\ensuremath{zx\text{-plane}}\xspace} +\newcommand*{\yxplane}{\ensuremath{yx\text{-plane}}\xspace} +\newcommand*{\zyplane}{\ensuremath{zy\text{-plane}}\xspace} +\newcommand*{\xzplane}{\ensuremath{xz\text{-plane}}\xspace} +\newcommand*{\plane}{\ensuremath{\text{-plane}}\xspace} +% Frequently used roots. Prepend |f| for fractional exponents. +\newcommand*{\cuberoot}[1]{\ensuremath{\sqrt[3]{#1}}} +\newcommand*{\fourthroot}[1]{\ensuremath{\sqrt[4]{#1}}} +\newcommand*{\fifthroot}[1]{\ensuremath{\sqrt[5]{#1}}} +\newcommand*{\fsqrt}[1]{\ensuremath{{#1}^\onehalf}} +\newcommand*{\fcuberoot}[1]{\ensuremath{{#1}^\onethird}} +\newcommand*{\ffourthroot}[1]{\ensuremath{{#1}^\onefourth}} +\newcommand*{\ffifthroot}[1]{\ensuremath{{#1}^\onefifth}} +\newcommand*{\relgamma}[1]{\ensuremath{% + \frac{1}{\sqrt{1-\inparens{\frac{#1}{c}}\squared}}}} +\newcommand*{\frelgamma}[1]{\ensuremath{% + \inparens{1-\frac{{#1}\squared}{c\squared}}^{-\onehalf}}} +\newcommand*{\oosqrtomxs}[1]{\ensuremath{\frac{1}{\sqrt{1-{#1}\squared}}}} +\newcommand*{\oosqrtomx}[1]{\ensuremath{\frac{1}{\sqrt{1-{#1}}}}} +\newcommand*{\ooomx}[1]{\ensuremath{\frac{1}{1-{#1}}}} +\newcommand*{\ooopx}[1]{\ensuremath{\frac{1}{1+{#1}}}} +\newcommand*{\isequals}{\wordoperator{?}{=}\xspace} +\newcommand*{\wordoperator}[2]{\ensuremath{% + \mathrel{\vcenter{\offinterlineskip + \halign{\hfil\tiny\upshape##\hfil\cr\noalign{\vskip-.5ex} + {#1}\cr\noalign{\vskip.5ex}{#2}\cr}}}}} +\newcommand*{\definedas}{\wordoperator{defined}{as}\xspace} +\newcommand*{\associated}{\wordoperator{associated}{with}\xspace} +\newcommand*{\adjustedby}{\wordoperator{adjusted}{by}\xspace} +\newcommand*{\earlierthan}{\wordoperator{earlier}{than}\xspace} +\newcommand*{\laterthan}{\wordoperator{later}{than}\xspace} +\newcommand*{\forevery}{\wordoperator{for}{every}\xspace} +\newcommand*{\pwordoperator}[2]{\ensuremath{\left(% + \mathrel{\vcenter{\offinterlineskip% + \halign{\hfil\tiny\upshape##\hfil\cr\noalign{\vskip-.5ex}% + {#1}\cr\noalign{\vskip.5ex}{#2}\cr}}}\right)}}% +\newcommand*{\pdefinedas}{\pwordoperator{defined}{as}\xspace} +\newcommand*{\passociated}{\pwordoperator{associated}{with}\xspace} +\newcommand*{\padjustedby}{\pwordoperator{adjusted}{by}\xspace} +\newcommand*{\pearlierthan}{\pwordoperator{earlier}{than}\xspace} +\newcommand*{\platerthan}{\pwordoperator{later}{than}\xspace} +\newcommand*{\pforevery}{\pwordoperator{for}{every}\xspace} +\newcommand*{\defines}{\ensuremath{\stackrel{\text{\tiny{def}}}{=}}\xspace} +\newcommand*{\inframe}[1][\relax]{\ensuremath{% + \xrightarrow[\text\tiny{\mathcal #1}]{}}\xspace} +\newcommand*{\associates}{\ensuremath{% + \xrightarrow{\text{\tiny{assoc}}}}\xspace} +\newcommand*{\becomes}{\ensuremath{% + \xrightarrow{\text{\tiny{becomes}}}}\xspace} +\newcommand*{\rrelatedto}[1]{\ensuremath{% + \xLongrightarrow{\text{\tiny{#1}}}}} +\newcommand*{\lrelatedto}[1]{\ensuremath{% + \xLongleftarrow[\text{\tiny{#1}}]{}}} +\newcommand*{\brelatedto}[2]{\ensuremath{% + \xLongleftrightarrow[\text{\tiny{#1}}]{\text{\tiny{#2}}}}} +\newcommand*{\genericinteractionplaces}[5]{\ensuremath{\inparens{#1} + \frac{\inparens{#2}\inparens{#3}}{\inparens{#4}^2}{{\ifblank{#5}{% + \mivector{\_ , \_ , \_}}{#5}}}}} +\newcommand*{\genericfieldofparticleplaces}[4]{\ensuremath{\inparens{#1} + \frac{\inparens{#2}}{\inparens{#3}^2}{{\ifblank{#4}{\mivector{\_ , \_ , \_}}{#4}}}}} +\newcommand*{\genericpotentialenergyplaces}[4]{\ensuremath{% + \inparens{#1}\frac{\inparens{#2}\inparens{#3}}{\inparens{#4}}}} +\newcommand*{\genericelectricdipoleplaces}[5]{% + \ensuremath{\inparens{#1}\frac{\inparens{#2}\inparens{#3}}{\inparens{#4}^3}% + {{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} +\newcommand*{\genericelectricdipoleonaxisplaces}[5]{% + \ensuremath{\inparens{#1}\frac{2\inparens{#2}\inparens{#3}}{\inparens{#4}^3}% + {{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} +\newcommand*{\gfieldofparticle}{\ensuremath{\universalgravmathsymbol\frac{M}% + {\magsquaredvect{r}}\inparens{-\dirvect{r}}}} +\newcommand*{\gravitationalinteractionplaces}[4]{% + \genericinteractionplaces{\universalgrav}{#1}{#2}{#3}{#4}} +\newcommand*{\gfieldofparticleplaces}[3]{% + \genericfieldofparticleplaces{\universalgrav}{#1}{#2}{#3}} +\newcommand*{\electricinteractionplaces}[4]{% + \genericinteractionplaces{\oofpez}{#1}{#2}{#3}{#4}} +\newcommand*{\Efieldofparticleplaces}[3]{% + \genericfieldofparticleplaces{\oofpez}{#1}{#2}{#3}} +\newcommand*{\Bfieldofparticleplaces}[5]{\ensuremath{\inparens{\mzofp}% + \frac{\inparens{#1}\inparens{#2}}{\inparens{#3}^2}{{\ifblank{#4}{% + \mivector{\_ , \_ , \_}}{#4}}}\times{{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} +\newcommand*{\springinteractionplaces}[3]{\ensuremath{\inparens{#1} + \inparens{#2}{{\ifblank{#3}{\mivector{\_ , \_ , \_}}{#3}}}}} +\newcommand*{\gravitationalpotentialenergyplaces}[3]{\ensuremath{% + -\genericpotentialenergyplaces{\universalgrav}{#1}{#2}{#3}}} +\newcommand*{\electricpotentialenergyplaces}[3]{% + \genericpotentialenergyplaces{\oofpez}{#1}{#2}{#3}} +\newcommand*{\springpotentialenergyplaces}[2]{\ensuremath{% + \onehalf\inparens{#1}\inparens{#2}^2}} +\newcommand*{\electricdipoleonaxisplaces}[4]{% + \genericelectricdipoleonaxisplaces{\oofpez}{\absof{#1}}{#2}{#3}{{\ifblank{#4}{% + \mivector{\_ , \_ , \_}}{#4}}}} +\newcommand*{\electricdipoleonbisectorplaces}[4]{% + \genericelectricdipoleplaces{\oofpez}{\absof{#1}}{#2}{#3}{{\ifblank{#4}{% + \mivector{\_ , \_ , \_}}{#4}}}} +\newcommand{\define}[2]{\newcommand{#1}{#2}} +\newcommand*{\momentumprinciple}{\ensuremath{% + \vectsub{p}{sys,final}=\vectsub{p}{sys,initial}+\Fnetsys\Delta t}} +\newcommand*{\LHSmomentumprinciple}{\ensuremath{\vectsub{p}{sys,final}}} +\newcommand*{\RHSmomentumprinciple}{\ensuremath{% + \vectsub{p}{sys,initial}+\Fnetsys\Delta t}} +\newcommand*{\momentumprinciplediff}{\ensuremath{% + \Dvectsub{p}{sys}=\Fnetsys\Delta t}} +\newcommand*{\energyprinciple}{\ensuremath{% + \ssub{E}{sys,final}=\ssub{E}{sys,initial}+W+Q}} +\newcommand*{\LHSenergyprinciple}{\ensuremath{\ssub{E}{sys,final}}} +\newcommand*{\RHSenergyprinciple}{\ensuremath{\ssub{E}{sys,initial}+W+Q}} +\newcommand*{\energyprinciplediff}{\ensuremath{\Delta\ssub{E}{sys}=W+Q}} +\newcommand*{\angularmomentumprinciple}{\ensuremath{% + \vectsub{L}{\(A\),sys,final}=\vectsub{L}{\(A\),sys,initial}+\Tsub{net}\Delta t}} +\newcommand*{\LHSangularmomentumprinciple}{\ensuremath{% + \vectsub{L}{\(A\),sys,final}}} +\newcommand*{\RHSangularmomentumprinciple}{\ensuremath{% + \vectsub{L}{\(A\),sys,initial}+\Tsub{net}\Delta t}} +\newcommand*{\angularmomentumprinciplediff}{\ensuremath{% + \Dvectsub{L}{\(A\),sys}=\Tsub{net}\Delta