From 290049375b418246b47914c316746543a0a7e11f Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Tue, 30 Dec 2014 22:59:31 +0000 Subject: mandi (30dec14) git-svn-id: svn://tug.org/texlive/trunk@35931 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/tex/latex/mandi/mandi.sty | 2220 ++++++++++++++------------- 1 file changed, 1149 insertions(+), 1071 deletions(-) (limited to 'Master/texmf-dist/tex/latex/mandi') diff --git a/Master/texmf-dist/tex/latex/mandi/mandi.sty b/Master/texmf-dist/tex/latex/mandi/mandi.sty index 46db7c1f230..700d2db36c8 100644 --- a/Master/texmf-dist/tex/latex/mandi/mandi.sty +++ b/Master/texmf-dist/tex/latex/mandi/mandi.sty @@ -6,7 +6,7 @@ %% %% mandi.dtx (with options: `package') %% -%% Copyright (C) 2011, 2012, 2013 by Paul J. Heafner +%% Copyright (C) 2014 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 @@ -28,15 +28,17 @@ %% mandi.pdf. %% --------------------------------------------------------------------------- %% -\ProvidesPackage{mandi}[2013/06/14 2.2.0 Macros for physics and astronomy] +\ProvidesPackage{mandi}[2014/12/29 2.4.0 Macros for physics and astronomy] \NeedsTeXFormat{LaTeX2e}[1999/12/01] + \RequirePackage{amsmath} \RequirePackage{amssymb} \RequirePackage{array} -\RequirePackage{bigints} \RequirePackage{cancel} \RequirePackage[dvipsnames]{xcolor} \RequirePackage{environ} +\RequirePackage{esint} +\RequirePackage[g]{esvect} \RequirePackage{etoolbox} \RequirePackage{filehook} \RequirePackage{extarrows} @@ -53,151 +55,182 @@ \RequirePackage{xspace} \RequirePackage{ifthen} \RequirePackage{calligra} +\RequirePackage{hyperref} \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{vpythoncolor}{rgb}{0.95,0.95,0.95} -\newcommand{\lstvpython}{\lstset{language=Python,numbers=left,numberstyle=\tiny, - backgroundcolor=\color{vpythoncolor},upquote=true,breaklines}} +\definecolor{vbgcolor}{rgb}{1,1,1} +\definecolor{vshadowcolor}{rgb}{0.5,0.5,0.5} +\lstdefinestyle{vpython}{% % style for VPython code + language=Python,% % select language + morekeywords={visual,arrow,box,cone,% % VPython specific keywords + convex,curve,cylinder,ellipsoid,extrusion,faces,helix,label,points,pyramid,ring,% + sphere,text,frame,graphs,vector,pos,axis,radius,color,opacity,material,up,% + make_trail,trail_type,trail_object,scene,mag,mag2,norm,dot,cross,proj,comp,% + diff_angle,rotate,astuple,radians,shaftwidth,headwidth,headlength,height,width,% + size,degrees,interval,retain,__future__,division,print_function,rate},% + 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 + 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 \newcolumntype{C}[1]{>{\centering}m{#1}} -\newboolean{@optitalicvectors} -\newboolean{@optdoubleabsbars} +\newboolean{@optromanvectors} +\newboolean{@optboldvectors} +\newboolean{@optsingleabsbars} \newboolean{@optbaseunits} \newboolean{@optdrvdunits} -\setboolean{@optitalicvectors}{false} -\setboolean{@optdoubleabsbars}{false} -\setboolean{@optbaseunits}{false} -\setboolean{@optdrvdunits}{false} -\DeclareOption{italicvectors}{\setboolean{@optitalicvectors}{true}} -\DeclareOption{doubleabsbars}{\setboolean{@optdoubleabsbars}{true}} +\newboolean{@optapproxconsts} +\setboolean{@optromanvectors}{false} % this is where you set the default option +\setboolean{@optboldvectors}{false} % this is where you set the default option +\setboolean{@optsingleabsbars}{false} % this is where you set the default option +\setboolean{@optbaseunits}{false} % this is where you set the default option +\setboolean{@optdrvdunits}{false} % this is where you set the default option +\setboolean{@optapproxconsts}{false} % this is where you set the default option +\DeclareOption{romanvectors}{\setboolean{@optromanvectors}{true}} +\DeclareOption{boldvectors}{\setboolean{@optboldvectors}{true}} +\DeclareOption{singleabsbars}{\setboolean{@optsingleabsbars}{true}} \DeclareOption{baseunits}{\setboolean{@optbaseunits}{true}} \DeclareOption{drvdunits}{\setboolean{@optdrvdunits}{true}} +\DeclareOption{approxconsts}{\setboolean{@optapproxconsts}{true}} \ProcessOptions\relax \@ifpackageloaded{amssymb}{% \csundef{square} - \typeout{mandi: Package amssymb detected. Its \protect\square\space has been redefined.} + \typeout{mandi: Package amssymb detected. Its \protect\square\space has been + redefined.} }{% \typeout{mandi: Package amssymb not detected.} }% -\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} -\newcommand{\J}{\joule} -\newcommand{\N}{\newton} -\newcommand{\Pa}{\pascal} -\newcommand{\rad}{\radian} -\newcommand{\sr}{\steradian} -\newcommand{\T}{\tesla} -\newcommand{\V}{\volt} -\newcommand{\W}{\watt} -\newcommand{\Wb}{\weber} -\newcommand{\square}[1]{\ensuremath{\mathrm{#1}^{2}}} % prefix 2 -\newcommand*{\cubic}[1]{\ensuremath{\mathrm{#1}^{3}}} % prefix 3 -\newcommand*{\quartic}[1]{\ensuremath{\mathrm{#1}^{4}}} % prefix 4 -\newcommand*{\reciprocal}[1]{\ensuremath{\mathrm{#1}^{-1}}} % prefix -1 -\newcommand*{\reciprocalsquare}[1]{\ensuremath{\mathrm{#1}^{-2}}} % prefix -2 -\newcommand*{\reciprocalcubic}[1]{\ensuremath{\mathrm{#1}^{-3}}} % prefix -3 -\newcommand*{\reciprocalquartic}[1]{\ensuremath{\mathrm{#1}^{-4}}} % prefix -4 -\newcommand*{\squared}{\ensuremath{^{\mathrm{2}}}} % postfix 2 -\newcommand*{\cubed}{\ensuremath{^{\mathrm{3}}}} % postfix 3 -\newcommand*{\quarted}{\ensuremath{^{\mathrm{4}}}} % postfix 4 -\newcommand*{\reciprocaled}{\ensuremath{^{\mathrm{-1}}}} % postfix -1 -\newcommand*{\reciprocalsquared}{\ensuremath{^{\mathrm{-2}}}} % postfix -2 -\newcommand*{\reciprocalcubed}{\ensuremath{^{\mathrm{-3}}}} % postfix -3 -\newcommand*{\reciprocalquarted}{\ensuremath{^{\mathrm{-4}}}} % postfix -4 -\newcommand\mi@exchangeargs[2]{#2#1}% -\newcommand\mi@name{}% +\newcommand*{\mandiversion}{2.4.0} +\typeout{mandi: You're using mandi version \mandiversion.