added 5 LaTeX examples

cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+%layout
+\usepackage[margin=2.5cm]{geometry}
+\usepackage{parskip}
+
+\pdfinfo{
+   /Author (Peter Merkert, Martin Thoma)
+   /Title  (Wichtige Formeln der Analysis I)
+   /CreationDate (D:20120221095400)
+   /Subject (Analysis I)
+   /Keywords (Analysis I; Formeln)
+}
+
+\everymath={\displaystyle}
+
+\begin{document}
+
+\title{Analysis Formelsammlung}
+\author{Peter Merkert, Martin Thoma}
+\date{21. Februar 2012}
+
+\section{Grenzwerte}
+\begin{table}[ht]
+\begin{minipage}[b]{0.5\linewidth}\centering
+
+\begin{align*}
+\lim_{x \to 0} \frac {\sin x}{x}  &= 1 \\
+\lim_{x \to 0} \frac {e^x - 1}{x} &= 1 \\
+\lim_{h \to 0} \frac {e^{{x_0} + h} - e^{x_0}}{h} &= e^{x_0} \\
+\sum_{n = 0}^{\infty} (-1)^n \frac {(-1)^{n + 1}}{n} &= \log 2 \\
+\cos x    &= \sum_{n = 0}^{\infty} (-1)^n \frac {x^{2n}}{(2n)!}  \\
+\sin x    &= \sum_{n = 0}^{\infty} (-1)^n \frac {x^{2n + 1}}{(2n + 1)!}
+\end{align*}
+
+\end{minipage}
+\hspace{0.5cm}
+\begin{minipage}[b]{0.5\linewidth}
+\centering
+
+\begin{align*}
+\cosh x = \frac {1}{2} (e^x + e^{-x}) &= \scriptstyle \sum_{n = 0}^{\infty} \frac {x^{2n}}{(2n)!} \\
+\sinh x = \frac {1}{2} (e^x - e^{-x}) &= \sum_{n = 0}^{\infty} \frac {x^{2n + 1}}{(2n + 1)!} \\
+e^x &= \sum_{n = 0}^{\infty} \frac {x^n}{n!} \\
+\sum_{n = 0}^{\infty} (-1)^n \frac {x^{n + 1}}{n + 1} &= \log (1+x)   (x \in (-1,1)) \\
+\sum_{n = 0}^{\infty} x^n &= \frac {1}{1 - x}    (x \in (-1,1)) \\
+0,\bar{3} &= \sum_{n = 1}^{\infty} \frac {3}{(10)^n}
+\end{align*}
+
+\end{minipage}
+\end{table}
+
+
+
+
+
+
+\section{Zusammenhänge}
+\begin{align*}
+	(\cos x)^2 + (\sin x)^2 &= 1 \\
+	(\cosh x)^2 - (\sinh x)^2 &= 1 \\
+	\tan x  &= \frac {\sin x}{\cos x} \\
+	\tanh x &= \frac {\sinh x}{\cosh x} \\
+  (x + y)^n &= \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k
+\end{align*}
+
+\section{Ableitungen}
+\begin{align*}
+	(\arctan x)' &= \frac {1}{1 + x^2} \\
+	(\sin x)'    &= \cos x \\
+	(\cos x)'    &= -\sin x \\
+	(\text{arctanh} x)' &= \frac {1}{\sqrt {1 + x^2}}
+\end{align*}
+
+
+\section{Potenzreihen}
+Zuerst den Potenzradius r berechnen:
+\(
+	r = \frac {1}{\lim \text{sup} \sqrt[n]{|a_n|}}
+\)
+
+\end{document}

cheat-sheets/analysis/Makefile

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+# CHANGELOG
+# Version 1.0: Erstellung des Makefile
+
+# Version des Makefile
+fileinfo	:= LaTeX Makefile
+author		:= Martin Thoma
+version		:= 1.0
+
+DATE=$(shell date +%Y-%m-%d)
+
+make:
+	pdflatex Analysis_Wichtige_Formeln.tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux

documents/semesterplan/Makefile

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+# CHANGELOG
+# Version 1.0: Erstellung des Makefile
+
+# Version des Makefile
+fileinfo	:= LaTeX Makefile
+author		:= Martin Thoma
+version		:= 1.0
+
+DATE=$(shell date +%Y-%m-%d)
+
+make:
+	pdflatex semesterplan.tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux

documents/semesterplan/semesterplan.tex

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+\documentclass[a4paper,10pt]{article}
+\usepackage{amssymb}        % needed for math
+\usepackage{amsmath}        % needed for math
+\usepackage{amsthm}         % needed for proof environment
+\usepackage[utf8]{inputenc} % this is needed for umlauts
+\usepackage[ngerman]{babel} % this is needed for umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage{wasysym}  % checkbox
+\usepackage{array}    % row height
+\usepackage[landscape]{geometry}
+\geometry{top=1.5cm,left=1cm,right=1cm,bottom=2cm}
+ 
+\pdfinfo{
+   /Author (Martin Thoma)
+   /Title  (Semesterplan)
+   /Subject (Semesterplan)
+   /Keywords (Semesterplan)
+}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Variables                                        %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newcommand{\semester}{Wintersemester}
+\newcommand{\jahr}{2012}
+\newcommand{\student}{Martin Thoma}
+ 
+\begin{document}
+\section*{Semesterplan für das \semester~\jahr~von~\student} 
+
+\begin{table}[h]
+	\setlength{\extrarowheight}{4.5pt}
+    \begin{tabular}{ |l|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|p {1.9 cm}|}
+        \hline
+        ~           & \textbf{Ü1} & \textbf{Ü2} & \textbf{Ü3} & \textbf{Ü4} & \textbf{Ü5} & \textbf{Ü6} & \textbf{Ü7} & \textbf{Ü8} & \textbf{Ü9} & \textbf{Ü10} & $\sum$ \\
+        \hline
+        \hline
+        LA II       & 144 & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ \\
+        \hline
+        Analysis II & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ \\
+        \hline
+        Algo        & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ \\
+        \hline
+        SWT         & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ \\
+        \hline
+        Rechner     & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ & ~ \\
+        \hline
+    \end{tabular}
+\end{table}
+
+\end{document}

source-code/AbstractClass.java

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+public class AbstractClass {
+    int templateMethod() {
+        return simpleOperation1() * simpleOperation2();
+    }
+
+    int simpleOperation1() {
+        return 2;
+    }
+
+    int simpleOperation2() {
+        return 3;
+    }
+}

source-code/ConcreteClass.java

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+import java.util.LinkedList;
+
+public class ConcreteClass extends AbstractClass {
+    @Override
+    int simpleOperation1() {
+        return 5;
+    }
+
+    @Override
+    int simpleOperation2() {
+        return 7;
+    }
+
+    public void testMe(int aVariable, double bT, LinkedList<Integer> c) {
+        System.out.println("Test!" + aVariable + bT + c);
+    }
+}

source-code/Documentation.tex

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+\documentclass[a4paper,12pt]{article}
+\usepackage{amssymb} % needed for math
+\usepackage{amsmath} % needed for math
+\usepackage[utf8]{inputenc} % this is needed for german umlauts
+\usepackage[ngerman]{babel} % this is needed for german umlauts
+\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
+\usepackage[margin=2cm]{geometry} %layout
+\usepackage{minted} % needed for the inclusion of source code
+
+\begin{document}
+\renewcommand{\theFancyVerbLine}{
+  \sffamily\textcolor[rgb]{0.5,0.5,0.5}{\scriptsize\arabic{FancyVerbLine}}}
+\inputminted[linenos,
+               numbersep=7pt,
+               gobble=0,
+               frame=lines,
+               framesep=2mm,
+				label=AbstractClass.java,
+				fontsize=\footnotesize, tabsize=4]{java}{AbstractClass.java}
+\clearpage
+\inputminted[linenos,
+               numbersep=7pt,
+               gobble=0,
+               frame=lines,
+               framesep=2mm,
+				label=ConcreteClass.java,
+				fontsize=\footnotesize, tabsize=4]{java}{ConcreteClass.java}
+
+\end{document}

source-code/Makefile

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+make:
+	pdflatex -shell-escape Documentation.tex -output-format=pdf 
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.out *.glo *.glg *.gls *.ist *.xdy *.1 *.pyg

tikz/countable-sets/Makefile

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+SOURCE = countable-sets
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/countable-sets/countable-sets.tex