t}} +\newcommand*{\gravitationalinteraction}{\ensuremath{% + \universalgravmathsymbol\frac{\msub{M}{1}\msub{M}{2}}{% + \magvectsub{r}{12}\squared}(-\dirvectsub{r}{12})}} +\newcommand*{\electricinteraction}{\ensuremath{% + \oofpezmathsymbol\frac{\msub{Q}{1}\msub{Q}{2}}{\magvectsub{r}{12}\squared} + \dirvectsub{r}{12}}} +\newcommand*{\springinteraction}{\ensuremath{\ks\magvect{s}(-\dirvect{s})}} +\newcommand*{\Bfieldofparticle}{\ensuremath{% + \mzofpmathsymbol\frac{Q\magvect{v}}{\magsquaredvect{r}}\dirvect{v}\times + \dirvect{r}}} +\newcommand*{\Efieldofparticle}{\ensuremath{% + \oofpezmathsymbol\frac{Q}{\magsquaredvect{r}}\dirvect{r}}} +\newcommandx{\Esys}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{E}{sys}}{\ssub{E}{sys,#1}}} +\newcommandx{\Us}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{U}{\(s\)}}{\ssub{U}{\(s\),#1}}} +\newcommandx{\Ug}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{U}{\(g\)}}{\ssub{U}{\(g\),#1}}} +\newcommandx{\Ue}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{U}{\(e\)}}{\ssub{U}{\(e\),#1}}} +\newcommandx{\Ktrans}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{K}{trans}} + {\ssub{K}{trans,#1}}} +\newcommandx{\Krot}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{K}{rot}}{\ssub{K}{rot,#1}}} +\newcommandx{\Kvib}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{K}{vib}}{\ssub{K}{vib,#1}}} +\newcommandx{\Eparticle}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{particle}} + {\ssub{E}{particle,#1}}} +\newcommandx{\Einternal}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{internal}} + {\ssub{E}{internal,#1}}} +\newcommandx{\Erest}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{rest}}{\ssub{E} + {rest,#1}}} +\newcommandx{\Echem}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{chem}}{\ssub{E} + {chem,#1}}} +\newcommandx{\Etherm}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{therm}} + {\ssub{E}{therm,#1}}} +\newcommandx{\Evib}[1][1]{\ifthenelse{% + \equal{#1}{}}{\ssub{E}{vib}}{\ssub{E}{vib,#1}}} +\newcommandx{\Ephoton}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{photon}} + {\ssub{E}{photon,#1}}} +\newcommand*{\DEsys}{\Changein\Esys} +\newcommand*{\DUs}{\Changein\Us} +\newcommand*{\DUg}{\Changein\Ug} +\newcommand*{\DUe}{\Changein\Ue} +\newcommand*{\DKtrans}{\Changein\Ktrans} +\newcommand*{\DKrot}{\Changein\Krot} +\newcommand*{\DKvib}{\Changein\Kvib} +\newcommand*{\DEparticle}{\Changein\Eparticle} +\newcommand*{\DEinternal}{\Changein\Einternal} +\newcommand*{\DErest}{\Changein\Erest} +\newcommand*{\DEchem}{\Changein\Echem} +\newcommand*{\DEtherm}{\Changein\Etherm} +\newcommand*{\DEvib}{\Changein\Evib} +\newcommand*{\DEphoton}{\Changein\Ephoton} +\newcommand*{\springpotentialenergy}{\onehalf\ks\magsquaredvect{s}} +\newcommand*{\finalspringpotentialenergy} + {\ssub{\left(\springpotentialenergy\right)}{\!\!final}} +\newcommand*{\initialspringpotentialenergy} + {\ssub{\left(\springpotentialenergy\right)}{\!\!initial}} +\newcommand*{\gravitationalpotentialenergy}{\ensuremath{% + -G\frac{\msub{M}{1}\msub{M}{2}}{\magvectsub{r}{12}}}} +\newcommand*{\finalgravitationalpotentialenergy} + {\ssub{\left(\gravitationalpotentialenergy\right)}{\!\!final}} +\newcommand*{\initialgravitationalpotentialenergy} + {\ssub{\left(\gravitationalpotentialenergy\right)}{\!\!initial}} +\newcommand*{\electricpotentialenergy}{\ensuremath{% + \oofpezmathsymbol\frac{\ssub{Q}{1}\ssub{Q}{2}}{\magvectsub{r}{12}}}} +\newcommand*{\finalelectricpotentialenergy} + {\ssub{\left(\electricpotentialenergy\right)}{\!\!final}} +\newcommand*{\initialelectricpotentialenergy} + {\ssub{\left(\electricpotentialenergy\right)}{\!