} +\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} +\newcommand*{\J}{\joule} +\newcommand*{\N}{\newton} +\newcommand*{\Pa}{\pascal} +\newcommand*{\rad}{\radian} +\newcommand*{\sr}{\steradian} +\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*\mi@exchangeargs[2]{#2#1}% +\newcommand*\mi@name{}% \long\def\mi@name#1#{\romannumeral0\mi@innername{#1}}% -\newcommand\mi@innername[2]{% +\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 + \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\selecttradunit[3]{#3} -\newcommand\selectunit{} -\newcommand\perpusebaseunit{\let\selectunit=\selectbaseunit} -\newcommand\perpusedrvdunit{\let\selectunit=\selectdrvdunit} -\newcommand\perpusetradunit{\let\selectunit=\selecttradunit} -\newcommand\hereusebaseunit[1]{% +\newcommand*\selectbaseunit[3]{#1} +\newcommand*\selectdrvdunit[3]{#2} +\newcommand*\selecttradunit[3]{#3} +\newcommand*\selectunit{} +\newcommand*\perpusebaseunit{\let\selectunit=\selectbaseunit} +\newcommand*\perpusedrvdunit{\let\selectunit=\selectdrvdunit} +\newcommand*\perpusetradunit{\let\selectunit=\selecttradunit} +\newcommand*\hereusebaseunit[1]{% \begingroup\perpusebaseunit#1\endgroup}% -\newcommand\hereusedrvdunit[1]{% +\newcommand*\hereusedrvdunit[1]{% \begingroup\perpusedrvdunit#1\endgroup}% -\newcommand\hereusetradunit[1]{% +\newcommand*\hereusetradunit[1]{% \begingroup\perpusetradunit#1\endgroup}% \newenvironment{usebaseunit}{\perpusebaseunit}{}% \newenvironment{usedrvdunit}{\perpusedrvdunit}{}% \newenvironment{usetradunit}{\perpusetradunit}{}% \newcommand*\newphysicsquantity{\definephysicsquantity{\newcommand}} \newcommand*\redefinephysicsquantity{\definephysicsquantity{\renewcommand}} -\newcommandx\definephysicsquantity[5][4=,5=]{% +\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=]{% +\newcommandx*\definephysicsconstant[7][6=,7=]{% \innerdefinewhatsoeverquantityfork{#5}{#6}{#7}{#1}{#2}{#3}{}{#4}}% -\newcommand\innerdefinewhatsoeverquantityfork[3]{% +\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{\ensuremath{\unit{#8}{\selectunit{#3}{#1}{#2}}}}% - \mi@name#4{#5baseunit}#7{\ensuremath{\unit{#8}{#3}}}% - \mi@name#4{#5drvdunit}#7{\ensuremath{\unit{#8}{#1}}}% - \mi@name#4{#5tradunit}#7{\ensuremath{\unit{#8}{#2}}}% - \mi@name#4{#5onlyunit}{\ensuremath{\selectunit{#3}{#1}{#2}}}% +\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{#5tradunit}#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{#5onlytradunit}{\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}}}{}}% -\ifthenelse{\boolean{@optitalicvectors}} - {\typeout{mandi: You'll get italic vector kernels.}} - {\typeout{mandi: You'll get Roman vector kernels.}} -\ifthenelse{\boolean{@optdoubleabsbars}} - {\typeout{mandi: You'll get double absolute value bars.}} + \mi@name\newcommand*{#5mathsymbol}{\ensuremath{#6}}}{}}% +\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{@optsingleabsbars}} {\typeout{mandi: You'll get single absolute value bars.}} + {\typeout{mandi: You'll get double absolute value bars.}} \ifthenelse{\boolean{@optbaseunits}} {\perpusebaseunit % \typeout{mandi: You'll get base units.}} @@ -206,6 +239,12 @@ \typeout{mandi: You'll get derived units.}} {\perpusetradunit % \typeout{mandi: You'll get traditional units.}}} +\ifthenelse{\boolean{@optapproxconsts}} + {\typeout{mandi: You'll get approximate constants.}} + {\typeout{mandi: You'll get precise constants.}} +\ifthenelse{\boolean{@optapproxconsts}} + {\newcommand*{\mi@p}[2]{#1}} % approximate value + {\newcommand*{\mi@p}[2]{#2}} % precise value \def\resetMathstrut@{% \setbox\z@\hbox{% \mathchardef\@tempa\mathcode`\[\relax @@ -217,23 +256,21 @@ \catcode`)\active \xdef){\right\string)} \endgroup \mathcode`(="8000 \mathcode`)="8000 -\typeout{mandi: parentheses made adjustable in math mode.} -\let\oldr@@t\r@@t -\def\r@@t#1#2{% -\setbox0=\hbox{\(\oldr@@t#1{#2\,}\)}\dimen0=\ht0 -\advance\dimen0-0.2\ht0 -\setbox2=\hbox{\vrule height\ht0 depth -\dimen0}% -{\box0\lower0.4pt\box2}} -\LetLtxMacro{\oldsqrt}{\sqrt} -\renewcommand*{\sqrt}[2][\relax]{\oldsqrt[#1]{#2}} -\typeout{mandi: square root symbol fixed.} -\newcommand{\m}{\metre} -\newcommand{\kg}{\kilogram} -\newcommand{\s}{\second} -\newcommand{\A}{\ampere} -\newcommand{\K}{\kelvin} -\newcommand{\mol}{\mole} -\newcommand{\cd}{\candela} +\typeout{mandi: Parentheses have been made adjustable in math mode.} +\newcommand*{\m}{\metre} +\newcommand*{\kg}{\kilogram} +\newcommand*{\s}{\second} +\newcommand*{\A}{\ampere} +\newcommand*{\K}{\kelvin} +\newcommand*{\mol}{\mole} +\newcommand*{\cd}{\candela} +\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}}} \newphysicsquantity{displacement}{\m}[\m][\m] \newphysicsquantity{mass}{\kg}[\kg][\kg] \newphysicsquantity{duration}{\s}[\s][\s] @@ -241,131 +278,156 @@ \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] -\newcommand{\indegrees}[1]{\ensuremath{\unit{#1}{\degree}}} -\newcommand{\inFarenheit}[1]{\ensuremath{\unit{#1}{\degree\mathrm{F}}}} -\newcommand{\inCelsius}[1]{\ensuremath{\unit{#1}{\degree\mathrm{C}}}} -\newcommand{\inarcminutes}[1]{\ensuremath{\unit{#1}{\arcminute}}} -\newcommand{\inarcseconds}[1]{\ensuremath{\unit{#1}{\arcsecond}}} -\newcommand{\ineV}[1]{\ensuremath{\unit{#1}{\electronvolt}}} -\newcommand{\inMeVocs}[1]{\ensuremath{\unit{#1}{\mathrm{MeV}\per\msup{c}{2}}}} -\newcommand{\inMeVoc}[1]{\ensuremath{\unit{#1}{\mathrm{MeV}\per c}}} -\newcommand{\inAU}[1]{\ensuremath{\unit{#1}{\mathrm{AU}}}} -\newcommand{\inly}[1]{\ensuremath{\unit{#1}{\mathrm{ly}}}} -\newcommand{\incyr}[1]{\ensuremath{\unit{#1}{c\usk\mathrm{year}}}} -\newcommand{\inpc}[1]{\ensuremath{\unit{#1}{\mathrm{pc}}}} -\newcommand{\insolarL}[1]{\ensuremath{\unit{#1}{\Lsolar}}} -\newcommand{\insolarT}[1]{\ensuremath{\unit{#1}{\Tsolar}}} -\newcommand{\insolarR}[1]{\ensuremath{\unit{#1}{\Rsolar}}} -\newcommand{\insolarM}[1]{\ensuremath{\unit{#1}{\Msolar}}} -\newcommand{\insolarF}[1]{\ensuremath{\unit{#1}{\Fsolar}}} -\newcommand{\insolarf}[1]{\ensuremath{\unit{#1}{\fsolar}}} -\newcommand{\insolarMag}[1]{\ensuremath{\unit{#1}{\Magsolar}}} -\newcommand{\insolarmag}[1]{\ensuremath{\unit{#1}{\magsolar}}} -\newcommand{\insolarD}[1]{\ensuremath{\unit{#1}{\Dsolar}}} -\newcommand{\insolard}[1]{\ensuremath{\unit{#1}{\dsolar}}} -\newcommand{\velocityc}[1]{\ensuremath{#1c}} +\newphysicsquantity{planeangle}{\m\usk\reciprocal\m}[\rad][\relax] +\newphysicsquantity{solidangle}{\m\squared\usk\reciprocalsquare\m}[\sr][\relax] +\newcommand*{\indegrees}[1]{\unit{#1}{\degree}} +\newcommand*{\inFarenheit}[1]{\unit{#1}{\degree\mathrm{F}}} +\newcommand*{\inCelsius}[1]{\unit{#1}{\degree\mathrm{C}}} +\newcommand*{\inarcminutes}[1]{\unit{#1}{\arcminute}} +\newcommand*{\inarcseconds}[1]{\unit{#1}{\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}} \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] -\newcommand{\lorentz}[1]{\ensuremath{#1}} +\newcommand*{\speed}{\velocity} +\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] +\newcommand*{\lorentz}[1]{\ensuremath{#1}} \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][\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{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}{\relax}[\relax][\relax] \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{energy}{\m\squared\usk\kg\usk\s\reciprocalsquared}[\N\usk\m][\J] +\newphysicsquantity{power}{\m\squared\usk\kg\usk\s\reciprocalcubed}[\J\per\s][\W] +\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{angularmomentum}{\m\squared\usk\kg\usk\reciprocal\s}[\J\usk\s] -[\kg\usk\m\squared\per\s] -\newphysicsquantity{momentofinertia}{\m\squared\usk\kg}[\J\usk\s\squared][\kg\usk\m\squared] -\newphysicsquantity{torque}{\m\squared\usk\kg\usk\s\reciprocalsquared}[\J\per\rad][\N\usk\m] +\newphysicsquantity{angularacceleration}{\rad\usk\s\reciprocalsquared}% + [\rad\per\s\squared][\rad\per\s\squared] +\newphysicsquantity{angularmomentum}{\m\squared\usk\kg\usk\reciprocal\s}[\J\usk\s]% + [\kg\usk\m\squared\per\s] +\newphysicsquantity{momentofinertia}{\m\squared\usk\kg}[\J\usk\s\squared]% + [\kg\usk\m\squared] +\newphysicsquantity{torque}{\m\squared\usk\kg\usk\s\reciprocalsquared}[\J\per\rad]% + [\N\usk\m] \newphysicsquantity{entropy}{\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\K} -[\J\per\K][\J\per\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} -[\F\per\m][\C\squared\per\N\usk\m\squared] -\newphysicsquantity{permeability} -{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}[\henry\per\m][\T\usk\m\per\A] -\newphysicsquantity{electricfield}{\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A} -[\V\per\m][\N\per\C] +{\m\reciprocalcubed\usk\reciprocal\kg\usk\s\reciprocalquarted\usk\A\squared}% + [\F\per\m][\C\squared\per\N\usk\m\squared] +\newphysicsquantity{permeability}% + {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}[\henry\per\m]% + [\T\usk\m\per\A] +\newphysicsquantity{electricfield}{\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\V\per\m][\N\per\C] \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} -[\V\usk\m][\N\usk\m\squared\per\C] -\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}[\volt\usk\s] -[\T\usk\m\squared] % also \Wb and \J\per\A -\newphysicsquantity{cmagneticfield}{\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A} -[\V\per\m][\N\per\C] +\newphysicsquantity{electricflux}% + {\m\cubed\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\V\usk\m][\N\usk\m\squared\per\C] +\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}[\volt\usk\s]% + [\T\usk\m\squared] % also \Wb and \J\per\A +\newphysicsquantity{cmagneticfield}{\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% + [\V\per\m][\N\per\C] \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{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}[\J\per\C][\V] -\newphysicsquantity{emf}{\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A} -[\J\per\C][\V] +\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}[\J\per\C][\V] +\newphysicsquantity{emf}{\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A}% + [\J\per\C][\V] \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{electroncurrent}{\reciprocal\s} -[\ensuremath{\mathrm{e}}\per\s][\ensuremath{\mathrm{e}}\per\s] +\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{electroncurrent}{\reciprocal\s}% + [\ensuremath{\mathrm{e}}\per\s][\ensuremath{\mathrm{e}}\per\s] \newphysicsquantity{conventionalcurrent}{\A}[\C\per\s][\A] \newphysicsquantity{magneticdipolemoment}{\square\m\usk\A}[\J\per\T][\A\usk\square\m] -\newphysicsquantity{currentdensity}{\reciprocalsquare\m\usk\A}[\C\usk\s\per\square\m] -[\A\per\square\m] -\newphysicsquantity{capacitance} -{\reciprocalsquare\m\usk\reciprocal\kg\usk\quartic\s\usk\square\A}[\F][\C\per\V] -\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}[\siemens\per\m] -[(\A\per\square\m)\per(\V\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}[\V\per\A][\ohm] -\newphysicsquantity{conductance} -{\reciprocalsquare\m\usk\reciprocal\kg\usk\cubic\s\usk\square\A}[\A\per\V][\siemens] +\newphysicsquantity{currentdensity}{\reciprocalsquare\m\usk\A}[\C\usk\s\per\square\m]% + [\A\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}[\siemens\per\m]% + [(\A\per\square\m)\per(\V\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}[\V\per\A][\ohm] +\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{\lv}{\ensuremath{\left\langle}} 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\compvectsub{#1}{#2}{x},% + \compvectsub{#1}{#2}{y},% + \compvectsub{#1}{#2}{z}\rv}} +\ifthenelse{\boolean{@optsingleabsbars}} + {\newcommand*{\magvectsub}[2]{\ensuremath{\abs{\vectsub{#1}{#2}}}}} + {\newcommand*{\magvectsub}[2]{\ensuremath{\magof{\vectsub{#1}{#2}}}}} +\newcommand*{\magsquaredvectsub}[2]{\ensuremath{\magvectsub{#1}{#2}\squared}} +\newcommand*{\magnvectsub}[3]{\ensuremath{\magvectsub{#1}{#2}^{#3}}} +\newcommand*{\magvectsubscomps}[2]{\ensuremath{\sqrt{% + \compvectsub{#1}{#2}{x}\squared +% + \compvectsub{#1}{#2}{y}\squared +% + \compvectsub{#1}{#2}{z}\squared}}} +\ifthenelse{\boolean{@optromanvectors}} + {\newcommand*{\dirvectsub}[2]{\ensuremath{\ssub{\widehat{\mathrm{#1}}}{#2}}}} + {\newcommand*{\dirvectsub}[2]{\ensuremath{\ssub{\widehat{#1}}{#2}}}} +\newcommand*{\directionsub}{\dirvectsub} +\newcommand*{\dvectsub}[2]{\ensuremath{\mathrm{d}\vectsub{#1}{#2}}} +\newcommand*{\Dvectsub}[2]{\ensuremath{\Delta\vectsub{#1}{#2}}} +\newcommand*{\compdvectsub}[3]{\ensuremath{\mathrm{d}\compvectsub{#1}{#2}{#3}}} +\newcommand*{\compDvectsub}[3]{\ensuremath{\Delta\compvectsub{#1}{#2}{#3}}} +\newcommand*{\scompsdvectsub}[2]{\ensuremath{\lv% + \compdvectsub{#1}{#2}{x},% + \compdvectsub{#1}{#2}{y},% + \compdvectsub{#1}{#2}{z}\rv}} +\newcommand*{\scompsDvectsub}[2]{\ensuremath{\lv% + \compDvectsub{#1}{#2}{x},% + \compDvectsub{#1}{#2}{y},% + \compDvectsub{#1}{#2}{z}\rv}} +\newcommand*{\dermagvectsub}[3]{\ensuremath{\dbyd{\magvectsub{#1}{#2}}{#3}}} +\newcommand*{\Dermagvectsub}[3]{\ensuremath{\DbyD{\magvectsub{#1}{#2}}{#3}}} +\newcommand*{\dervectsub}[3]{\ensuremath{\dbyd{\vectsub{#1}{#2}}{#3}}} +\newcommand*{\Dervectsub}[3]{\ensuremath{\DbyD{\vectsub{#1}{#2}}{#3}}} +\ifthenelse{\boolean{@optsingleabsbars}} + {\newcommand*{\magdervectsub}[3]{\ensuremath{\abs{\dervectsub{#1}{#2}{#3}}}} + \newcommand*{\magDervectsub}[3]{\ensuremath{\abs{\Dervectsub{#1}{#2}{#3}}}}} + {\newcommand*{\magdervectsub}[3]{\ensuremath{\magof{\dervectsub{#1}{#2}{#3}}}} + \newcommand*{\magDervectsub}[3]{\ensuremath{\magof{\Dervectsub{#1}{#2}{#3}}}}} +\newcommand*{\compdervectsub}[4]{\ensuremath{\dbyd{\compvectsub{#1}{#2}{#3}}{#4}}} +\newcommand*{\compDervectsub}[4]{\ensuremath{\DbyD{\compvectsub{#1}{#2}{#3}}{#4}}} +\newcommand*{\scompsdervectsub}[3]{\ensuremath{\lv% + \compdervectsub{#1}{#2}{x}{#3},% + \compdervectsub{#1}{#2}{y}{#3},% + \compdervectsub{#1}{#2}{z}{#3}\rv}} +\newcommand*{\scompsDervectsub}[3]{\ensuremath{\lv% + \compDervectsub{#1}{#2}{x}{#3},% + \compDervectsub{#1}{#2}{y}{#3},% + \compDervectsub{#1}{#2}{z}{#3}\rv}} +\newcommand*{\vectdotvect}[2]{\ensuremath{{#1}\bullet{#2}}} +\newcommand*{\vectdotsvect}[2]{\ensuremath{\scompsvect{#1}\bullet\scompsvect{#2}}} +\newcommand*{\vectdotevect}[2]{\ensuremath{% + \compvect{#1}{x}\compvect{#2}{x}+% + \compvect{#1}{y}\compvect{#2}{y}+% \compvect{#1}{z}\compvect{#2}{z}}} 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\scompsdervect{#1}{#2}\bullet\scompsvect{#3}}} -\newcommand{\Dervectdotsvect}[3]{\ensuremath{ +\newcommand*{\Dervectdotsvect}[3]{\ensuremath{% \scompsDervect{#1}{#2}\bullet\scompsvect{#3}}} -\newcommand{\dervectdotevect}[3]{\ensuremath{ - \compdervect{#1}{x}{#2}\compvect{x}{#3}+ - \compdervect{#1}{y}{#2}\compvect{y}{#3}+ - \compdervect{#1}{z}{#2}\compvect{z}{#3}}} -\newcommand{\Dervectdotevect}[3]{\ensuremath{ - \compDervect{#1}{x}{#2}\compvect{x}{#3}+ - \compDervect{#1}{y}{#2}\compvect{y}{#3}+ - \compDervect{#1}{z}{#2}\compvect{z}{#3}}} -\newcommand{\vectdotsdervect}[3]{\ensuremath{ +\newcommand*{\dervectdotevect}[3]{\ensuremath{% + \compdervect{#1}{x}{#2}\compvect{#3}{x}+% + \compdervect{#1}{y}{#2}\compvect{#3}{y}+% + \compdervect{#1}{z}{#2}\compvect{#3}{z}}} +\newcommand*{\Dervectdotevect}[3]{\ensuremath{% + \compDervect{#1}{x}{#2}\compvect{#3}{x}+% + \compDervect{#1}{y}{#2}\compvect{#3}{y}+% + \compDervect{#1}{z}{#2}\compvect{#3}{z}}} +\newcommand*{\vectdotsdervect}[3]{\ensuremath{% \scompsvect{#1}\bullet\scompsdervect{#2}{#3}}} -\newcommand{\vectdotsDervect}[3]{\ensuremath{ +\newcommand*{\vectdotsDervect}[3]{\ensuremath{% \scompsvect{#1}\bullet\scompsDervect{#2}{#3}}} -\newcommand{\vectdotedervect}[3]{\ensuremath{ - \compvect{#1}{x}\compdervect{#2}{x}{#3}+ - \compvect{#1}{y}\compdervect{#2}{y}{#3}+ +\newcommand*{\vectdotedervect}[3]{\ensuremath{% + \compvect{#1}{x}\compdervect{#2}{x}{#3}+% + \compvect{#1}{y}\compdervect{#2}{y}{#3}+% \compvect{#1}{z}\compdervect{#2}{z}{#3}}} -\newcommand{\vectdoteDervect}[3]{\ensuremath{ - \compvect{#1}{x}\compDervect{#2}{x}{#3}+ - \compvect{#1}{y}\compDervect{#2}{y}{#3}+ +\newcommand*{\vectdoteDervect}[3]{\ensuremath{% + \compvect{#1}{x}\compDervect{#2}{x}{#3}+% + \compvect{#1}{y}\compDervect{#2}{y}{#3}+% \compvect{#1}{z}\compDervect{#2}{z}{#3}}} -\newcommand{\dervectdotspos}[2]{\ensuremath{ - \scompsdervect{#1}{#2}\bullet\scompspos}} -\newcommand{\Dervectdotspos}[2]{\ensuremath{ - 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-\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{\msup{\mathbf{e}}{0}}} -\newcommand{\euone}{\ensuremath{\msup{\mathbf{e}}{1}}} -\newcommand{\eutwo}{\ensuremath{\msup{\mathbf{e}}{2}}} -\newcommand{\euthree}{\ensuremath{\msup{\mathbf{e}}{3}}} -\newcommand{\eufour}{\ensuremath{\msup{\mathbf{e}}{4}}} -\newcommand{\euk}[1]{\ensuremath{\msup{\mathbf{e}}{#1}}} -\newcommand{\eu}{\euk} -\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{\msub{\mathbf{\gamma}}{0}}} -\newcommand{\gone}{\ensuremath{\msub{\mathbf{\gamma}}{1}}} -\newcommand{\gtwo}{\ensuremath{\msub{\mathbf{\gamma}}{2}}} -\newcommand{\gthree}{\ensuremath{\msub{\mathbf{\gamma}}{3}}} -\newcommand{\gfour}{\ensuremath{\msub{\mathbf{\gamma}}{4}}} -\newcommand{\gk}[1]{\ensuremath{\msub{\mathbf{\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{\msup{\mathbf{\gamma}}{0}}} -\newcommand{\guone}{\ensuremath{\msup{\mathbf{\gamma}}{1}}} -\newcommand{\gutwo}{\ensuremath{\msup{\mathbf{\gamma}}{2}}} -\newcommand{\guthree}{\ensuremath{\msup{\mathbf{\gamma}}{3}}} -\newcommand{\gufour}{\ensuremath{\msup{\mathbf{\gamma}}{4}}} -\newcommand{\guk}[1]{\ensuremath{\msup{\mathbf{\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}} +\newcommand*{\vectcrossvect}[2]{\ensuremath{{#1}\boldsymbol{\times}{#2}}} +\newcommand*{\ltriplecross}[3]{\ensuremath{({#1}\boldsymbol{\times}{#2})% + \boldsymbol{\times}{#3}}} +\newcommand*{\rtriplecross}[3]{\ensuremath{{#1}\boldsymbol{\times}% + ({#2}\boldsymbol{\times}{#3})}} +\newcommand*{\ltriplescalar}[3]{\ensuremath{{#1}\boldsymbol{\times}{#2}\bullet{#3}}} +\newcommand*{\rtriplescalar}[3]{\ensuremath{{#1}\bullet{#2}\boldsymbol{\times}{#3}}} +\newcommand*{\ezero}{\ensuremath{\msub{\boldsymbol{e}}{0}}} +\newcommand*{\eone}{\ensuremath{\msub{\boldsymbol{e}}{1}}} +\newcommand*{\etwo}{\ensuremath{\msub{\boldsymbol{e}}{2}}} +\newcommand*{\ethree}{\ensuremath{\msub{\boldsymbol{e}}{3}}} +\newcommand*{\efour}{\ensuremath{\msub{\boldsymbol{e}}{4}}} +\newcommand*{\ek}[1]{\ensuremath{\msub{\boldsymbol{e}}{#1}}} +\newcommand*{\e}{\ek} +\newcommand*{\uezero}{\ensuremath{\msub{\widehat{\boldsymbol{e}}}{0}}} +\newcommand*{\ueone}{\ensuremath{\msub{\widehat{\boldsymbol{e}}}{1}}} +\newcommand*{\uetwo}{\ensuremath{\msub{\widehat{\boldsymbol{e}}}{2}}} +\newcommand*{\uethree}{\ensuremath{\msub{\widehat{\boldsymbol{e}}}{3}}} +\newcommand*{\uefour}{\ensuremath{\msub{\widehat{\boldsymbol{e}}}{4}}} +\newcommand*{\uek}[1]{\ensuremath{\msub{\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*{\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{\msub{\boldsymbol{\gamma}}{0}}} +\newcommand*{\gone}{\ensuremath{\msub{\boldsymbol{\gamma}}{1}}} +\newcommand*{\gtwo}{\ensuremath{\msub{\boldsymbol{\gamma}}{2}}} +\newcommand*{\gthree}{\ensuremath{\msub{\boldsymbol{\gamma}}{3}}} +\newcommand*{\gfour}{\ensuremath{\msub{\boldsymbol{\gamma}}{4}}} +\newcommand*{\gk}[1]{\ensuremath{\msub{\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 }% {% @@ -859,261 +849,246 @@ \rowvector[,]{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% }% -\newphysicsconstant{oofpez}{\ensuremath{\frac{1}{\phantom{_o}4\pi\ssub{\epsilon}{o}}}} -{\scin[8.9876]{9}}{\m\cubed\usk\kg\usk\reciprocalquartic\s\usk\A\reciprocalsquared} -[\m\per\farad][\newton\usk\m\squared\per\coulomb\squared] -\newcommand{\coulombconstant}{\oofpez} -\newphysicsconstant{oofpezcs}{\ensuremath{\frac{1}{\phantom{_o}4\pi\ssub{\epsilon}{o} -c^2\phantom{_o}}}}{\scin{-7}}{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared} +\newphysicsconstant{oofpez}{\ensuremath{\frac{1} +{\phantom{_o}4\pi\epsilon_0}}}{\mi@p{9}{8.9876}\timestento{9}} +{\m\cubed\usk\kg\usk\reciprocalquartic\s\usk\A\reciprocalsquared}[\m\per\farad] +[\newton\usk\m\squared\per\coulomb\squared] +\newcommand*{\coulombconstant}{\oofpez} +\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} [\T\usk\m\squared][\N\usk\s\squared\per\C\squared] -\newcommand{\altcoulombconstant}{\oofpezcs} -\newphysicsconstant{vacuumpermittivity}{\ensuremath{\ssub{\epsilon}{o}}}{\scin[8.8542]{-12}} +\newcommand*{\altcoulombconstant}{\oofpezcs} +\newphysicsconstant{vacuumpermittivity}{\ensuremath{\epsilon_0}} +{\mi@p{9.0}{8.8542}\timestento{-12}} {\m\reciprocalcubed\usk\reciprocal\kg\usk\s\quarted\usk\A\squared}[\F\per\m] [\C\squared\per\N\usk\m\squared] -\newphysicsconstant{mzofp}{\ensuremath{\frac{\phantom{_oo}\ssub{\mu}{o}\phantom{_o}} -{4\pi}}}{\scin{-7}}{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared} +\newphysicsconstant{mzofp} +{\ensuremath{\frac{\phantom{_oo}\mu_0\phantom{_o}}{4\pi}}} +{\tento{-7}}{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared} [\henry\per\m][\tesla\usk\m\per\A] -\newcommand{\biotsavartconstant}{\mzofp} -\newphysicsconstant{vacuumpermeability}{\ensuremath{\ssub{\mu}{o}}}{\scin[4\pi]{-7}} -{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}[\henry\per\m] -[\T\usk\m\per\A] -\newphysicsconstant{boltzmann}{\ensuremath{\ssub{k}{B}}}{\scin[1.3806]{-23}} +\newcommand*{\biotsavartconstant}{\mzofp} +\newphysicsconstant{vacuumpermeability}{\ensuremath{\mu_0}} +{4\pi\timestento{-7}}{\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared} +[\henry\per\m][\T\usk\m\per\A] +\newphysicsconstant{boltzmann}{\ensuremath{k_B}} +{\mi@p{1.4}{1.3806}\timestento{-23}} {\m\squared\usk\kg\usk\reciprocalsquare\s\usk\reciprocal\K}[\joule\per\K][\J\per\K] -\newcommand{\boltzmannconstant}{\boltzmann} -\newphysicsconstant{boltzmanninev}{\ensuremath{\ssub{k}{B}}}{\scin[8.6173]{-5}} +\newcommand*{\boltzmannconstant}{\boltzmann} +\newphysicsconstant{boltzmannineV}{\ensuremath{k_B}} +{\mi@p{8.6}{8.6173}\timestento{-5}} {\eV\usk\reciprocal\K}[\eV\per\K][\eV\per\K] -\newphysicsconstant{stefanboltzmann}{\ensuremath{\sigma}}{\scin[5.6704]{-8}} +\newphysicsconstant{stefanboltzmann}{\ensuremath{\sigma}} +{\mi@p{5.7}{5.6704}\timestento{-8}} {\kg\usk\s\reciprocalcubed\usk\K\reciprocalquarted}[\W\per\m\squared\usk\K^4] [\W\per\m\squared\usk\K\quarted] -\newcommand{\stefanboltzmannconstant}{\stefanboltzmann} -\newphysicsconstant{planck}{\ensuremath{h}}{\scin[6.6261]{-34}} +\newcommand*{\stefanboltzmannconstant}{\stefanboltzmann} +\newphysicsconstant{planck}{\ensuremath{h}}{\mi@p{6.6}{6.6261}\timestento{-34}} {\m\squared\usk\kg\usk\reciprocal\s}[\J\usk\s][\J\usk\s] -\newcommand{\planckconstant}{\planck} -\newphysicsconstant{planckinev}{\ensuremath{h}}{\scin[4.1357]{-15}} +\newcommand*{\planckconstant}{\planck} +\newphysicsconstant{planckineV}{\ensuremath{h}}{\mi@p{4.1}{4.1357}\timestento{-15}} {\eV\usk\s}[\eV\usk\s][\eV\usk\s] -\newphysicsconstant{planckbar}{\ensuremath{\hbar}}{\scin[1.0546]{-34}} +\newphysicsconstant{planckbar}{\ensuremath{\hslash}}{\mi@p{1.1}{1.0546}\timestento{-34}} {\m\squared\usk\kg\usk\reciprocal\s}[\J\usk\s][\J\usk\s] -\newcommand{\reducedplanckconstant}{\planckbar} -\newphysicsconstant{planckbarinev}{\ensuremath{\hbar}}{\scin[6.5821]{-16}} -{\eV\usk\s}[\eV\usk\s][\eV\usk\s] -\newphysicsconstant{planckc}{\ensuremath{hc}}{\scin[1.9864]{-25}} +\newcommand*{\reducedplanckconstant}{\planckbar} +\newphysicsconstant{planckbarineV}{\ensuremath{\hslash}} +{\mi@p{6.6}{6.5821}\timestento{-16}}{\eV\usk\s}[\eV\usk\s][\eV\usk\s] +\newphysicsconstant{planckc}{\ensuremath{hc}}{\mi@p{2.0}{1.9864}\timestento{-25}} {\m\cubed\usk\kg\usk\reciprocalsquare\s}[\J\usk\m][\J\usk\m] -\newcommand{\planckconstanttimesc}{\planckc} -\newphysicsconstant{planckcinev}{\ensuremath{hc}}{\scin[1.9864]{-25}} -{\eV\usk\ensuremath{\mathrm{n}\m}}[\eV\usk\ensuremath{\mathrm{n}\m}] -[\eV\usk\ensuremath{\mathrm{n}\m}] -\newphysicsconstant{rydberg}{\ensuremath{\msub{R}{\infty}}}{\scin[1.0974]{7}} -{\reciprocal\m}[\reciprocal\m][\reciprocal\m] -\newcommand{\rydbergconstant}{\rydberg} -\newphysicsconstant{bohrradius}{\ensuremath{\msub{a}{0}}}{\scin[5.2918]{-11}}{\m}[\m][\m] -\newphysicsconstant{finestructure}{\ensuremath{\alpha}}{\scin[7.2974]{-3}}{\relax} -\newcommand{\finestructureconstant}{\finestructure} -\newphysicsconstant{avogadro}{\ensuremath{\ssub{N}{A}}}{\scin[6.0221]{23}} -{\reciprocal\mol}[\reciprocal\mol][\reciprocal\mol] -\newcommand{\avogadroconstant}{\avogadro} -\newphysicsconstant{universalgrav}{\ensuremath{G}}{\scin[6.6738]{-11}} +\newcommand*{\planckconstanttimesc}{\planckc} +\newphysicsconstant{planckcineV}{\ensuremath{hc}} +{\mi@p{2.0}{1.9864}\timestento{-25}}{\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}{1.0974}\timestento{7}}{\reciprocal\m}[\reciprocal\m][\reciprocal\m] +\newcommand*{\rydbergconstant}{\rydberg} +\newphysicsconstant{bohrradius}{\ensuremath{a_0}}{\mi@p{5.3}{5.2918}\timestento{-11}} +{\m}[\m][\m] +\newphysicsconstant{finestructure}{\ensuremath{\alpha}} +{\mi@p{\frac{1}{137}}{7.2974\timestento{-3}}}{\relax} +\newcommand*{\finestructureconstant}{\finestructure} +\newphysicsconstant{avogadro}{\ensuremath{N_A}} +{\mi@p{6.0}{6.0221}\timestento{23}}{\reciprocal\mol}[\reciprocal\mol][\reciprocal\mol] +\newcommand*{\avogadroconstant}{\avogadro} +\newphysicsconstant{universalgrav}{\ensuremath{G}}{\mi@p{6.7}{6.6738}\timestento{-11}} {\m\cubed\usk\reciprocal\kg\usk\s\reciprocalsquared}[\J\usk\m\per\kg\squared] [\N\usk\m\squared\per\kg\squared] -\newcommand{\universalgravitationalconstant}{\universalgrav} -\newphysicsconstant{surfacegravfield}{\ensuremath{g}}{9.80}{\m\usk\s\reciprocalsquared} -[\N\per\kg][\m\per\s\squared] -\newcommand{\earthssurfacegravitationalfield}{\surfacegravfield} -\newphysicsconstant{clight}{\ensuremath{c}}{\scin[2.9979]{8}}{\m\usk\reciprocal\s} -[\m\per\s][\m\per\s] -\newcommand{\photonconstant}{\clight} -\newphysicsconstant{clightinfeet}{\ensuremath{c}}{0.9836} -{\ensuremath{\mathrm{ft}\usk\reciprocal\mathrm{n}\s}} -[\ensuremath{\mathrm{ft}\per\mathrm{n}\s}][\ensuremath{\mathrm{ft}\per\mathrm{n}\s}] -\newphysicsconstant{Ratom}{\ensuremath{\ssub{r}{atom}}}{\scin{-10}}{\m}[\m][\m] -\newcommand{\radiusofatom}{\Ratom} -\newphysicsconstant{Mproton}{\ensuremath{\ssub{m}{proton}}}{\scin[1.6726]{-27}} -{\kg}[\kg][\kg] -\newcommand{\massofproton}{\Mproton} -\newphysicsconstant{Mneutron}{\ensuremath{\ssub{m}{neutron}}}{\scin[1.6749]{-27}} -{\kg}[\kg][\kg] -\newcommand{\massofneutron}{\Mneutron} -\newphysicsconstant{Mhydrogen}{\ensuremath{\ssub{m}{hydrogen}}}{\scin[1.6737]{-27}} -{\kg}[\kg][\kg] -\newcommand{\massofhydrogen}{\Mhydrogen} -\newphysicsconstant{Melectron}{\ensuremath{\ssub{m}{electron}}}{\scin[9.1094]{-31}} -{\kg}[\kg][\kg] -\newcommand{\massofelectron}{\Melectron} -\newphysicsconstant{echarge}{\ensuremath{e}}{\scin[1.6022]{-19}}{\A\usk\s}[\C][\C] -\newcommand{\elementarycharge}{\echarge} -\newphysicsconstant{Qelectron}{\ensuremath{\ssub{Q}{electron}}}{-\echargevalue} +\newcommand*{\universalgravitationalconstant}{\universalgrav} +\newphysicsconstant{surfacegravfield}{\ensuremath{g}}{\mi@p{9.8}{9.80}} +{\m\usk\s\reciprocalsquared}[\N\per\kg][\N\per\kg] +\newcommand*{\earthssurfacegravitationalfield}{\surfacegravfield} +\newphysicsconstant{clight}{\ensuremath{c}} +{\mi@p{3}{2.9979}\timestento{8}}{\m\usk\reciprocal\s}[\m\per\s][\m\per\s] +\newcommand*{\photonconstant}{\clight} +\newphysicsconstant{clightinfeet}{\ensuremath{c}}{\mi@p{1}{0.9836}} +{\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}{1.6726}\timestento{-27}}{\kg}[\kg][\kg] +\newphysicsconstant{Mneutron}{\ensuremath{m_n}} +{\mi@p{1.7}{1.6749}\timestento{-27}}{\kg}[\kg][\kg] +\newphysicsconstant{Mhydrogen}{\ensuremath{m_H}} +{\mi@p{1.7}{1.6737}\timestento{-27}}{\kg}[\kg][\kg] +\newphysicsconstant{Melectron}{\ensuremath{m_e}} +{\mi@p{9.1}{9.1094}\timestento{-31}}{\kg}[\kg][\kg] +\newphysicsconstant{echarge}{\ensuremath{e}} +{\mi@p{1.6}{1.6022}\timestento{-19}}{\A\usk\s}[\C][\C] +\newcommand*{\elementarycharge}{\echarge} +\newphysicsconstant{Qelectron}{\ensuremath{Q_e}}{-\echargevalue} {\A\usk\s}[\C][\C] -\newphysicsconstant{qelectron}{\ensuremath{\ssub{q}{electron}}}{-\echargevalue} +\newphysicsconstant{qelectron}{\ensuremath{q_e}}{-\echargevalue} {\A\usk\s}[\C][\C] -\newcommand{\chargeofelectron}{\Qelectron} -\newphysicsconstant{Qproton}{\ensuremath{\ssub{Q}{proton}}}{+\echargevalue} +\newphysicsconstant{Qproton}{\ensuremath{Q_p}}{+\echargevalue} {\A\usk\s}[\C][\C] -\newphysicsconstant{qproton}{\ensuremath{\ssub{q}{proton}}}{+\echargevalue} +\newphysicsconstant{qproton}{\ensuremath{q_p}}{+\echargevalue} {\A\usk\s}[\C][\C] -\newcommand{\chargeofproton}{\Qproton} -\newphysicsconstant{MEarth}{\ensuremath{\ssub{M}{Earth}}}{\scin[5.9736]{24}}{\kg}[\kg][\kg] -\newcommand{\massofEarth}{\MEarth} -\newphysicsconstant{MMoon}{\ensuremath{\ssub{M}{Moon}}}{\scin[7.3459]{22}}{\kg}[\kg][\kg] -\newcommand{\massofMoon}{\MMoon} -\newphysicsconstant{MSun}{\ensuremath{\ssub{M}{Sun}}}{\scin[1.9891]{30}}{\kg}[\kg][\kg] -\newcommand{\massofSun}{\MSun} -\newphysicsconstant{REarth}{\ensuremath{\ssub{R}{Earth}}}{\scin[6.3675]{6}}{\m}[\m][\m] -\newcommand{\radiusofEarth}{\REarth} -\newphysicsconstant{RMoon}{\ensuremath{\ssub{R}{Moon}}}{\scin[1.7375]{6}}{\m}[\m][\m] -\newcommand{\radiusofMoon}{\RMoon} -\newphysicsconstant{RSun}{\ensuremath{\ssub{R}{Sun}}}{\scin[6.9634]{8}}{\m}[\m][\m] -\newcommand{\radiusofSun}{\RSun} -\newphysicsconstant{ESdist}{\magvectsub{r}{ES}}{\scin[1.4960]{11}}{\m}[\m][\m] -\newphysicsconstant{SEdist}{\magvectsub{r}{SE}}{\scin[1.4960]{11}}{\m}[\m][\m] -\newcommand{\EarthSundistance}{\ESdist} -\newcommand{\SunEarthdistance}{\SEdist} -\newphysicsconstant{EMdist}{\magvectsub{r}{EM}}{\scin[3.8440]{8}}{\m}[\m][\m] -\newphysicsconstant{MEdist}{\magvectsub{r}{ME}}{\scin[3.8440]{8}}{\m}[\m][\m] -\newcommand{\EarthMoondistance}{\ESdist} -\newcommand{\MoonEarthdistance}{\SEdist} -\newphysicsconstant{LSun}{\ensuremath{\ssub{L}{Sun}}}{\scin[3.8460]{26}} - {\m\squared\usk\kg\usk\s\reciprocalcubed}[\W][\J\per\s] -\newphysicsconstant{TSun}{\ensuremath{\ssub{T}{Sun}}}{5778}{\K}[\K][\K] -\newphysicsconstant{MagSun}{\ensuremath{\ssub{M}{Sun}}}{+4.83}{}[][] -\newphysicsconstant{magSun}{\ensuremath{\ssub{m}{Sun}}}{-26.74}{}[][] -\newcommand{\Lstar}[1][\(\star\)]{\ensuremath{\ssub{L}{#1}}} -\newcommand{\Lsolar}{\ensuremath{\Lstar[\(\odot\)]}} -\newcommand{\Tstar}[1][\(\star\)]{\ensuremath{\ssub{T}{#1}}} -\newcommand{\Tsolar}{\ensuremath{\Tstar[\(\odot\)]}} -\newcommand{\Rstar}[1][\(\star\)]{\ensuremath{\ssub{R}{#1}}} -\newcommand{\Rsolar}{\ensuremath{\Rstar[\(\odot\)]}} -\newcommand{\Mstar}[1][\(\star\)]{\ensuremath{\ssub{M}{#1}}} -\newcommand{\Msolar}{\ensuremath{\Mstar[\(\odot\)]}} -\newcommand{\Fstar}[1][\(\star\)]{\ensuremath{\ssub{F}{#1}}} -\newcommand{\fstar}[1][\(\star\)]{\ensuremath{\ssub{f}{#1}}} -\newcommand{\Fsolar}{\ensuremath{\Fstar[\(\odot\)]}} -\newcommand{\fsolar}{\ensuremath{\fstar[\(\odot\)]}} -\newcommand{\Magstar}[1][\(\star\)]{\ensuremath{\ssub{M}{#1}}} -\newcommand{\magstar}[1][\(\star\)]{\ensuremath{\ssub{m}{#1}}} -\newcommand{\Magsolar}{\ensuremath{\Magstar[\(\odot\)]}} -\newcommand{\magsolar}{\ensuremath{\magstar[\(\odot\)]}} -\newcommand{\Dstar}[1][\(\star\)]{\ensuremath{\ssub{D}{#1}}} -\newcommand{\dstar}[1][\(\star\)]{\ensuremath{\ssub{d}{#1}}} -\newcommand{\Dsolar}{\ensuremath{\Dstar[\(\odot\)]}} -\newcommand{\dsolar}{\ensuremath{\dstar[\(\odot\)]}} -\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} 