diff --git a/tikz/stetigkeit-differenzierbarkeit/Makefile b/tikz/stetigkeit-differenzierbarkeit/Makefile new file mode 100644 index 0000000..45e49bc --- /dev/null +++ b/tikz/stetigkeit-differenzierbarkeit/Makefile @@ -0,0 +1,31 @@ +SOURCE = stetigkeit-differenzierbarkeit +DELAY = 80 +DENSITY = 300 +WIDTH = 1024 + +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 diff --git a/tikz/stetigkeit-differenzierbarkeit/stetigkeit-differenzierbarkeit.tex b/tikz/stetigkeit-differenzierbarkeit/stetigkeit-differenzierbarkeit.tex new file mode 100644 index 0000000..35c679a --- /dev/null +++ b/tikz/stetigkeit-differenzierbarkeit/stetigkeit-differenzierbarkeit.tex @@ -0,0 +1,96 @@ +\documentclass{article} + +\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[pdftex,active,tightpage]{preview} +\setlength\PreviewBorder{2mm} +\usepackage{tikz} +\usetikzlibrary{shapes,snakes,calc} +\usepackage{amsmath,amssymb} +\begin{document} +\begin{preview} + +%\begin{align*} +% f: \mathbb{R} \rightarrow \mathbb{R}\\ +% g: \mathbb{R} \rightarrow \mathbb{R}\\ +%\end{align*} + +\begin{tikzpicture}[% + auto, + example/.style={ + rectangle, + draw=blue, + thick, + fill=blue!20, + text width=4.5em, + align=center, + rounded corners, + minimum height=2em + }, + algebraicName/.style={ + text width=7em, + align=center, + minimum height=2em + }, + explanation/.style={ + text width=10em, + align=left, + minimum height=3em + } + ] + \draw[fill=yellow!20,yellow!20, rounded corners] (-1.85, 0.70) rectangle (13.4,-6.85); + \draw[fill=lime!20,lime!20, rounded corners] (-1.75, 0.45) rectangle (7.3,-6.75); + \draw[fill=purple!20,purple!20, rounded corners] (-1.65,-1.55) rectangle (7.2,-6.65); + \draw (0, 0) node[algebraicName] (A) {gleichmäßig stetig} + (3, 0) node[explanation] (B) { + \begin{minipage}{0.90\textwidth} + \tiny + $\forall \varepsilon >0 \ \exists \delta=\delta(\varepsilon)>0\colon\\ |f(x)-f(z)| < \varepsilon\\ \forall x,z \in D \text{ mit } |x-z|<\delta$ + \end{minipage} + } + (6, 0) node[example, draw=lime, fill=lime!15] (X) {\tiny$f(x)=\sin(x)$} + (6,-1) node[example, draw=lime, fill=lime!15] (X) {\tiny$g(x)=\cos(x)$} + (0,-2) node[algebraicName, purple] (C) {Lipschitz-stetig} + (3.5,-2) node[explanation] (X) { + \begin{minipage}{90\textwidth} + \tiny +$f$ heißt auf $D$ \textbf{Lipschitz-stetig}\\ +$:\Leftrightarrow \exists L\ge 0: |f(x)-f(z)|\le L|x-z|\ \forall x,z \in D$ + \end{minipage} + } + %(2, -3) node[example, draw=purple, fill=purple!15] (D) {$(\mathbb{Z}, +)$} + %(4, -3) node[example, draw=purple, fill=purple!15] (E) {$(\mathbb{Q} \setminus \{0\}, \cdot)$} + %(6, -3) node[example, draw=purple, fill=purple!15] (X) {$\mathbb{Z}_1$} + + %(10,-6) node[example, draw=black, fill=black!15] (F) {$(\mathbb{N}_0, +)$} + (12,-6) node[example, draw=black, fill=black!15] (G) {$(\mathbb{N}_0, \cdot)$} + + + (0,-6) node[example, draw=red, fill=red!15] (K) {\tiny$h(x) = |x|$} + %(2,-6) node[example, draw=red, fill=red!15] (L) {$(\mathbb{R}, +, \cdot)$} + %(4,-6) node[example, draw=red, fill=red!15] (M) {$(\mathbb{C}, +, \cdot)$} + (6,-6) node[example, draw=red, fill=red!15] (N) {\tiny$f_1(x) = 42$} + + + (9, 0) node[algebraicName] (O) {Stetige Funktionen} + (12,0) node[explanation] (X) { + \begin{minipage}{0.9\textwidth} + \tiny + $f$ heißt stetig in $x_0 :\Leftrightarrow$\\ + für jede Folge $(x_n)$ in $D$ mit $x_n \rightarrow x_0$ gilt:\\ + $f(x_n) \rightarrow f(x_0)$ + \end{minipage} + } + (12,-1) node[example, draw=yellow, fill=yellow!15] (P) {\tiny$f_2(x) = \frac{1}{x}$}; + + % LP-Stetig + \draw[purple, thick, rounded corners] ($(C.north west)+(-0.3,0.1)$) rectangle ($(N.south east)+(0.3,-0.3)$); + % gleichmäßig stetig + \draw[lime, thick, rounded corners] ($(A.north west)+(-0.4,0.1)$) rectangle ($(N.south east)+(0.4,-0.4)$); + % stetige funktionen + \draw[yellow, thick, rounded corners] ($(A.north west)+(-0.5,0.2)$) rectangle ($(G.south east)+(0.5,-0.5)$); +\end{tikzpicture} +\end{preview} +\end{document}