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author | Karl Berry <karl@freefriends.org> | 2020-06-06 21:22:16 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2020-06-06 21:22:16 +0000 |
commit | 776d1f6812d6d62ea7bb8860b199b9f99dd5e170 (patch) | |
tree | f1a6c0558caa25137dc2cec1fd7a849ca1a49dc9 /Master/texmf-dist/doc/latex/math-e/03-07-1.ltx | |
parent | 32844d45f401c937044cdf7b9f1f6bf234db007a (diff) |
rm math-e, author request
git-svn-id: svn://tug.org/texlive/trunk@55450 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/math-e/03-07-1.ltx')
-rw-r--r-- | Master/texmf-dist/doc/latex/math-e/03-07-1.ltx | 84 |
1 files changed, 0 insertions, 84 deletions
diff --git a/Master/texmf-dist/doc/latex/math-e/03-07-1.ltx b/Master/texmf-dist/doc/latex/math-e/03-07-1.ltx deleted file mode 100644 index 4e8ae16558e..00000000000 --- a/Master/texmf-dist/doc/latex/math-e/03-07-1.ltx +++ /dev/null @@ -1,84 +0,0 @@ -%% -%% An UIT Edition example -%% -%% Example 03-07-1 on page 30. -%% -%% Copyright (C) 2010 Herbert Voss -%% -%% It may be distributed and/or modified under the conditions -%% of the LaTeX Project Public License, either version 1.3 -%% of this license or (at your option) any later version. -%% -%% See http://www.latex-project.org/lppl.txt for details. -%% -%% -%% ==== -% Show page(s) 1 -%% -\documentclass[]{exaarticle} -\pagestyle{empty} -\setlength\textwidth{375.57637pt} -\usepackage[utf8]{inputenc} -\usepackage[english]{babel} -\setcounter{equation}{35} -\renewcommand\theequation{3.\arabic{equation}} -\usepackage{amsmath,esint,array,esvect} -\setlength\parindent{0pt} -\StartShownPreambleCommands -\def\Q#1#2{\frac{\partial #1}{\partial #2}} -\def\half{\frac{1}{2}} -\def\vvec#1{\vv{#1}} -\newcommand*\diff{\mathop{}\!\mathrm{d}} -\newcommand*\<{\negthickspace} -\newcommand*\TT{\boldsymbol{\mathsf{T}}} -\def\DD{\boldsymbol{\mathsf{D}}} -\StopShownPreambleCommands -\begin{document} -The conservation principles for mass, torque, and energy can be given in -differential or integral form: -\setlength\jot{15pt} - -\begin{description} -\item[Differential form] -\begin{align} -\begin{aligned} - \Q{\varrho}{t}+\mathrm{div}(\varrho\vv{v}) &= 0 \\ - \varrho\Q{\vv{v}}{t}+(\varrho\vv{v}\times\nabla)\vv{v} &= \vv{f}_0+\mathrm{div}\TT=\vv{f}_0 - -\mathrm{grad}p+\mathrm{div}\TT' \\ - \varrho T\frac{\diff s}{\diff t} &= \varrho\frac{\diff e}{\diff t} - -\frac{p}{\varrho}\frac{\diff\varrho}{\diff t}=-\mathrm{div}\vv{q}+\TT':\DD -\end{aligned} -\end{align} - -\item[Integral form] -\begin{align} - \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vv{v}\times\vv{v}ec{n})\diff^2A &= 0\\ - \Q{}{t}\iiint\<\varrho\vv{v}\diff^3V+\oiint\varrho\vv{v}(\vv{v}\times\vv{n}\,)\diff^2A &= - \iiint\<f_0\diff^3V+\oiint\vv{n}\times T\diff^2A \\ - \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) - \varrho\left(\vv{v}\times\vv{n}\,\right)\diff^2A & =\\ - \multispan2{\hfill${\displaystyle-\oiint\left(\vv{q}\times\vv{v}ec{n}\right)\diff^2A+ - \iiint\<\left(\vv{v}\times\vv{f}_0\right)\diff^3V+\oiint\left(\vv{v} - \times\vv{n}~\TT\right)\diff^2A}$}.\nonumber -\end{align} -\end{description} - -\def\QQ#1#2{\frac{\partial^2 #1}{\partial #2^2}} -\def\ee#1{\vv{e}_{#1}} -The $\nabla$ operator in Cartesian coordinates: -% -\[ - \vv{\nabla}=\Q{}{x}\ee{x}+\Q{}{y}\ee{y}+\Q{}{z}\ee{z}~~,~~ - \mathrm{grad}f=\vv{\nabla}f=\Q{f}{x}\ee{x}+\Q{f}{y}\ee{y}+\Q{f}{z}\ee{z} -\] -% -\[ - \mathrm{div}~\vv{a}=\vv{\nabla}\times\vv{a}=\Q{a_x}{x}+\Q{a_y}{y}+\Q{a_z}{z}~~,~~\nabla^2 f=\QQ{f}{x}+\QQ{f}{y}+\QQ{f}{z} -\] -% -\[ -\mathrm{rot}~\vv{a}=\vv{\nabla}\times\vv{a}= - \left(\Q{a_z}{y}-\Q{a_y}{z}\right)\ee{x}+\left(\Q{a_x}{z}-\Q{a_z}{x}\right)\ee{y}+ - \left(\Q{a_y}{x}-\Q{a_x}{y}\right)\ee{z} -\] -\end{document} |