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+\documentclass{standalone}
+\usepackage{pgfplots}
+\usepackage{sansmath} % for sans serif math
+
+%%%<
+% The data files, written on the first run.
+\begin{filecontents}{function.data}
+# n     m
+1 1
+1 2
+2 1
+1 3
+2 2
+3 1
+1 4
+2 3
+3 2
+4 1
+1 5
+2 4
+3 3
+4 2
+5 1
+\end{filecontents}
+
+\begin{document}
+
+\begin{tikzpicture}
+\begin{axis}[
+    compat=newest, % for better label placement
+    font=\sansmath\sffamily, % math and normal text in sans serif
+    xlabel=n, ylabel=m, % the label texts
+    xmin=0, ymin=0, % axis origin
+    enlarge y limits=false, % don't enlarge the y axis beyond the data range
+    enlarge x limits={upper,abs=0.02}, % enlarge x axis slightly to make sure the last tick mark is drawn completely
+    axis lines*=left, % only draw the left axis lines, not a box
+    unit vector ratio*={1 1 1}, % equal axis scaling. "*" to make sure the axes can only be reduced in size, not enlarged
+    width=6cm, % set the overall width of the plot
+    try min ticks=5, % adjusts how many ticks are printed
+    tick align=center, % tick marks centered on the axes
+    legend style={
+        draw=none, % no frame around axes
+        at={(1,1)}, % place at upper right of plot
+        anchor=north % use upper middle edge of legend for alignment
+    },
+]
+\addplot [
+    mark=square*, mark size=0.5em, % square, filled ("*"), radius of 0.5em
+    nodes near coords={
+        \pgfmathparse{int(\coordindex+1)}
+        \pgfmathresult
+    }, % print labels on each data point, using `\coordindex` (the data point counter) increased by 1
+    every node near coord/.style={
+        font=\scriptsize\sffamily\bfseries, % smaller text size, bold for the data point labels
+        text=white,
+        anchor=center % center the labels on the plot marks
+    }
+    ] table {function.data};
+\addlegendentry{f(m,n)}
+\end{axis}
+\end{tikzpicture}
+\end{document}

tikz/pairing-function/Makefile

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+SOURCE = pairing-function
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/pairing-function/pairing-function.tex

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+\documentclass{standalone}
+\usepackage{pgfplots}
+\usepackage{sansmath} % for sans serif math
+
+%%%<
+% The data files, written on the first run.
+\begin{filecontents}{function.data}
+# x     y
+0 0
+0 1
+1 0
+0 2
+1 1
+2 0
+0 3
+1 2
+2 1
+3 0
+0 4
+1 3
+2 2
+3 1
+4 0
+\end{filecontents}
+
+\begin{document}
+
+\begin{tikzpicture}
+\begin{axis}[
+    compat=newest, % for better label placement
+    font=\sansmath\sffamily, % math and normal text in sans serif
+    xlabel=$y$, ylabel=$x$, % the label texts
+    xmin=0, ymin=0, % axis origin
+    enlarge y limits=false, % don't enlarge the y axis beyond the data range
+    enlarge x limits={upper,abs=0.02}, % enlarge x axis slightly to make sure the last tick mark is drawn completely
+    axis lines*=left, % only draw the left axis lines, not a box
+    unit vector ratio*={1 1 1}, % equal axis scaling. "*" to make sure the axes can only be reduced in size, not enlarged
+    width=6cm, % set the overall width of the plot
+    try min ticks=5, % adjusts how many ticks are printed
+    tick align=center, % tick marks centered on the axes
+    legend style={
+        draw=none, % no frame around axes
+        at={(1,1)}, % place at upper right of plot
+        anchor=north, % use upper middle edge of legend for alignment
+        fill=none
+    },
+]
+\addplot [
+    mark=square*, mark size=0.5em, % square, filled ("*"), radius of 0.5em
+    nodes near coords={
+        \pgfmathparse{int(\coordindex)}
+        \pgfmathresult
+    }, % print labels on each data point, using `\coordindex` (the data point counter) increased by 1
+    every node near coord/.style={
+        font=\scriptsize\sffamily\bfseries, % smaller text size, bold for the data point labels
+        text=white,
+        anchor=center % center the labels on the plot marks
+    }
+    ] table {function.data};
+\addlegendentry{$\displaystyle\pi(x, y) = y + \sum_{i=0}^{x+y} i$}
+\end{axis}
+\end{tikzpicture}
+\end{document}