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changed position and color of boxes; added stripes

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Martin Thoma 2012-09-22 16:16:22 +02:00
parent 5a44ac6bfc
commit b2372f6f8d
2 changed files with 33 additions and 12 deletions
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14
tikz/stetigkeit-differenzierbarkeit/README Normal file
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@ -0,0 +1,14 @@
Interessante Funktionen:
Dirichlet-Funktion
* Überall unstetig
Weierstraß-Funktion:
* Überall stetig
* Nirgends differenzierbar
f:(0,1)->R
* Stetig, aber nicht gleichmäßig stetig
* Differenzierbar

31
tikz/stetigkeit-differenzierbarkeit/stetigkeit-differenzierbarkeit.tex
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@ -7,7 +7,7 @@
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{shapes,snakes,calc}
\usetikzlibrary{shapes,snakes,calc,patterns}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{preview}
@ -40,6 +40,18 @@
minimum height=3em
}
]
\pgfdeclarepatternformonly{north east lines wide}%
{\pgfqpoint{-1pt}{-1pt}}%
{\pgfqpoint{10pt}{10pt}}%
{\pgfqpoint{9pt}{9pt}}%
{
\pgfsetlinewidth{3pt}
\pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
\pgfpathlineto{\pgfqpoint{9.1pt}{9.1pt}}
\pgfusepath{stroke}
}
\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);
@ -60,18 +72,12 @@ $f$ 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) {$(\mathbb{N}_0, \cdot)$}
(12,-6) node[example, draw=black, fill=black!15] (G) {\tiny$f_2(x) = e^x$}
(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$f_1(x) = 42$}
(6,-6) node[example, draw=red, fill=red!15, pattern=north east lines wide, pattern color=black!25] (N) {\tiny$f_1(x) = 42$}
(12,-2) node[example, draw=yellow, fill=yellow!15] (Q) {\tiny$f_4(x) = |x|$}
(9, 0) node[algebraicName] (O) {Stetige Funktionen}
@ -83,7 +89,8 @@ $:\Leftrightarrow \exists L\ge 0: |f(x)-f(z)|\le L|x-z|\ \forall x,z \in D$
$f(x_n) \rightarrow f(x_0)$
\end{minipage}
}
(12,-1) node[example, draw=yellow, fill=yellow!15] (P) {\tiny$f_2(x) = \frac{1}{x}$};
(12,-4) node[example, draw=black, fill=black!15] (P) {\tiny$f_3(x) = \frac{1}{x}$};
% LP-Stetig
\draw[purple, thick, rounded corners] ($(C.north west)+(-0.3,0.1)$) rectangle ($(N.south east)+(0.3,-0.3)$);