Add function graphs

tikz/exponential-functions/Makefile

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+SOURCE = exponential-functions
+DELAY = 80
+DENSITY = 300
+WIDTH = 1000
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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/exponential-functions/README.md

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+Compiled example
+----------------
+![Example](exponential-functions.png)

tikz/exponential-functions/exponential-functions.tex

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+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\pgfplotsset{compat=1.17}
+\usepackage{tikz}
+\usepackage{nicefrac}
+\pgfplotsset{every axis legend/.append style={
+at={(0,0)},
+anchor=north east}}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=16cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin=-2.1,   % start the diagram at this x-coordinate
+        xmax= 4.1,   % end   the diagram at this x-coordinate
+        ymin= 0,     % start the diagram at this y-coordinate
+        ymax= 17,    % end   the diagram at this y-coordinate
+        xlabel=$x$,
+        ylabel=$y$,
+        ytick={0,2,3,4,8,9,12,16},
+        yticklabels={0,2,3,4,8,9,12,16},
+        legend cell align=left,
+        legend pos=south east,
+        legend style={draw=none},
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+      \addplot[domain=-2:4, red, ultra thick,samples=500] {2^x};
+      \addplot[domain=-2:4, green!50!black, ultra thick,dashed,samples=500] {3^x};
+      \addplot[domain=-2:4, blue, ultra thick,dotted,samples=500] {4^x};
+      \legend{$2^x$,$3^x$,$4^{x}$}
+    \end{axis}
+\end{tikzpicture}
+\end{document}

tikz/inverse-function/Makefile

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+SOURCE = inverse-function
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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 $(SOURCE).svg --export-width=$(WIDTH) --export-plain-svg=$(SOURCE)1.svg
+	rsvg-convert -a -w 720 -f svg $(SOURCE)1.svg -o $(SOURCE).svg
+	rm $(SOURCE)1.svg

tikz/inverse-function/README.md

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+Compiled example
+----------------
+![Example](inverse-function.png)

tikz/inverse-function/inverse-function.tex

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+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{shapes,snakes,shapes.geometric,positioning,decorations.text}
+
+\begin{document}
+\tikzstyle{arrow}=[bend left,->,very thick, line cap=round]
+\begin{tikzpicture}[node distance=2cm]
+    \node[ellipse,draw,minimum width=80pt,minimum height=20pt,fill=gray!5] (a) {1\\2\\3};
+    \node[ellipse,draw,minimum width=80pt,minimum height=20pt,fill=gray!5,below of=a] (u) {a\\b\\c};
+
+    % Arrows
+    \draw[arrow,postaction={decorate,decoration={text along path,raise=0.08cm,text align=center,text={Aktion {$a_k$}}}}] (a.east) to node {} (u.east);
+    \draw[arrow,postaction={decorate,decoration={text along path,raise=0.08cm,text align=center,text={Zustand {$x_k$}}}}] (u.west) to node {} (a.west);
+\end{tikzpicture}
+\end{document}

tikz/logarithmic-functions/Makefile

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+SOURCE = logarithmic-functions
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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/logarithmic-functions/README.md

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+Compiled example
+----------------
+![Example](logarithmic-functions.png)

tikz/logarithmic-functions/logarithmic-functions.tex

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+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+\usepackage{nicefrac}
+\pgfplotsset{every axis legend/.append style={
+at={(0,0)},
+anchor=north east}}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=8cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin= 0,   % start the diagram at this x-coordinate
+        xmax=10,   % end   the diagram at this x-coordinate
+        ymin=-5,   % start the diagram at this y-coordinate
+        ymax= 5,   % end   the diagram at this y-coordinate
+        xlabel=$x$,
+        ylabel=$y$,
+        legend cell align=left,
+        legend pos=south east,
+        legend style={draw=none},
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+      \addplot[domain=0:10, red, ultra thick,samples=500] {log2(x)};
+      \addplot[domain=0:10, green!50!black,dashed,ultra thick,samples=500] {log2(0.5*x)};
+      \addplot[domain=0:10, blue,dotted, ultra thick,samples=500] {log10(x)};
+      \legend{$\log_2(x)$,$\log_2(\nicefrac{x}{2})$,$\log_{10}(x)$}
+    \end{axis}
+\end{tikzpicture}
+\end{document}

