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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
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% LaTeX4EI Example for Cheat Sheets
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%
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% @encode: UTF-8, tabwidth = 4, newline = LF
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% @author: LaTeX4EI
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
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% ======================================================================
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% Document Settings
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% ======================================================================
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% possible options: color/nocolor, english/german, threecolumn
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% default: color, english
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\documentclass[english]{latex4ei/latex4ei_sheet}
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% set document information
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\title{Example\\ Cheat Sheet}
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\author{LaTeX4EI} % optional, delete if unchanged
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\myemail{info@latex4ei.de} % optional, delete if unchanged
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% DOCUMENT_BEGIN ===============================================================
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\begin{document}
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% SECTION ====================================================================================
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\section{Temporal Tests}
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% ============================================================================================
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Unicode Tests:\\
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⊭⊨∫∬∮∯∝∂∑∑Σ∧∧„“” α $β$ ℝ a
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% SECTION ====================================================================================
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\section{Mathematik}
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% ============================================================================================
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\begin{sectionbox}
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\subsection{Sinus, Cosinus}
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Abstandtest
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\begin{tablebox}{c|c|c|c|c||c|c|c|c}
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$x$ & $0$ & $\pi / 6$ & $\pi / 4$ & $\pi / 3$ & $\frac{1}{2}\pi$ & $\pi$ & $1\frac{1}{2}\pi$ & $2 \pi$ \\
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$\scriptstyle{ \varphi }$ & $\scriptstyle{0^\circ}$ & $\scriptstyle{30^\circ}$ & $\scriptstyle{45^\circ}$ & $\scriptstyle{60^\circ}$ & $\scriptstyle{90^\circ}$ & $\scriptstyle{180^\circ}$ & $\scriptstyle{270^\circ}$ & $\scriptstyle{360^\circ}$ \\ \cmrule
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$\sin$ & $0$ & $\frac{1}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{\sqrt 3}{2}$ & $1$ & $0$ & $-1$ & $0$ \\
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$\cos$ & $1$ & $\frac{\sqrt 3}{2}$ & $\frac{1}{\sqrt 2}$ & $\frac{1}{2}$ & $0$ & $-1$ & $0$ & $1$ \\
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$\tan$ & $0$ & $\frac{\sqrt{3}}{3}$ & $1$ & $\sqrt{3}$ & $\pm \infty$ & $0$ & $\mp \infty$ & $0$\\
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\end{tablebox}
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\subsection{$2 \times 2$ Matrix}
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$\ma A = \mat{a & b\\ c & d}$ \quad\ $\ma A^{-1} = \frac{1}{\det \ma A} \mat{d & -b\\ -c& a}$ \quad\ \parbox{1.9cm}{ $\det(\ma A) = ad-bc$ \\[0.5em] $\Sp(\ma A) = a+d$ } \\
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\\
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\\
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Eigenwerte $\displaystyle \lambda_{1/2} = \frac{\Sp \ma A}{2} \pm \sqrt{ \left( \frac{\Sp \ma A}{2} \right)^2 - \det \ma A }$
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\begin{cookbox}{Eigenwertzerlegung}
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\item Schritt 1
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\item Schritt 2
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\end{cookbox}
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\end{sectionbox}
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\begin{sectionbox}
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\subsection{Fouriertransformation}
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\begin{emphbox}
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$\displaystyle \underset{\text{Zeitbereich}}{\large f(t)} \FT \underset{\text{Frequenzspektrum}}{\large F(\omega)} := \int\limits_{-\infty}^\infty f(t) \exp(-\i \omega t) \diff t$
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\end{emphbox}
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Anmerkung: Es gibt unterschiedliche Normungen ($1, \frac{1}{\sqrt{2\pi}}$)\\
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\end{sectionbox}
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% SECTION ====================================================================================
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\section{Physik}
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% ============================================================================================
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\begin{symbolbox}
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\renewcommand{\arraystretch}{1.5}
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\begin{tabular}{rl}
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\textbf{Naturkonstanten} & \\ \mrule
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Lichtgeschwindigkeit & $\mathrm{c}_0 \equiv \frac{1}{\sqrt{\varepsilon_0 \mu_0}} := \SI{299 792 458}{\meter\per\second}$\\
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Elementarladung & $\mathrm{e} \approx \SI{1.602 177e-19}{\coulomb}$\\
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\textsc{Planck}-Konst. & $h \approx \SI{6,626 069 57e-34}{\joule\second}$\\
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& $\hbar \equiv \frac{h}{2 \pi} \approx \SI{1.05457e-34}{\joule\second}$ \\
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Elektr. Feldkonst. & $\varepsilon_0 = \SI{8.854 188e-12}{\farad\per\meter}$\\ % \equiv \frac{1}{\mu_0 c_0^2}