\!initial}} +\newcommand*{\ks}{\msub{k}{s}} +\newcommand*{\Fnet}{\ensuremath{\vectsub{F}{net}}} +\newcommand*{\Fnetext}{\ensuremath{\vectsub{F}{net,ext}}} +\newcommand*{\Fnetsys}{\ensuremath{\vectsub{F}{net,sys}}} +\newcommand*{\Fsub}[1]{\ensuremath{\vectsub{F}{#1}}} +\newcommand*{\Ltotal}{\ensuremath{\vectsub{L}{\(A\),total}}} +\newcommand*{\Lsys}{\ensuremath{\vectsub{L}{\(A\),sys}}} +\newcommand*{\Lsub}[1]{\ensuremath{\vectsub{L}{\(A\),{#1}}}} +\newcommand*{\Tnet}{\ensuremath{\vectsub{\tau}{\(A\),net}}} +\newcommand*{\Tnetext}{\ensuremath{\vectsub{\tau}{\(A\),net,ext}}} +\newcommand*{\Tnetsys}{\ensuremath{\vectsub{\tau}{\(A\),net,sys}}} +\newcommand*{\Tsub}[1]{\ensuremath{\vectsub{\tau}{\(A\),#1}}} +\newcommand*{\LHSmaxwelliint}[1][\partial V]{\ensuremath{% + \closedsurfaceintegral{#1}{\vect{E}}}} +\newcommand*{\RHSmaxwelliint}{\ensuremath{\frac{\ssub{Q}{\(e\),net}}% + {\vacuumpermittivitymathsymbol}}} +\newcommand*{\RHSmaxwelliinta}[1][V]{\ensuremath{% + \frac{1}{\vacuumpermittivitymathsymbol}\volumeintegral{#1}{\msub{\rho}{e}}}} +\newcommand*{\RHSmaxwelliintfree}{\ensuremath{0}} +\newcommand*{\maxwelliint}[1][\partial V]{\ensuremath{% + \LHSmaxwelliint[#1]=\RHSmaxwelliint}} +\newcommandx*{\maxwelliinta}[2][1={\partial V},2={V},usedefault]{\ensuremath{% + \LHSmaxwelliint[#1]=\RHSmaxwelliinta[#2]}} +\newcommand*{\maxwelliintfree}[1][\partial V]{\ensuremath{% + \LHSmaxwelliint[#1]=\RHSmaxwelliintfree}} +\newcommand*{\LHSmaxwelliiint}[1][\partial V]{\ensuremath{% + \closedsurfaceintegral{#1}{\vect{B}}}} +\newcommand*{\RHSmaxwelliiint}{\ensuremath{0}} +\newcommand*{\RHSmaxwelliiintm}{\ensuremath{% + \vacuumpermeabilitymathsymbol\ssub{Q}{\(m\),net}}} +\newcommand*{\RHSmaxwelliiintma}[1][V]{\ensuremath{% + \vacuumpermeabilitymathsymbol\volumeintegral{#1}{\msub{\rho}{m}}}} +\newcommand*{\RHSmaxwelliiintfree}{\ensuremath{0}} +\newcommand*{\maxwelliiint}[1][\partial V]{\ensuremath{% + \LHSmaxwelliiint[#1]=\RHSmaxwelliiint}} +\newcommand*{\maxwelliiintm}[1][\partial V]{\ensuremath{% + \LHSmaxwelliiint[#1]=\RHSmaxwelliiintm}} +\newcommandx*{\maxwelliiintma}[2][1={\partial V},2={V},usedefault]{\ensuremath{% + \LHSmaxwelliiint[#1]=\RHSmaxwelliiintma[#2]}} +\newcommand*{\maxwelliiintfree}[1][\partial V]{\ensuremath{% + \LHSmaxwelliiint[#1]=\RHSmaxwelliiintfree}} +\newcommand*{\LHSmaxwelliiiint}[1][\partial\Omega]{\ensuremath{% + \closedlineintegral{#1}{\vect{E}}}} +\newcommand*{\RHSmaxwelliiiint}[1][\Omega]{\ensuremath{% + -\dbydt\opensurfaceintegral{#1}{\vect{B}}}} +\newcommand*{\RHSmaxwelliiiintm}[1][\Omega]{\ensuremath{% + -\dbydt\opensurfaceintegral{#1}{\vect{B}}% + -\vacuumpermeabilitymathsymbol\ssub{I}{\(m\),net}}} +\newcommand*{\RHSmaxwelliiiintma}[1][\Omega]{\ensuremath{% + -\dbydt\opensurfaceintegral{#1}{\vect{B}}% + -\vacuumpermeabilitymathsymbol\opensurfaceintegral{#1}{\vectsub{J}{\(m\)}}}} +\newcommand*{\RHSmaxwelliiiintfree}{\RHSmaxwelliiiint} +\newcommandx*{\maxwelliiiint}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiint[#2]}} +\newcommandx*{\maxwelliiiintm}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiintm[#2]}} +\newcommandx*{\maxwelliiiintma}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiintma[#2]}} +\newcommand*{\maxwelliiiintfree}{\maxwelliiiint} +\newcommand*{\LHSmaxwellivint}[1][\partial\Omega]{\ensuremath{% + \closedlineintegral{#1}{\vect{B}}}} +\newcommand*{\RHSmaxwellivint}[1][\Omega]{\ensuremath{% + \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% + \dbydt\opensurfaceintegral{#1}{\vect{E}}+% + \vacuumpermeabilitymathsymbol\ssub{I}{\(e\),net}}} +\newcommand*{\RHSmaxwellivinta}[1][\Omega]{\ensuremath{% + \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% + \dbydt\opensurfaceintegral{#1}{\vect{E}}+% + \vacuumpermeabilitymathsymbol\opensurfaceintegral{#1}{\vectsub{J}{\(e\)}}}} +\newcommand*{\RHSmaxwellivintfree}[1][\Omega]{\ensuremath{% + \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% + \dbydt\opensurfaceintegral{#1}{\vect{E}}}} +\newcommandx*{\maxwellivint}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivint[#2]}} +\newcommandx*{\maxwellivinta}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivinta[#2]}} +\newcommandx*{\maxwellivintfree}[2][1={\partial\Omega},2={\Omega},usedefault]% + {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivintfree[#2]}} +\newcommand*{\LHSmaxwellidif}{\ensuremath{\divergence{\vect{E}}}} +\newcommand*{\RHSmaxwellidif}{\ensuremath{\frac{\msub{\rho}{e}} + {\vacuumpermittivitymathsymbol}}} +\newcommand*{\RHSmaxwellidiffree}{\ensuremath{0}} +\newcommand*{\maxwellidif}{\ensuremath{\LHSmaxwellidif=\RHSmaxwellidif}} +\newcommand*{\maxwellidiffree}{\ensuremath{\LHSmaxwellidif=\RHSmaxwellidiffree}} +\newcommand*{\LHSmaxwelliidif}{\ensuremath{\divergence{\vect{B}}}} +\newcommand*{\RHSmaxwelliidif}{\ensuremath{0}} +\newcommand*{\RHSmaxwelliidifm}{\ensuremath{\vacuumpermeabilitymathsymbol% + \msub{\rho}{m}}} +\newcommand*{\RHSmaxwelliidiffree}{\ensuremath{0}} +\newcommand*{\maxwelliidif}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidif}} +\newcommand*{\maxwelliidifm}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidifm}} +\newcommand*{\maxwelliidiffree}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidiffree}} +\newcommand*{\LHSmaxwelliiidif}{\ensuremath{\curl{\vect{E}}}} +\newcommand*{\RHSmaxwelliiidif}{\ensuremath{-\pbypt[\vect{B}]}} +\newcommand*{\RHSmaxwelliiidifm}{\ensuremath{-\pbypt[\vect{B}]-% + \vacuumpermeabilitymathsymbol\vectsub{J}{\(m\)}}} +\newcommand*{\RHSmaxwelliiidiffree}{\RHSmaxwelliiidif} +\newcommand*{\maxwelliiidif}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidif}} +\newcommand*{\maxwelliiidifm}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidifm}} +\newcommand*{\maxwelliiidiffree}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidif}} +\newcommand*{\LHSmaxwellivdif}{\ensuremath{\curl{\vect{B}}}} +\newcommand*{\RHSmaxwellivdif}{\ensuremath{\vacuumpermeabilitymathsymbol% + \vacuumpermittivitymathsymbol\pbypt[\vect{E}]+% + \vacuumpermeabilitymathsymbol\vectsub{J}{\(e\)}}} +\newcommand*{\RHSmaxwellivdiffree}{\ensuremath{\vacuumpermeabilitymathsymbol + \vacuumpermittivitymathsymbol\pbypt[\vect{E}]}} +\newcommand*{\maxwellivdif}{\ensuremath{\LHSmaxwellivdif=\RHSmaxwellivdif}} +\newcommand*{\maxwellivdiffree}{\ensuremath{\LHSmaxwellivdif=\RHSmaxwellivdiffree}} +\newcommand*{\RHSlorentzforce}{\ensuremath{\msub{q}{e}\left(\vect{E}+% + \vectcrossvect{\vect{v}}{\vect{B}}\right)}} +\newcommand*{\RHSlorentzforcem}{\ensuremath{\RHSlorentzforce+\msub{q}{m}\left(% + \vect{B}-\vectcrossvect{\vect{v}}{\frac{\vect{E}}{c^2}}\right)}} +\newcommandx{\eulerlagrange}[1][1={q_i},usedefault]{\ensuremath{% + \pbyp{\mathcal{L}}{#1}-\dbydt\inparens{\pbyp{\mathcal{L}}{\dot{#1}}} = 0}} +\newcommandx{\Eulerlagrange}[1][1={q_i},usedefault]{\ensuremath{% + \DbyD{\mathcal{L}}{#1}-\DbyDt\inparens{\DbyD{\mathcal{L}}{\dot{#1}}} = 