From a9987369125a138a236c5d31affb3ea7535be106 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Wed, 16 Mar 2016 23:24:03 +0000 Subject: mandi (16mar16) git-svn-id: svn://tug.org/texlive/trunk@40050 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/tex/latex/mandi/mandi.sty | 1385 +++++++++++++++++++-------- 1 file changed, 1004 insertions(+), 381 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 700d2db36c8..652a6bdbf6e 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) 2014 by Paul J. Heafner +%% Copyright (C) 2016 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 @@ -21,14 +21,14 @@ %% %% This work consists of the files mandi.dtx %% README +%% mandi.pdf %% %% and includes the derived files mandi.ins -%% mandi.sty -%% vdemo.py and -%% mandi.pdf. +%% mandi.sty and +%% vdemo.py. %% --------------------------------------------------------------------------- %% -\ProvidesPackage{mandi}[2014/12/29 2.4.0 Macros for physics and astronomy] +\ProvidesPackage{mandi}[2016/03/15 2.5.1 Macros for physics and astronomy] \NeedsTeXFormat{LaTeX2e}[1999/12/01] \RequirePackage{amsmath} @@ -48,7 +48,9 @@ \RequirePackage{textcomp} \RequirePackage{letltxmacro} \RequirePackage{listings} +\RequirePackage{mathtools} \RequirePackage[framemethod=TikZ]{mdframed} +\RequirePackage{stackengine} \RequirePackage{suffix} \RequirePackage{xargs} \RequirePackage{xparse} @@ -61,28 +63,37 @@ \DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `basename #1 .tif`.png} \DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} \usetikzlibrary{shadows} -\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 +\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,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} @@ -90,28 +101,31 @@ \newboolean{@optbaseunits} \newboolean{@optdrvdunits} \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{@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 +\setboolean{@optuseradians}{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}} +\DeclareOption{useradians}{\setboolean{@optuseradians}{true}} \ProcessOptions\relax +\newcommand*{\mandiversion}{2.5.0} +\typeout{mandi: You're using mandi version \mandiversion.} \@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*{\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}}} @@ -242,21 +256,12 @@ \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.}} \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 - \def\@tempb##1"##2##3{\the\textfont"##3\char"}% - \expandafter\@tempb\meaning\@tempa \relax}% - \ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@} -\begingroup - \catcode`(\active \xdef({\left\string(} - \catcode`)\active \xdef){\right\string)} -\endgroup -\mathcode`(="8000 \mathcode`)="8000 -\typeout{mandi: Parentheses have been made adjustable in math mode.} \newcommand*{\m}{\metre} \newcommand*{\kg}{\kilogram} \newcommand*{\s}{\second} @@ -271,15 +276,6 @@ \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] -\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][\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}}} @@ -312,120 +308,329 @@ \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] +\newcommand*{\lorentz}[1]{\ensuremath{#1}} \newcommand*{\speed}{\velocity} -\newphysicsquantity{acceleration}{\m\usk\s\reciprocalsquared}[\N\per\kg]% +\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]% + [] +\newphysicsquantity{solidangle}% + {\m\squared\usk\reciprocalsquare\m}% + [\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]% +\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][\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]% +\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]% +\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}[\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]% +\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}% + [\N\usk\m]% + [\J] +\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{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}% - [\F\per\m][\C\squared\per\N\usk\m\squared] +\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