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Magn. Feldkonst. & $\mu_0 := 4\pi \times \SI{e-7}{\henry\per\meter}$\\
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\textsc{Avogadro}-Konst. & $\NA \approx \SI{6.022 141e23}{\per\mole}$\\
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Atomare Masse & $\mathrm{u} \approx \SI{1.660 539e-27}{\kilogram}$\\
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Elektronenmasse & $m_{\ir e} \approx \SI{9,109 383e-31}{\kilogram}$\\
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Protonenmasse & $m_{\ir p} \approx \SI{1,674 927e-27}{\kilogram}$\\
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Neutronenmasse & $m_{\ir n} \approx \SI{1,672 622e-27}{\kilogram}$\\
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Gravitationskonst. & $\mathrm{G} \approx \SI{6,673 84e-11}{\kilogram\per\second\squared}$\\
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\textsc{Boltzmann}-Konst. & $\kB \approx \SI{1.380 655e-23}{\joule\per\kelvin}$\\
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\end{tabular}
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\end{symbolbox}
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\begin{sectionbox}
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\subsection{Einheitpräfixe}
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\begin{tablebox}{l | ccccccccc}
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$10^\pm$ & $21$ & $18$ & $15$ & $12$ & $9$ & $6$ & $3$ & $2$ & $1$ \\ \cmrule
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$+$ & $\underset{\ir zetta}{\si{\zetta}}$ & $\underset{\ir exa}{\si{\exa}}$ & $\underset{\ir peta}{\si{\peta}}$ & $\underset{\ir tera}{\si{\tera}}$ & $\underset{\ir giga}{\si{\giga}}$ & $\underset{\ir mega}{\si{\mega}}$ & $\underset{\ir kilo}{\si{\kilo}}$ & $\underset{\ir hecto}{\si{\hecto}}$ & $\underset{\ir deca}{\si{\deca}}$ \\
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$-$ & $\underset{\ir zepto}{\si{\zepto}}$ & $\underset{\ir atto}{\si{\atto}}$ & $\underset{\ir femto}{\si{\femto}}$ & $\underset{\ir pico}{\si{\pico}}$ & $\underset{\ir nano}{\si{\nano}}$ & $\underset{\ir micro}{\si{\micro}}$ & $\underset{\ir milli}{\si{\milli}}$ & $\underset{\ir centi}{\si{\centi}}$& $\underset{\ir deci}{\si{\deci}}$
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\end{tablebox}
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\end{sectionbox}
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\begin{sectionbox}
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\subsection{Maxwellsche Gleichungen (Naturgesetze)}
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\begin{emphbox}
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\begin{tabular}{ll}
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Gaußsches Gesetz: & Faradaysches ind. Gesetz\\
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\large $\div \vec D = \varrho $ & \large $\rot \vec E + \frac{\partial \vec B}{\partial t} = 0$ \\[1em]
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Quellfreiheit des magn. Feldes & Ampèrsches Gesetz\\
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\large $\div \vec B = 0$ & \large $\rot \vec H = \vec j + \frac{\partial \vec D}{\partial t}$\\[0.3em]
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\end{tabular}
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\end{emphbox}
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\end{sectionbox}
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% SECTION ====================================================================================
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\section{Informatik}
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% ============================================================================================
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\begin{sectionbox}
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\subsection{c Programming Language}
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% gobble indicates leading spaces. 1 tab = 4 spaces
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\begin{lstlisting}[language=C, gobble=4]
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#include <stdio.h>
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int main(int argc, char *argv[]){
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// global variables
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float percent = 0.0f;
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}
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// custom functions
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int readIntFromFile(path){
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FILE *fp;
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int i;
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fp=fopen(path,"rb");
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fscanf(fp, "%d\n", &i);
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return i
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}
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\end{lstlisting}
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\end{sectionbox}
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% SECTION ====================================================================================
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\section{Chemie}
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% ============================================================================================
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% latex4ei uses the "mhchem" package version 3. Use the \ce{...} command to typeset chemical equations
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\begin{sectionbox}
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\subsection{Bleibatterie}
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\subsubsection{Reaktion an der positiven Elektrode}
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\begin{center}
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\boxed{$\ce{PbO2 + 3H+ +HSO4- +2e- <=>[\text{disch.}][\text{charge}] PbSO4 + 2H2O}$}
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\end{center}
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$\ce{O2}$ Entwicklung (Selbstentladung): $\ce{H2O -> 1/2O2 + 2H+ +2e-}$\\
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Korrosion $\ce{Pb}$ (Alterung): $\ce{Pb + 2H2O -> PbO2 + 4H+ +4e-}$
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\end{sectionbox}
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% DOCUMENT_END =================================================================
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\end{document}
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