0}} +\newcommand*{\vpythonline}{\lstinline[style=vpython]} +\newcommand*{\glowscriptline}{\lstinline[style=vpython]} +\lstnewenvironment{vpythonblock}[2]{% + \lstset{style=vpython,caption={#1},label={#2}}}{} +\lstnewenvironment{glowscriptblock}[2]{% + \lstset{style=vpython,caption={#1},label={#2}}}{} +\newcommand*{\vpythonfile}[3]{% + \newpage\lstinputlisting[style=vpython,caption={#1},label={#2}]{#3}} +\newcommand*{\glowscriptfile}[3]{% + \newpage\lstinputlisting[style=vpython,caption={#1},label={#2}]{#3}} +\newcommandx{\emptyanswer}[2][1=0.80,2=0.1,usedefault] + {\begin{minipage}{#1\textwidth}\hfill\vspace{#2\textheight}\end{minipage}} +\newenvironmentx{activityanswer}[5][1=white,2=black,3=black,4=0.90,% 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\ifthenelse{\equal{#1}{}}% + {\begin{center}% + \fcolorbox{#3}{#2}{% + \emptyanswer[#5][#6]}% + \vspace{\baselineskip}% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% +}% +\newcommandx{\fullpageanswerform}[4][1=q1,2=Response,3=1.00,4=0.90,usedefault]{% + \vspace{\baselineskip}% + \begin{Form} + \begin{center}% + \TextField[value={#2},% + name=#1,% + width=#4\linewidth,% + height=#3\textheight,% + backgroundcolor=formcolor,% + multiline=true,% + charsize=10pt,% + bordercolor=black]{}% + \end{center}% + \end{Form}% + \vspace{\baselineskip}% +}% +\mdfdefinestyle{miinstructornotestyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={INSTRUCTOR NOTE}, + frametitlebackgroundcolor=cyan!60,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=cyan!25, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{miinstructornote}{% + \begin{mdframed}[style=miinstructornotestyle] + \begin{adjactivityanswer}[cyan!25][cyan!25][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\mdfdefinestyle{mistudentnotestyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={STUDENT NOTE}, + frametitlebackgroundcolor=cyan!60,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=cyan!25, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{mistudentnote}{% + \begin{mdframed}[style=mistudentnotestyle] + \begin{adjactivityanswer}[cyan!25][cyan!25][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\mdfdefinestyle{miderivationstyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=0pt,rightmargin=0pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={DERIVATION}, + frametitlebackgroundcolor=orange!60,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=orange!25, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{miderivation}{% + \begin{mdframed}[style=miderivationstyle] + \setcounter{equation}{0} + \begin{align} + \BODY + \end{align} + \end{mdframed} +}% +\NewEnviron{miderivation*}{% + \begin{mdframed}[style=miderivationstyle] + \setcounter{equation}{0} + \begin{align*} + \BODY + \end{align*} + \end{mdframed} +}% +\mdfdefinestyle{mistandardstyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={STANDARD}, + frametitlebackgroundcolor=cyan!60,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=cyan!25, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{mistandard}{% + \begin{mdframed}[style=mistandardstyle] + \begin{adjactivityanswer}[cyan!25][cyan!25][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\mdfdefinestyle{bwinstructornotestyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={INSTRUCTOR