%%
%% Ein Beispiel der DANTE-Edition
%% Mathematiksatz mit LaTeX
%% 3. Auflage
%% Beispiel 03-06-2 auf Seite 31.
%% Copyright (C) 2018 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
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\documentclass[10pt]{screxa}
\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}
\usepackage{libertinust1math}
\setlength\parindent{0pt}
%StartShownPreambleCommands
\def\Q#1#2{\frac{\uppartial #1}{\uppartial #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}
