added tikz examples

tikz/half-space/Makefile

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+SOURCE = half-space
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux
+
+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/half-space/half-space.tex

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+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+\usepackage{tikz}
+\usetikzlibrary{patterns}
+
+\begin{document}
+\begin{preview}
+\begin{tikzpicture}
+    \pgfdeclarepatternformonly{north east lines wide}%
+    {\pgfqpoint{-1pt}{-1pt}}%
+    {\pgfqpoint{10pt}{10pt}}%
+    {\pgfqpoint{9pt}{9pt}}%
+    {
+    \pgfsetlinewidth{0.7pt}
+    \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
+    \pgfpathlineto{\pgfqpoint{9.1pt}{9.1pt}}
+    \pgfusepath{stroke}
+    }
+
+    \pgfdeclarepatternformonly{north west lines wide}
+    {\pgfqpoint{-1pt}{-1pt}}%
+    {\pgfqpoint{7pt}{7pt}}%
+    {\pgfqpoint{6pt}{6pt}}%
+    {
+    \pgfsetlinewidth{0.7pt}
+    \pgfpathmoveto{\pgfqpoint{0pt}{6pt}}
+    \pgfpathlineto{\pgfqpoint{6.1pt}{-0.1pt}}
+    \pgfusepath{stroke}
+    }
+
+    % Draw two intersecting lines
+    \draw[thick, red]   (-1,-1) coordinate (a) -- (2,-1) coordinate (b);
+    \draw[thick, green] ( 1,-1) coordinate (c) -- (1, 2) coordinate (d);
+
+    \fill[pattern=north east lines wide, pattern color=red!50]   (a) -- (b) -- (2,2) -- (-1,2) -- (a);
+    \fill[pattern=north west lines wide, pattern color=green!50] (a) -- (1,-1) -- (1,2) -- (-1,2) -- (a);
+
+    \draw[thick, green] (c) -- (d);
+    \draw[thick, red]   (a) -- (b);
+
+
+    % Draw axes
+    \draw [<->,thick] (0,2.5) node (yaxis) [above] {$x_2$}
+        |- (2.5,0) node (xaxis) [right] {$x_1$};
+    \node[red]   at (1.5,2.8) {$H_2^+(-1)$};
+    \node[green] at (1.5,2.3) {$H_1^-(1)$};
+\end{tikzpicture}
+\end{preview}
+\end{document}

tikz/multidimensional-intervall/Makefile

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+SOURCE = multidimensional-intervall
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux
+
+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/multidimensional-intervall/multidimensional-intervall.tex

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+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+\usepackage{tikz}
+
+\begin{document}
+\begin{preview}
+\begin{tikzpicture}
+    % Draw axes
+    \draw [<->,thick] (0,2.5) node (yaxis) [above] {$x_2$}
+        |- (2.5,0) node (xaxis) [right] {$x_1$};
+
+    % Draw two intersecting lines
+    \draw[thick, dashed] (1,1) coordinate (a) -- (2,1) coordinate (b);
+    \draw[thick, dashed] (a) -- (1,2) coordinate (d);
+    \draw[thick]         (d) -- (2,2) coordinate (c);
+    \draw[thick]         (b) -- (2,2);
+
+    \fill[green!15] (a) -- (b) -- (c) -- (d) -- (a);
+
+    % Draw lines indicating intersection with y and x axis. Here we 
+    % use the perpendicular coordinate system
+    \draw[dotted] (yaxis |- a) node[left] {$a_2$}
+        -| (xaxis -| a) node[below] {$a_1$};
+
+    \draw[dotted] (yaxis |- c) node[left] {$b_2$}
+        -| (xaxis -| c) node[below] {$b_1$};
+\end{tikzpicture}
+\end{preview}
+\end{document}

tikz/riemann-sum/Makefile

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+SOURCE = riemann-sum
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux
+
+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/riemann-sum/riemann-sum.tex

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+% Thanks to http://tex.stackexchange.com/a/30782/5645 for this 
+% example!
+\documentclass{article}
+\usepackage[pdftex,active,tightpage]{preview}
+\setlength\PreviewBorder{2mm}
+\usepackage{pgfplots}
+\pgfplotsset{
+    integral segments/.code={\pgfmathsetmacro\integralsegments{#1}},
+    integral segments=3,
+    integral/.style args={#1:#2}{
+        ybar interval,
+        domain=#1+((#2-#1)/\integralsegments)/2:#2+((#2-#1)/\integralsegments)/2,
+        samples=\integralsegments+1,
+        x filter/.code=\pgfmathparse{\pgfmathresult-((#2-#1)/\integralsegments)/2}
+    }
+}
+
+\begin{document}
+\begin{preview}
+  \begin{tikzpicture}[/pgf/declare function={f=-15*(x-5)+(x-5)^3+50;}]
+    \begin{axis}[
+        domain=0:10,
+        samples=100,
+        axis lines=middle
+    ]
+    \addplot [
+        red,
+        fill=red!50,
+        integral=2:6
+    ] {f};
+    \addplot [thick] {f};
+    \end{axis}
+  \end{tikzpicture}
+\end{preview}
+\end{document}