%% 
%%  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}
