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Diffstat (limited to 'info/examples/Math/03-06-6.ltx')
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diff --git a/info/examples/Math/03-06-6.ltx b/info/examples/Math/03-06-6.ltx new file mode 100644 index 0000000000..1ca6d3ac27 --- /dev/null +++ b/info/examples/Math/03-06-6.ltx @@ -0,0 +1,58 @@ +%% +%% Ein Beispiel der DANTE-Edition +%% Mathematiksatz mit LaTeX +%% 3. Auflage +%% Beispiel 03-06-6 auf Seite 32. +%% 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 +%% +%% +\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} +\def\QQ#1#2{\frac{\partial^2 #1}{\partial #2^2}} +\def\ee#1{\vv{e}_{#1}} +Der $\nabla$-Operator in kartesischen Koordinaten: +% +\[ + \vv{\nabla}=\Q{}{x}\ee{x}+\Q{}{y}\ee{y}+\Q{}{z}\ee{z}~~,~~ + \mathrm{grad}f=\vv{\nabla}f=\Q{f}{x}\ee{x}+\Q{f}{y}\ee{y}+\Q{f}{z}\ee{z} +\] +% +\[ + \mathrm{div}~\vv{a}=\vv{\nabla}\cdot\vv{a}=\Q{a_x}{x}+\Q{a_y}{y}+\Q{a_z}{z}~~,~~\nabla^2 f=\QQ{f}{x}+\QQ{f}{y}+\QQ{f}{z} +\] +% +\[ +\mathrm{rot}~\vv{a}=\vv{\nabla}\times\vv{a}= + \left(\Q{a_z}{y}-\Q{a_y}{z}\right)\ee{x}+\left(\Q{a_x}{z}-\Q{a_z}{x}\right)\ee{y}+ + \left(\Q{a_y}{x}-\Q{a_x}{y}\right)\ee{z} +\] +\end{document} |