NOTE}, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=gray!20, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{bwinstructornote}{% + \begin{mdframed}[style=bwinstructornotestyle] + \begin{adjactivityanswer}[gray!20][gray!20][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\mdfdefinestyle{bwstudentnotestyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={STUDENT NOTE}, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=gray!20, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{bwstudentnote}{% + \begin{mdframed}[style=bwstudentnotestyle] + \begin{adjactivityanswer}[gray!20][gray!20][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\mdfdefinestyle{bwderivationstyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=0pt,rightmargin=0pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={DERIVATION}, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=gray!20, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{bwderivation}{% + \begin{mdframed}[style=bwderivationstyle] + \setcounter{equation}{0} + \begin{align} + \BODY + \end{align} + \end{mdframed} +}% +\NewEnviron{bwderivation*}{% + \begin{mdframed}[style=bwderivationstyle] + \setcounter{equation}{0} + \begin{align*} + \BODY + \end{align*} + \end{mdframed} +}% +\mdfdefinestyle{bwstandardstyle}{% + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, + nobreak=true, + frametitle={STANDARD}, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, + backgroundcolor=gray!20, + linecolor=black,fontcolor=black,shadow=true} +\NewEnviron{bwstandard}{% + \begin{mdframed}[style=bwstandardstyle] + \begin{adjactivityanswer}[gray!20][gray!20][black] + \BODY + \end{adjactivityanswer} + \end{mdframed} +}% +\NewEnviron{mysolution}{% + \setcounter{equation}{0} + \begin{align} + \BODY + \end{align} +}% +\NewEnviron{mysolution*}{% + \setcounter{equation}{0} + \begin{align*} + \BODY + \end{align*} +}% +\newenvironment{problem}[1]{% + \newpage% + \section*{#1}% + \newlist{parts}{enumerate}{2}% + \setlist[parts]{label=(\alph*)}}{\newpage} +\newcommand{\problempart}{\item}% +\newcommand{\reason}[1]{\begin{minipage}{5cm}{#1}\end{minipage}} +\newcommand*{\checkpoint}{% + \vspace{1cm}\begin{center}% + \colorbox{yellow!80}{|--------- CHECKPOINT ---------|}% + \end{center}}% +\newcommandx*{\image}[4][1={scale=1},usedefault]{% + \begin{figure}[H] + \begin{center}% + \includegraphics[#1]{#2}% + \end{center}% + \caption{#3}% + \label{#4}% + \end{figure}} +\newcommand*{\sneakyone}[1]{\ensuremath{\cancelto{1}{#1}}} +\newcommand*{\parallelto}{\ensuremath{{{\mkern3mu\vphantom{\perp}\vrule depth 0pt + \mkern2mu\vrule depth 0pt\mkern3mu}}}} +\newcommand*{\perpendicularto}{\ensuremath{\perp}} +\newcommand*{\qed}{\ensuremath{\text{ Q.E.D.}}} +\newcommand*{\chkquantity}[1]{% + \begin{center} + \begin{tabular}{C{4.5cm} C{4cm} C{4cm} C{4cm}} + name & baseunit & drvdunit & altnunit \tabularnewline + \cs{#1} & \csname #1onlybaseunit\endcsname & \csname #1onlydrvdunit\endcsname & + \csname #1onlyaltnunit\endcsname + \end{tabular} + \end{center} +}% +\newcommand*{\chkconstant}[1]{% + \begin{center} + \begin{tabular}{C{4cm} C{4cm} C{4cm}} + name & symbol & value \tabularnewline + \cs{#1} & \csname #1mathsymbol\endcsname & \csname #1value\endcsname + \tabularnewline + baseunit & drvdunit & altnunit \tabularnewline + \csname #1onlybaseunit\endcsname & \csname #1onlydrvdunit\endcsname & + \csname #1onlyaltnunit\endcsname + \end{tabular} + \end{center} +}% +% \end{macrocode} +% \newpage +% \section{Acknowledgements} +% I thank Marcel Heldoorn, Joseph Wright, Scott Pakin, Thomas Sturm, Aaron Titus, +% David