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added 5 LaTeX examples

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86
cheat-sheets/analysis/Analysis_Wichtige_Formeln.tex Normal file
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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}

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cheat-sheets/analysis/Makefile Normal file
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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

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documents/semesterplan/Makefile Normal file
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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

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documents/semesterplan/semesterplan.tex Normal file
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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}

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source-code/AbstractClass.java Normal file
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public class AbstractClass {
int templateMethod() {
return simpleOperation1() * simpleOperation2();
}
int simpleOperation1() {
return 2;
}
int simpleOperation2() {
return 3;
}
}

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source-code/ConcreteClass.java Normal file
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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);
}
}

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source-code/Documentation.tex Normal file
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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}

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source-code/Makefile Normal file
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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

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tikz/countable-sets/Makefile Normal file
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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

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tikz/countable-sets/countable-sets.tex Normal file
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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}

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tikz/pairing-function/Makefile Normal file
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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

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tikz/pairing-function/pairing-function.tex Normal file
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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}