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Diffstat (limited to 'info/examples/Math/03-06-4.ltx')
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diff --git a/info/examples/Math/03-06-4.ltx b/info/examples/Math/03-06-4.ltx new file mode 100644 index 0000000000..b13e5094f7 --- /dev/null +++ b/info/examples/Math/03-06-4.ltx @@ -0,0 +1,68 @@ +%% +%% Ein Beispiel der DANTE-Edition +%% Mathematiksatz mit LaTeX +%% 2. Auflage +%% +%% Beispiel 03-06-4 auf Seite 32. +%% +%% Copyright (C) 2012 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{352.81416pt} +\usepackage[utf8]{inputenc} +\usepackage[ngerman]{babel} +\setcounter{equation}{32} +\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} +%Die Erhaltungssätze für Masse, Drehmoment und Energie können jeweils in differentieller Form +%oder Integralform geschreiben werden: +\setlength\jot{15pt} + +\begin{description} +\item[Differentielle Form] +\begin{align} +\begin{aligned} + \Q{\varrho}{t}+\mathrm{div}(\varrho\vv{v}) &= 0 \\ + \varrho\Q{\vv{v}}{t}+(\varrho\vv{v}\cdot\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[Integralform] +\begin{align} + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vv{v}\cdot\vv{v}ec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\vv{v}\diff^3V+\oiint\varrho\vv{v}(\vv{v}\cdot\vv{n}\,)\diff^2A &= + \iiint\<f_0\diff^3V+\oiint\vv{n}\cdot 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}\cdot\vv{n}\,\right)\diff^2A & =\\ + \multispan2{\hfill${\displaystyle-\oiint\left(\vv{q}\cdot\vv{v}ec{n}\right)\diff^2A+ + \iiint\<\left(\vv{v}\cdot\vv{f}_0\right)\diff^3V+\oiint\left(\vv{v} + \cdot\vv{n}~\TT\right)\diff^2A}$}.\nonumber +\end{align} +\end{description} +\end{document} |