%% %% 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}