\usk\kg\squared]% + [\J\usk\s\squared] +\ifthenelse{\boolean{@optuseradians}} + {% + \newphysicsquantity{angularmomentum}% + {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% + [\N\usk\m\usk\s\per\rad]% + [\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad] + \newphysicsquantity{angularimpulse}% + {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% + [\N\usk\m\usk\s\per\rad]% + [\J\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}% + [\N\usk\m\usk\s]% + [\m\squared\usk\kg\usk\reciprocal\s] + \newphysicsquantity{angularimpulse}% + {\m\squared\usk\kg\usk\reciprocal\s}% + [\N\usk\m\usk\s]% + [\J\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}% + [\F\per\m]% + [\C\squared\per\N\usk\m\squared] \newphysicsquantity{permeability}% - {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}[\henry\per\m]% + {\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{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]% + [\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]% + {\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{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\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{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{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{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]% + {\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{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] - % also \C\squared\per\N\usk\m, \s\per\ohm + {\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]% + {\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]% + {\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]% + {\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] + {\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] + {\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}} \newcommand*{\rv}{\ensuremath{\right\rangle}} \ExplSyntaxOn % Written in LaTeX3 @@ -439,14 +644,15 @@ {% \clist_set:Nn \l_tmpa_clist { #1 } \ensuremath{% - \sqrt{(\clist_use:Nnnn \l_tmpa_clist { )^2+( } { )^2+( } { )^2+( } )^2 } + \sqrt{\left(\clist_use:Nnnn \l_tmpa_clist { \right)^2+\left( } { \right)^2+ + \left( } { \right)^2+\left( } \right)^2 } }% }% {% \clist_set:Nn \l_tmpa_clist { #1 } \ensuremath{% - \sqrt{(\clist_use:Nnnn \l_tmpa_clist {\;{ #2 })^2+(} {\;{ #2 })^2+(} - {\;{ #2 })^2+(} \;{ #2 })^2} + \sqrt{\left(\clist_use:Nnnn \l_tmpa_clist {\;{ #2 }\right)^2+\left(} {\; + { #2 }\right)^2+\left(} {\;{ #2 }\right)^2+\left(} \;{ #2 }\right)^2} }% }% }% @@ -459,7 +665,7 @@ {\newcommand*{\vect}[1]{\ensuremath{\vv{\mathrm{#1}}}}} {\newcommand*{\vect}[1]{\ensuremath{\vv{#1}}}}} \ifthenelse{\boolean{@optsingleabsbars}} - {\newcommand*{\magvect}[1]{\ensuremath{\abs{\vect{#1}}}}} + {\newcommand*{\magvect}[1]{\ensuremath{\absof{\vect{#1}}}}} {\newcommand*{\magvect}[1]{\ensuremath{\magof{\vect{#1}}}}} \newcommand*{\magsquaredvect}[1]{\ensuremath{\magvect{#1}\squared}} \newcommand*{\magnvect}[2]{\ensuremath{\magvect{#1}^{#2}}} @@ -471,6 +677,15 @@ {\newcommand*{\dirvect}[1]{\ensuremath{\widehat{\mathrm{#1}}}}} {\newcommand*{\dirvect}[1]{\ensuremath{\widehat{#1}}}}} \newcommand*{\direction}{\dirvect} +\newcommand*{\componentalong}[2]{\ensuremath{\mathrm{comp}_{#1}{#2}}} +\newcommand*{\expcomponentalong}[2]{\ensuremath{\frac{\vectdotvect{#2}{#1}} +{\magof{#1}}}} +\newcommand*{\ucomponentalong}[2]{\ensuremath{\vectdotvect{#2}{#1}}} +\newcommand*{\projectiononto}[2]{\ensuremath{\mathrm{proj}_{#1}{#2}}} +\newcommand*{\expprojectiononto}[2]{\ensuremath{% + \inparens{\frac{\vectdotvect{#2}{#1}}{\magof{#1}}}\frac{#1}{\magof{#1}}}} +\newcommand*{\uprojectiononto}[2]{\ensuremath{% + \inparens{\vectdotvect{#2}{#1}}#1}} \ifthenelse{\boolean{@optromanvectors}} {\newcommand*{\compvect}[2]{\ensuremath{\ssub{\mathrm{#1}}{\(#2\)}}}} {\newcommand*{\compvect}[2]{\ensuremath{\ssub{#1}{\(#2\)}}}} @@ -478,6 +693,15 @@ \compvect{#1}{x},% \compvect{#1}{y},% \compvect{#1}{z}\rv}} +\newcommand*{\scompsdirvect}[1]{\ensuremath{\lv% + \compvect{\widehat{#1}}{x},% + \compvect{\widehat{#1}}{y},% + \compvect{\widehat{#1}}{z}\rv}} +\ifthenelse{\boolean{@optromanvectors}} + {\newcommand*{\compdirvect}[2]{\ensuremath{% + \ssub{\widehat{\mathrm{#1}}}{\(#2\)}}}} + {\newcommand*{\compdirvect}[2]{\ensuremath{% + \ssub{\widehat{#1}}{\(#2\)}}}} \newcommand*{\magvectscomps}[1]{\ensuremath{\sqrt{% \compvect{#1}{x}\squared +% \compvect{#1}{y}\squared +% @@ -491,8 +715,8 @@ \newcommand*{\Ddirvect}[1]{\ensuremath{\Delta\dirvect{#1}}} \newcommand*{\Ddirection}{\Ddirvect} \ifthenelse{\boolean{@optsingleabsbars}} - {\newcommand*{\magdvect}[1]{\ensuremath{\abs{\dvect{#1}}}} - \newcommand*{\magDvect}[1]{\ensuremath{\abs{\Dvect{#1}}}}} + {\newcommand*{\magdvect}[1]{\ensuremath{\absof{\dvect{#1}}}} + \newcommand*{\magDvect}[1]{\ensuremath{\absof{\Dvect{#1}}}}} {\newcommand*{\magdvect}[1]{\ensuremath{\magof{\dvect{#1}}}} \newcommand*{\magDvect}[1]{\ensuremath{\magof{\Dvect{#1}}}}} \newcommand*{\compdvect}[2]{\ensuremath{\mathrm{d}\compvect{#1}{#2}}} @@ -518,8 +742,8 @@ \compDervect{#1}{y}{#2},% \compDervect{#1}{z}{#2}\rv}} \ifthenelse{\boolean{@optsingleabsbars}} - {\newcommand*{\magdervect}[2]{\ensuremath{\abs{\dervect{#1}{#2}}}} - \newcommand*{\magDervect}[2]{\ensuremath{\abs{\Dervect{#1}{#2}}}}} + {\newcommand*{\magdervect}[2]{\ensuremath{\absof{\dervect{#1}{#2}}}} + \newcommand*{\magDervect}[2]{\ensuremath{\absof{\Dervect{#1}{#2}}}}} {\newcommand*{\magdervect}[2]{\ensuremath{\magof{\dervect{#1}{#2}}}} \newcommand*{\magDervect}[2]{\ensuremath{\magof{\Dervect{#1}{#2}}}}} \newcommand*{\dermagvect}[2]{\ensuremath{\dbyd{\magvect{#1}}{#2}}} @@ -541,7 +765,7 @@ \compvectsub{#1}{#2}{y},% \compvectsub{#1}{#2}{z}\rv}} \ifthenelse{\boolean{@optsingleabsbars}} - {\newcommand*{\magvectsub}[2]{\ensuremath{\abs{\vectsub{#1}{#2}}}}} + {\newcommand*{\magvectsub}[2]{\ensuremath{\absof{\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}}} @@ -570,8 +794,8 @@ \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{\absof{\dervectsub{#1}{#2}{#3}}}} + \newcommand*{\magDervectsub}[3]{\ensuremath{\absof{\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}}} @@ -666,26 +890,29 @@ \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{({#1}\boldsymbol{\times}{#2})% - \boldsymbol{\times}{#3}}} +\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}% - ({#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}}} + \inparens{{#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{\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{\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*{\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}} @@ -715,6 +942,13 @@ \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}} @@ -736,12 +970,12 @@ \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*{\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}} @@ -840,6 +1074,15 @@ \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}{}}% {% @@ -849,131 +1092,314 @@ \rowvector[,]{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% }% -\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] +\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*{\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}{8.9876}\timestento{9}}% + {\m\cubed\usk\kg\usk\reciprocalquartic\s\usk\A\reciprocalsquared}% + [\m\per\farad]% + [\newton\usk\m\squared\per\coulomb\squared] +\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] +\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}\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] +\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] +\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}}% + {\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] +\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] +\newphysicsconstant{planckineV}% + {\ensuremath{h}}% + {\mi@p{4.1}{4.1357}\timestento{-15}}% + {\eV\usk\s}% + [\eV\usk\s]% + [\eV\usk\s] +\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] +\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] +\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] +\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