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+\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} +\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-(\frac{#1}{c})\squared}}}} +\newcommand*{\frelgamma}[1]{\ensuremath{% + (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} +\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{% +\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{\momentumprinciple}{\ensuremath{ - \vectsub{p}{sys,f}=\vectsub{p}{sys,i}+\Fnetsys\Delta t}} -\newcommand{\LHSmomentumprinciple}{\ensuremath{% - \vectsub{p}{sys,f}}} -\newcommand{\RHSmomentumprinciple}{\ensuremath{% - \vectsub{p}{sys,i}+\Fnetsys\Delta t}} -\newcommand{\energyprinciple}{\ensuremath{\ssub{E}{sys,f}=\ssub{E}{sys,i}+ - \ssub{W}{ext}+Q}} -\newcommand{\LHSenergyprinciple}{\ensuremath{\ssub{E}{sys,f}}} -\newcommand{\RHSenergyprinciple}{\ensuremath{\ssub{E}{sys,i}+\ssub{W}{ext}+Q}} -\newcommand{\angularmomentumprinciple}{\ensuremath{\vectsub{L}{sys,A,f}= - \vectsub{L}{sys,A,i}+\Tnetsys\Delta t}} -\newcommand{\LHSangularmomentumprinciple}{\ensuremath{\vectsub{L}{sys,A,f}}} -\newcommand{\RHSangularmomentumprinciple}{\ensuremath{\vectsub{L}{sys,A,i}+ - \Tnetsys\Delta t}} -\newcommand{\gravitationalinteraction}{\ensuremath{% - \universalgravmathsymbol\frac{\msub{M}{1}\msub{M}{2}}{\msup{\magvectsub{r}{12}}{2}} - \quant{-\dirvectsub{r}{12}}}} -\newcommand{\electricinteraction}{\ensuremath{% - \oofpezmathsymbol\frac{\msub{Q}{1}\msub{Q}{2}}{\msup{\magvectsub{r}{12}}{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{\Bfieldofparticle}{\ensuremath{% - \mzofpmathsymbol\frac{Q\magvect{v}}{\msup{\magvect{r}}{2}}\dirvect{v}\times\dirvect{r}}} -\newcommand{\Efieldofparticle}{\ensuremath{% - \oofpezmathsymbol\frac{Q}{\msup{\magvect{r}}{2}}\dirvect{r}}} -\newcommand{\Esys}{\ssub{E}{sys}} -\newcommandx{\Us}[1][1]{\ssub{\ssub{U}{s}}{#1}} -\newcommandx{\Ug}[1][1]{\ssub{\ssub{U}{g}}{#1}} -\newcommandx{\Ue}[1][1]{\ssub{\ssub{U}{e}}{#1}} -\newcommandx{\Ktrans}[1][1]{\ssub{\ssub{K}{trans}}{#1}} -\newcommandx{\Krot}[1][1]{\ssub{\ssub{K}{rot}}{#1}} -\newcommandx{\Eparticle}[1][1]{\ssub{\ssub{E}{particle}}{#1}} -\newcommandx{\Einternal}[1][1]{\ssub{\ssub{E}{internal}}{#1}} -\newcommandx{\Erest}[1][1]{\ssub{\ssub{E}{rest}}{#1}} -\newcommandx{\Echem}[1][1]{\ssub{\ssub{E}{chem}}{#1}} -\newcommandx{\Etherm}[1][1]{\ssub{\ssub{E}{therm}}{#1}} -\newcommandx{\Evib}[1][1]{\ssub{\ssub{E}{vib}}{#1}} -\newcommandx{\Ephoton}[1][1]{\ssub{\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{\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{\Usfinal}{\ssub{\left(\onehalf\ks \msup{s}{2}\right)}{f}} -\newcommand{\Usinitial}{\ssub{\left(\onehalf\ks \msup{s}{2}\right)}{i}} -\newcommand{\Ugfinal}{\ssub{\left(-G\frac{\msub{M}{1}\msub{M}{2}} - {\magvectsub{r}{12}}\right)}{f}} -\newcommand{\Uginitial}{\ssub{\left(-G\frac{\msub{M}{1}\msub{M}{2}} - {\magvectsub{r}{12}}\right)}{i}} -\newcommand{\Uefinal}{\ssub{\left(\oofpezmathsymbol\frac{\ssub{Q}{1}\ssub{Q}{2}} - {\magvectsub{r}{12}}\right)}{f}} -\newcommand{\Ueinitial}{\ssub{\left(\oofpezmathsymbol\frac{\ssub{Q}{1}\ssub{Q}{2}} - {\magvectsub{r}{12}}\right)}{i}} -\newcommand{\ks}{\ssub{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{\Tnet}{\ensuremath{\vectsub{T}{net}}} -\newcommand{\Tnetext}{\ensuremath{\vectsub{T}{net,ext}}} -\newcommand{\Tnetsys}{\ensuremath{\vectsub{T}{net,sys}}} -\newcommand{\Tsub}[1]{\ensuremath{\vectsub{T}{#1}}} -\newcommand{\vpythonline}{\lstinline[language=Python,numbers=left,numberstyle=\tiny,% - upquote=true,breaklines]} -\lstnewenvironment{vpythonblock}{\lstvpython}{} -\newcommand{\vpythonfile}{\lstinputlisting[language=Python,numbers=left,% - numberstyle=\tiny,upquote=true,breaklines]} +\newcommand*{\springinteraction}{\ensuremath{\ks\magvect{s}(-\dirvect{s})}} +\newcommand*{\Bfieldofparticle}{\ensuremath{% + \mzofpmathsymbol\frac{Q\magvect{v}}{\magvect{r}\squared}\dirvect{v}\times\dirvect{r}}} +\newcommand*{\Efieldofparticle}{\ensuremath{% + \oofpezmathsymbol\frac{Q}{\magvect{r}\squared}\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)}} +\newcommand*{\vpythonline}{\lstinline[style=vpython]} +\lstnewenvironment{vpythonblock}{\lstset{style=vpython}}{} +\newcommand*{\vpythonfile}{\lstinputlisting[style=vpython]} \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=0.90,5=0.10,usedefault]{% @@ -1340,7 +1447,8 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \vspace{\baselineskip}% \end{center}% }% -\newcommandx{\adjemptybox}[7][1=\hfill,2=white,3=black,4=black,5=0.90,6=,7=0.0,usedefault] +\newcommandx{\adjemptybox}[7][1=\hfill,2=white,3=black,4=black,5=0.90,6=, +7=0.0,usedefault] {\begin{center}% \fcolorbox{#3}{#2}{% \begin{minipage}[c]{#5\textwidth}\color{#4}% @@ -1385,65 +1493,50 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% - \emptyanswer[#5][#6]% - }% + \emptyanswer[#5][#6]}% \vspace{\baselineskip}% - \end{center}% - }% - {\emptybox[#1][#2][#3][#4][#5][#6]% - }% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \newcommandx{\largeanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.25,% usedefault]{% \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% - \emptyanswer[#5][#6]% - }% + \emptyanswer[#5][#6]}% \vspace{\baselineskip}% - \end{center}% - }% - {\emptybox[#1][#2][#3][#4][#5][#6]% - }% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \newcommandx{\largeranswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.33,% usedefault]{% \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% - \emptyanswer[#5][#6]% - }% + \emptyanswer[#5][#6]}% \vspace{\baselineskip}% - \end{center}% - }% - {\emptybox[#1][#2][#3][#4][#5][#6]% - }% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \newcommandx{\hugeanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.50,% usedefault]{% \ifthenelse{\equal{#1}{}} {\begin{center}% \fcolorbox{#3}{#2}{% - \emptyanswer[#5][#6]% - }% + \emptyanswer[#5][#6]}% \vspace{\baselineskip}% - \end{center}% - }% - {\emptybox[#1][#2][#3][#4][#5][#6]% - }% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \newcommandx{\hugeranswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.75,% usedefault]{% \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% - \emptyanswer[#5][#6]% - }% + \emptyanswer[#5][#6]}% \vspace{\baselineskip}% - \end{center}% - }% - {\emptybox[#1][#2][#3][#4][#5][#6]% - }% + \end{center}}% + {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \newcommandx{\fullpageanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=1.00,% usedefault]{% @@ -1456,12 +1549,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld {\emptybox[#1][#2][#3][#4][#5][#6]}% }% \mdfdefinestyle{miinstructornotestyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=40pt, rightmargin=40pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, frametitle={INSTRUCTOR NOTE}, - frametitlebackgroundcolor=cyan!60, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=cyan!60,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=cyan!25, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{miinstructornote}{% \begin{mdframed}[style=miinstructornotestyle] \begin{adjactivityanswer}[cyan!25][cyan!25][black] @@ -1470,12 +1563,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \mdfdefinestyle{mistudentnotestyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=40pt, rightmargin=40pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, frametitle={STUDENT NOTE}, - frametitlebackgroundcolor=cyan!60, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=cyan!60,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=cyan!25, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{mistudentnote}{% \begin{mdframed}[style=mistudentnotestyle] \begin{adjactivityanswer}[cyan!25][cyan!25][black] @@ -1484,12 +1577,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \mdfdefinestyle{miderivationstyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=0pt, rightmargin=0pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=0pt,rightmargin=0pt,linewidth=1,roundcorner=10, frametitle={DERIVATION}, - frametitlebackgroundcolor=orange!60, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=orange!60,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=orange!25, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{miderivation}{% \begin{mdframed}[style=miderivationstyle] \setcounter{equation}{0} @@ -1499,12 +1592,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \mdfdefinestyle{bwinstructornotestyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=40pt, rightmargin=40pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, frametitle={INSTRUCTOR NOTE}, - frametitlebackgroundcolor=gray!50, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=gray!20, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{bwinstructornote}{% \begin{mdframed}[style=bwinstructornotestyle] \begin{adjactivityanswer}[gray!20][gray!20][black] @@ -1513,12 +1606,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \mdfdefinestyle{bwstudentnotestyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=40pt, rightmargin=40pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, frametitle={STUDENT NOTE}, - frametitlebackgroundcolor=gray!50, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=gray!20, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{bwstudentnote}{% \begin{mdframed}[style=bwstudentnotestyle] \begin{adjactivityanswer}[gray!20][gray!20][black] @@ -1527,12 +1620,12 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \mdfdefinestyle{bwderivationstyle}{% - hidealllines=false, skipbelow=\baselineskip, skipabove=\baselineskip, - leftmargin=0pt, rightmargin=0pt, linewidth=1, roundcorner=10, + hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, + leftmargin=0pt,rightmargin=0pt,linewidth=1,roundcorner=10, frametitle={DERIVATION}, - frametitlebackgroundcolor=gray!50, frametitlerule=true, frametitlerulewidth=1, + frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=gray!20, - linecolor=black, fontcolor=black, shadow=true} + linecolor=black,fontcolor=black,shadow=true} \NewEnviron{bwderivation}{% \begin{mdframed}[style=bwderivationstyle] \setcounter{equation}{0} @@ -1541,9 +1634,14 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{align*} \end{mdframed} }% -\newcommand{\checkpoint}{% +\NewEnviron{mysolution}{% + \begin{align*} + \BODY + \end{align*} +}% +\newcommand*{\checkpoint}{% \vspace{1cm}\begin{center}|--------- CHECKPOINT ---------|\end{center}}% -\newcommand{\image}[2]{% +\newcommand*{\image}[2]{% \begin{figure}[h!] \begin{center}% \includegraphics[scale=1]{#1}% @@ -1551,19 +1649,19 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \label{#1}% \end{center}% \end{figure}} -\newcommand{\sneakyone}[1]{\ensuremath{\cancelto{1}{\frac{#1}{#1}}}} -\newcommand{\chkquantity}[1]{% +\newcommand*{\sneakyone}[1]{\ensuremath{\cancelto{1}{\frac{#1}{#1}}}} +\newcommand*{\chkquantity}[1]{% \begin{center} - \begin{tabular}{C{3cm} C{3cm} C{3cm} C{3cm}} + \begin{tabular}{C{4.5cm} C{4cm} C{4cm} C{4cm}} name & baseunit & drvdunit & tradunit \tabularnewline \cs{#1} & \csname #1onlybaseunit\endcsname & \csname #1onlydrvdunit\endcsname & \csname #1onlytradunit\endcsname \end{tabular} \end{center} }% -\newcommand{\chkconstant}[1]{% +\newcommand*{\chkconstant}[1]{% \begin{center} - \begin{tabular}{C{3cm} C{1cm} C{2cm} C{3cm} C{3cm} C{3cm}} + \begin{tabular}{C{4cm} C{2cm} C{3cm} C{3cm} C{3cm} C{3cm}} name & symbol & value & baseunit & drvdunit & tradunit \tabularnewline \cs{#1} & \csname #1mathsymbol\endcsname & \csname #1value\endcsname & \csname #1onlybaseunit\endcsname & \csname #1onlydrvdunit\endcsname & @@ -1571,26 +1669,6 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{tabular} \end{center} }% -\newcommandx{\vecto}[2][2,usedefault]{\ensuremath{% - \ifthenelse{\equal{#2}{}}% - {\vec{#1}}% - {\ssub{\vec{#1}}{#2}}}}% -\newcommandx{\compvecto}[3][3,usedefault]{\ensuremath{% - \ifthenelse{\equal{#3}{}}% - {\ssub{#1}{\(#2\)}}% - {\ssub{#1}{\(#2\),#3}}}}% -\newcommandx{\scompsvecto}[2][2,usedefault]{\ensuremath{% - \ifthenelse{\equal{#2}{}}% - {\lv\compvecto{#1}{x},\compvecto{#1}{y},\compvecto{#1}{z}\rv}% - {\lv\compvecto{#1}{x}[#2],\compvecto{#1}{y}[#2],\compvecto{#1}{z}[#2]\rv}}}% -\newcommandx{\compposo}[2][2,usedefault]{\ensuremath{% - \ifthenelse{\equal{#1}{}}% - {#1}% - {\ssub{#1}{#2}}}}% -\newcommandx{\scompsposo}[1][1,usedefault]{\ensuremath{% - \ifthenelse{\equal{#1}{}}% - {\lv\compposo{x},\compposo{y},\compposo{z}\rv}% - {\lv\compposo{x}[#1],\compposo{y}[#1],\compposo{z}[#1]\rv}}}% \endinput %% %% End of file `mandi.sty'. -- cgit v1.2.3