Zaslavsky, Ruth Chabay, and Bruce Sherwood. Special thanks to Martin +% Scharrer for his \texttt{sty2dtx.pl} utility, which saved me days of typing. +% Special thanks also to Herbert Schulz for his custom \texttt{dtx} engine for +% \texttt{TeXShop}. Very special thanks to Ulrich Diez for providing the mechanism +% that defines physics quantities and constants. Also very special thanks to +% students who helped test recent versions of this package. +% +% \iffalse +% +% \fi +% +% \Finale diff --git a/macros/latex/contrib/mandi/mandi.ins b/macros/latex/contrib/mandi/mandi.ins new file mode 100644 index 0000000000..363aaa3520 --- /dev/null +++ b/macros/latex/contrib/mandi/mandi.ins @@ -0,0 +1,81 @@ +%% +%% This is file `mandi.ins', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% mandi.dtx (with options: `install') +%% +%% Copyright (C) 2018 by Paul J. Heafner +%% --------------------------------------------------------------------------- +%% This work may be distributed and/or modified under the conditions of the +%% LaTeX Project Public License, either version 1.3 of this license or (at +%% your option) any later version. The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.3 or later is part of all distributions of LaTeX version +%% 2005/12/01 or later. +%% +%% This work has the LPPL maintenance status `maintained'. +%% +%% The Current Maintainer of this work is Paul J. Heafner. +%% +%% This work consists of the files mandi.dtx +%% mandi.ins +%% mandi.pdf +%% README +%% +%% and includes the derived files mandi.sty +%% vdemo.py. +%% --------------------------------------------------------------------------- +%% +\input docstrip.tex +\keepsilent +\askforoverwritefalse +\usedir{tex/latex/mandi} +\preamble + +Copyright (C) 2018 by Paul J. Heafner +--------------------------------------------------------------------------- +This work may be distributed and/or modified under the conditions of the +LaTeX Project Public License, either version 1.3 of this license or (at +your option) any later version. The latest version of this license is in + http://www.latex-project.org/lppl.txt +and version 1.3 or later is part of all distributions of LaTeX version +2005/12/01 or later. + +This work has the LPPL maintenance status `maintained'. + +The Current Maintainer of this work is Paul J. Heafner. + + This work consists of the files mandi.dtx + mandi.ins + mandi.pdf + README + + and includes the derived files mandi.sty + vdemo.py. +--------------------------------------------------------------------------- + +\endpreamble + +\generate{\file{\jobname.sty}{\from{\jobname.dtx}{package}}} +\generate{\usepreamble\empty\usepostamble\empty + \file{vdemo.py}{\from{\jobname.dtx}{vdemo}}} + +\obeyspaces +\Msg{*************************************************************} +\Msg{* *} +\Msg{* To finish the installation you have to move the following *} +\Msg{* file into a directory searched by TeX: *} +\Msg{* *} +\Msg{* mandi.sty *} +\Msg{* *} +\Msg{* To produce the documentation run the file mandi.dtx *} +\Msg{* through pdfLaTeX. *} +\Msg{* *} +\Msg{*************************************************************} +\endbatchfile + +\endinput +%% +%% End of file `mandi.ins'. diff --git a/macros/latex/contrib/mandi/mandi.pdf b/macros/latex/contrib/mandi/mandi.pdf new file mode 100644 index 0000000000..bb4f4fc947 Binary files /dev/null and b/macros/latex/contrib/mandi/mandi.pdf differ -- cgit v1.2.3