}}}% + {}% + []% + [] +\newphysicsconstant{avogadro}% + {\ensuremath{N_A}}% + {\mi@p{6.0}{6.0221}\timestento{23}}% + {\reciprocal\mol}% + [\reciprocal\mol]% + [\reciprocal\mol] +\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] +\newphysicsconstant{surfacegravfield}% + {\ensuremath{g}}% + {\mi@p{9.8}{9.80}}% + {\m\usk\s\reciprocalsquared}% + [\N\per\kg]% + [\N\per\kg] +\newphysicsconstant{clight}% + {\ensuremath{c}}% + {\mi@p{3}{2.9979}\timestento{8}}% + {\m\usk\reciprocal\s}% + [\m\per\s]% + [\m\per\s] +\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] +\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}{5.9736}\timestento{24}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{MMoon}% + {\ensuremath{M_{\text{Moon}}}}% + {\mi@p{7.3}{7.3459}\timestento{22}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{MSun}% + {\ensuremath{M_{\text{Sun}}}}% + {\mi@p{2.0}{1.9891}\timestento{30}}% + {\kg}% + [\kg]% + [\kg] +\newphysicsconstant{REarth}% + {\ensuremath{R_{\text{Earth}}}}% + {\mi@p{6.4}{6.3675}\timestento{6}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{RMoon}% + {\ensuremath{R_{\text{Moon}}}}% + {\mi@p{1.7}{1.7375}\timestento{6}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{RSun}% + {\ensuremath{R_{\text{Sun}}}}% + {\mi@p{7.0}{6.9634}\timestento{8}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{ESdist}% + {\magvectsub{r}{ES}}% + {\mi@p{1.5}{1.4960}\timestento{11}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{SEdist}% + {\magvectsub{r}{SE}}% + {\mi@p{1.5}{1.4960}\timestento{11}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{EMdist}% + {\magvectsub{r}{EM}}% + {\mi@p{3.8}{3.8440}\timestento{8}}% + {\m}% + [\m]% + [\m] +\newphysicsconstant{MEdist}% + {\magvectsub{r}{ME}}% + {\mi@p{3.8}{3.8440}\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} -\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{\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}\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{\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{k_B}} -{\mi@p{8.6}{8.6173}\timestento{-5}} -{\eV\usk\reciprocal\K}[\eV\per\K][\eV\per\K] -\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}}{\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}}{\mi@p{4.1}{4.1357}\timestento{-15}} -{\eV\usk\s}[\eV\usk\s][\eV\usk\s] -\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{\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}} -{\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}}{\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{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}{5.9736}\timestento{24}}{\kg}[\kg][\kg] -\newphysicsconstant{MMoon}{\ensuremath{M_{\text{Moon}}}} -{\mi@p{7.3}{7.3459}\timestento{22}}{\kg}[\kg][\kg] -\newphysicsconstant{MSun}{\ensuremath{M_{\text{Sun}}}} -{\mi@p{2.0}{1.9891}\timestento{30}} -{\kg}[\kg][\kg] -\newphysicsconstant{REarth}{\ensuremath{R_{\text{Earth}}}} -{\mi@p{6.4}{6.3675}\timestento{6}}{\m}[\m][\m] -\newphysicsconstant{RMoon}{\ensuremath{R_{\text{Moon}}}} -{\mi@p{1.7}{1.7375}\timestento{6}}{\m}[\m][\m] -\newphysicsconstant{RSun}{\ensuremath{R_{\text{Sun}}}}{\mi@p{7.0}{6.9634}\timestento{8}} -{\m}[\m][\m] -\newphysicsconstant{ESdist}{\magvectsub{r}{ES}}{\mi@p{1.5}{1.4960}\timestento{11}}{\m} -[\m][\m] -\newphysicsconstant{SEdist}{\magvectsub{r}{SE}}{\mi@p{1.5}{1.4960}\timestento{11}}{\m} -[\m][\m] \newcommand*{\EarthSundistance}{\ESdist} \newcommand*{\SunEarthdistance}{\SEdist} -\newphysicsconstant{EMdist}{\magvectsub{r}{EM}} -{\mi@p{3.8}{3.8440}\timestento{8}}{\m}[\m][\m] -\newphysicsconstant{MEdist}{\magvectsub{r}{ME}} -{\mi@p{3.8}{3.8440}\timestento{8}}{\m}[\m][\m] \newcommand*{\EarthMoondistance}{\ESdist} \newcommand*{\MoonEarthdistance}{\SEdist} -\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*{\Lstar}[1][\(\star\)]{\ensuremath{L_{\text{#1}}}\xspace} \newcommand*{\Lsolar}{\ensuremath{\Lstar[\(\odot\)]}\xspace} \newcommand*{\Tstar}[1][\(\star\)]{\ensuremath{T_{\text{#1}}}\xspace} @@ -1033,15 +1459,16 @@ \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*{\sumoverall}[1]{\ensuremath{\displaystyle + \sum_{\substack{\text{\tiny{all }}\text{\tiny{{#1}}}}}}} \newcommand*{\dx}[1]{\ensuremath{\,\mathrm{d}{#1}}} -\newcommand*{\evalfromto}[3]{\ensuremath{\Bigg.