tikz/logistic-functions/Makefile

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+SOURCE = logistic-functions
+DELAY = 80
+DENSITY = 300
+WIDTH = 1000
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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/logistic-functions/README.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](logistic-functions.png)

tikz/logistic-functions/logistic-functions.tex

@@ -0,0 +1,37 @@
+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+\usepackage{nicefrac}
+\pgfplotsset{every axis legend/.append style={
+at={(0,0)},
+anchor=north east}}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=16cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin=-5,   % start the diagram at this x-coordinate
+        xmax= 5,   % end   the diagram at this x-coordinate
+        ymin= 0,   % start the diagram at this y-coordinate
+        ymax= 1.1,   % end   the diagram at this y-coordinate
+        xlabel=$x$,
+        ylabel=$y$,
+        legend cell align=left,
+        legend pos=south east,
+        legend style={draw=none},
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+      \addplot[domain=-5:5, red, ultra thick,samples=500] {1/(1+exp(-1*(x - 0)))};
+      \addplot[domain=-5:5, blue, ultra thick,dotted,samples=500] {1/(1+exp(-2*(x - 0)))};
+      \addplot[domain=-5:5, green!50!black, ultra thick,dashed,samples=500] {1/(1+exp(-1*(x - 1)))};
+      \legend{$\frac{1}{1 + e^{-x}}$,$\frac{1}{1 + e^{-2 \cdot x}}$,$\frac{1}{1 + e^{-(x-1)}}$}
+    \end{axis}
+\end{tikzpicture}
+\end{document}

tikz/quadratic-functions/Makefile

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+SOURCE = quadratic-functions
+DELAY = 80
+DENSITY = 300
+WIDTH = 1000
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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/quadratic-functions/README.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](linear-functions.png)

tikz/quadratic-functions/quadratic-functions.tex

@@ -0,0 +1,37 @@
+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+\usepackage{nicefrac}
+\pgfplotsset{every axis legend/.append style={
+at={(0,0)},
+anchor=north east}}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=8cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin=-5,   % start the diagram at this x-coordinate
+        xmax= 5,   % end   the diagram at this x-coordinate
+        ymin=-1.1,   % start the diagram at this y-coordinate
+        ymax= 9,   % end   the diagram at this y-coordinate
+        xlabel=$x$,
+        ylabel=$y$,
+        legend cell align=left,
+        legend pos=north west,
+        legend style={draw=none},
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+      \addplot[domain=-5:5, red, ultra thick,samples=500] {x^2};
+      \addplot[domain=-5:5, green!50!black, ultra thick,dashed,samples=500] {x^2+2*x};
+      \addplot[domain=-5:5, blue, ultra thick,dotted,samples=500] {x^2-x};
+      \legend{$x^2$,$x^2 + 2x$,$x^2-x$}
+    \end{axis}
+\end{tikzpicture}
+\end{document}

tikz/trigonometric-function-graphs/Makefile

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+SOURCE = trigonometric-function-graphs
+DELAY = 80
+DENSITY = 300
+WIDTH = 1000
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+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/trigonometric-function-graphs/README.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](trigonometric-function-graphs.png)

tikz/trigonometric-function-graphs/trigonometric-function-graphs.tex

@@ -0,0 +1,38 @@
+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+\usepackage{nicefrac}
+\pgfplotsset{every axis legend/.append style={
+at={(0,0)},
+anchor=north east}}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=16cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin= 0,   % start the diagram at this x-coordinate
+        xmax= 7,   % end   the diagram at this x-coordinate
+        ymin=-1.1,   % start the diagram at this y-coordinate
+        ymax= 1.1,   % end   the diagram at this y-coordinate
+        xlabel=$x$,
+        ylabel=$y$,
+        xtick={0,pi/2,pi,1.5*pi,2*pi},
+        xticklabels={0,$\frac{\pi}{2}$,$\pi$,$\frac{3 \cdot \pi}{2}$,$2 \pi$},
+        legend cell align=left,
+        legend pos=south east,
+        legend style={draw=none},
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+      \addplot[domain=0:7, red, ultra thick,samples=1000] {sin(deg(x))};
+      \addplot[domain=0:7, blue, ultra thick,dotted,samples=1000] {cos(deg(x))};
+      \legend{$\sin(x)$, $\cos(x)$}
+    \end{axis}
+\end{tikzpicture}
+\end{document}