{#1}\Bigg\rvert_{#2}^{#3}}} +\newcommand*{\evalfromto}[3]{\ensuremath{% + \Bigg.{#1}\Bigg\rvert_{#2}^{#3}}} \newcommand*{\evalat}[2]{\ensuremath{\Bigg.{#1}\Bigg\rvert_{#2}}} \newcommand*{\evaluatedat}[1]{\ensuremath{\Bigg.\Bigg\rvert_{#1}}} \newcommandx{\integral}[4][1,2,usedefault]{\ensuremath{% - \int_{\ifthenelse{\equal{#1}{}}{}{#4=#1}}^{\ifthenelse{\equal{#2}{}}{}{#4=#2}}} - {#3}\dx{#4}} + \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{% @@ -1050,41 +1477,64 @@ \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}}}} +\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}}}} \newcommand*{\seriesfofx}{\ensuremath{% -f(x) \approx f(a) + \frac{f^\prime (a)}{1!}(x-a) + \frac{f^{\prime\prime}(a)}{2!}(x-a)^2 -+ \frac{f^{\prime\prime\prime}(a)}{3!}(x-a)^3 + \ldots}\xspace} + f(x) \approx f(a) + \frac{f^\prime (a)}{1!}(x-a) + \frac{f^{\prime\prime}(a)}{2!} + (x-a)^2 + \frac{f^{\prime\prime\prime}(a)}{3!}(x-a)^3 + \ldots}\xspace} \newcommand*{\seriesexpx}{\ensuremath{% -e^x \approx 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots}\xspace} + e^x \approx 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots}\xspace} \newcommand*{\seriessinx}{\ensuremath{% -\sin x \approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \ldots}\xspace} + \sin x \approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \ldots}\xspace} \newcommand*{\seriescosx}{\ensuremath{% -\cos x \approx 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \ldots}\xspace} + \cos x \approx 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \ldots}\xspace} \newcommand*{\seriestanx}{\ensuremath{% -\tan x \approx x + \frac{x^3}{3} + \frac{2x^5}{15} + \ldots}\xspace} + \tan x \approx x + \frac{x^3}{3} + \frac{2x^5}{15} + \ldots}\xspace} \newcommand*{\seriesatox}{\ensuremath{% -a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ldots} -\xspace} + a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + % + \ldots}\xspace} \newcommand*{\serieslnoneplusx}{\ensuremath{% -\ln(1 \pm x) \approx \pm\; x - \frac{x^2}{2} \pm \frac{x^3}{3} - \frac{x^4}{4} \pm -\ldots}\xspace} + \ln(1 \pm x) \approx \pm\; x - \frac{x^2}{2} \pm \frac{x^3}{3} - % + \frac{x^4}{4} \pm \ldots}\xspace} \newcommand*{\binomialseries}{\ensuremath{% -(1 + x)^n \approx 1 + nx + \frac{n(n-1)}{2!}x^2 + \ldots}\xspace} + (1 + x)^n \approx 1 + nx + \frac{n(n-1)}{2!}x^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)} @@ -1113,18 +1563,18 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld {\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}}} -\@ifpackageloaded{commath}{% - \typeout{mandi: Package commath detected. Its \protect\abs\space command will - be used.} -}{% - \typeout{mandi: Package commath not detected. mandi's \protect\abs\space command - will be used.} - \newcommand*{\abs}[1]{\ensuremath{\left\lvert{#1}\right\rvert}} -}% -\newcommand*{\magof}[1]{\ensuremath{\left\lVert{#1}\right\rVert}} -\newcommand*{\dimsof}[1]{\ensuremath{\left[{#1}\right]}} -\newcommand*{\unitsof}[1]{\ensuremath{\left[{#1}\right]_u}} +\newcommand*{\absof}[1]{\ensuremath{% + \left\lvert{\ifblank{#1}{\:\cdot\:}{#1}}\right\rvert}} +\newcommand*{\inparens}[1]{\ensuremath{% + \left({\ifblank{#1}{\:\cdot\:}{#1}}\right)}} +\newcommand*{\magof}[1]{\ensuremath{% + \left\lVert{\ifblank{#1}{\:\cdot\:}{#1}}\right\rVert}} +\newcommand*{\dimsof}[1]{\ensuremath{% + \left[{\ifblank{#1}{\:\cdot\:}{#1}}\right]}} +\newcommand*{\unitsof}[1]{\ensuremath{% + \left[{\ifblank{#1}{\:\cdot\:}{#1}}\right]_u}} \newcommand*{\changein}[1]{\ensuremath{\delta{#1}}} \newcommand*{\Changein}[1]{\ensuremath{\Delta{#1}}} \newcommandx{\scin}[3][1,3=\!\!,usedefault]{\ensuremath{% @@ -1142,8 +1592,10 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld {\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*{\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}{\degree}} \newcommand*{\latitudeN}[1]{\unit{#1}{\degree\;\mathrm{N}}} @@ -1157,8 +1609,10 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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*{\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} @@ -1179,9 +1633,9 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \newcommand*{\ffourthroot}[1]{\ensuremath{{#1}^\onefourth}} \newcommand*{\ffifthroot}[1]{\ensuremath{{#1}^\onefifth}} \newcommand*{\relgamma}[1]{\ensuremath{% - \frac{1}{\sqrt{1-(\frac{#1}{c})\squared}}}} + \frac{1}{\sqrt{1-\inparens{\frac{#1}{c}}\squared}}}} \newcommand*{\frelgamma}[1]{\ensuremath{% - (1-\frac{{#1}\squared}{c\squared})^{-\onehalf}}} + \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}}}} @@ -1208,60 +1662,76 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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*{\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,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*{\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}= +\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*{\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*{\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})}} + \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}}{\magvect{r}\squared}\dirvect{v}\times\dirvect{r}}} + \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{\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{\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{\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{\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} @@ -1399,19 +1869,25 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \newcommand*{\RHSmaxwellivdif}{\ensuremath{\vacuumpermeabilitymathsymbol% \vacuumpermittivitymathsymbol\pbypt[\vect{E}]+% \vacuumpermeabilitymathsymbol\vectsub{J}{\(e\)}}} -\newcommand*{\RHSmaxwellivdiffree}{\ensuremath{\vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol\pbypt[\vect{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]} -\lstnewenvironment{vpythonblock}{\lstset{style=vpython}}{} -\newcommand*{\vpythonfile}{\lstinputlisting[style=vpython]} +\lstnewenvironment{vpythonblock}[1][]{\lstset{style=vpython,caption={#1}}}{} +\newcommand*{\vpythonfile}[1][]{\newpage\lstinputlisting[style=vpython,caption={#1}]} \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]{% +\newenvironmentx{activityanswer}[5][1=white,2=black,3=black,4=0.90,% + 5=0.10,usedefault]{% \def\skipper{#5}% \def\response@fbox{\fcolorbox{#2}{#1}}% \begin{center}% @@ -1438,7 +1914,8 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \response@fbox{\usebox{\@tempboxa}}% \end{center}% }% -\newcommandx{\emptybox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.10,usedefault] +\newcommandx{\emptybox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=0.10,usedefault]% {\begin{center}% \fcolorbox{#3}{#2}{% \begin{minipage}[c][#6\textheight][c]{#5\textwidth}\color{#4}% @@ -1447,8 +1924,8 @@ 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}% @@ -1459,7 +1936,8 @@ 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{\answerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.1,usedefault] +\newcommandx{\answerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=0.1,usedefault]% {\ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% @@ -1468,8 +1946,8 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{center}}% {\emptybox[#1][#2][#3][#4][#5][#6]}% }% -\newcommandx{\adjanswerbox}[7][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.1,7=0.0,% - usedefault]% +\newcommandx{\adjanswerbox}[7][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=0.1,7=0.0,usedefault]% {\ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% @@ -1478,8 +1956,8 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{center}}% {\adjemptybox[#1][#2][#3][#4][#5][#6][#7]}% }% -\newcommandx{\smallanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.10,% - usedefault]% +\newcommandx{\smallanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=0.10,usedefault]% {\ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% @@ -1488,8 +1966,24 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{center}}% {\emptybox[#1][#2][#3][#4][#5][#6]}% }% -\newcommandx{\mediumanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,6=0.20,% - usedefault]{% +\newcommandx{\smallanswerform}[4][1=q1,2=Response,3=0.10,4=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}% +}% +\newcommandx{\mediumanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=0.20,usedefault]{% \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% @@ -1498,8 +1992,24 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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]{% +\newcommandx{\mediumanswerform}[4][1=q1,2=Response,3=0.20,4=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}% +}% +\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}{% @@ -1508,8 +2018,24 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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]{% +\newcommandx{\largeanswerform}[4][1=q1,2=Response,3=0.25,4=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}% +}% +\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}{% @@ -1518,8 +2044,25 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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,% +\newcommandx{\largeranswerform}[4][1=q1,2=Response,3=0.33,4=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}% +}% +\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}{% @@ -1528,8 +2071,24 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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]{% +\newcommandx{\hugeanswerform}[4][1=q1,2=Response,3=0.50,4=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}% +}% +\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}{% @@ -1538,8 +2097,24 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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]{% +\newcommandx{\hugeranswerform}[4][1=q1,2=Response,3=0.75,4=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}% +}% +\newcommandx{\fullpageanswerbox}[6][1=\hfill,2=white,3=black,4=black,5=0.90,% + 6=1.00,usedefault]{% \ifthenelse{\equal{#1}{}}% {\begin{center}% \fcolorbox{#3}{#2}{% @@ -1548,9 +2123,26 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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, @@ -1565,6 +2157,7 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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, @@ -1579,11 +2172,20 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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*} @@ -1594,6 +2196,7 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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, @@ -1608,6 +2211,7 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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, @@ -1622,11 +2226,20 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \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*} @@ -1635,12 +2248,21 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{mdframed} }% \NewEnviron{mysolution}{% + \setcounter{equation}{0} + \begin{align} + \BODY + \end{align} +}% +\NewEnviron{mysolution*}{% + \setcounter{equation}{0} \begin{align*} \BODY \end{align*} }% \newcommand*{\checkpoint}{% - \vspace{1cm}\begin{center}|--------- CHECKPOINT ---------|\end{center}}% + \vspace{1cm}\begin{center}% + \colorbox{yellow!80}{|--------- CHECKPOINT ---------|}% + \end{center}}% \newcommand*{\image}[2]{% \begin{figure}[h!] \begin{center}% @@ -1649,7 +2271,7 @@ 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*{\sneakyone}[1]{\ensuremath{\cancelto{1}{#1}}} \newcommand*{\chkquantity}[1]{% \begin{center} \begin{tabular}{C{4.5cm} C{4cm} C{4cm} C{4cm}} @@ -1659,6 +2281,7 @@ a^x \approx 1 + x \ln{a} + \frac{(x \ln a)^2}{2!} + \frac{(x \ln a)^3}{3!} + \ld \end{tabular} \end{center} }% +\newcommand*{\qed}{\ensuremath{\text{ Q.E.D.}}} \newcommand*{\chkconstant}[1]{% \begin{center} \begin{tabular}{C{4cm} C{2cm} C{3cm} C{3cm} C{3cm} C{3cm}} -- cgit v1.2.3