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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-10-09 21:13:51 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-10-09 21:13:51 +0200 |
commit | d4046eef3dee4b3de6f1d456132cda22fef8743f (patch) | |
tree | 3b35dbed85504bca2888be0097a04ecc86f5514e /buch/chapters/080-funktionentheorie/images/integralanalytisch.tex | |
parent | add ad presentation (diff) | |
download | SeminarSpezielleFunktionen-d4046eef3dee4b3de6f1d456132cda22fef8743f.tar.gz SeminarSpezielleFunktionen-d4046eef3dee4b3de6f1d456132cda22fef8743f.zip |
erster Entwurf Kapitel Funktionentheorie
Diffstat (limited to 'buch/chapters/080-funktionentheorie/images/integralanalytisch.tex')
-rw-r--r-- | buch/chapters/080-funktionentheorie/images/integralanalytisch.tex | 51 |
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diff --git a/buch/chapters/080-funktionentheorie/images/integralanalytisch.tex b/buch/chapters/080-funktionentheorie/images/integralanalytisch.tex new file mode 100644 index 0000000..a407eed --- /dev/null +++ b/buch/chapters/080-funktionentheorie/images/integralanalytisch.tex @@ -0,0 +1,51 @@ +% +% integralanalytisch.tex -- Illustration zum Beweis, das das Cauchy-Integral +% auf eine analytische Funktion führt +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\fill[color=blue!20] (0,0) circle[radius=1.5]; +\draw[color=blue,line width=0.7pt] (0,0) circle[radius=1.5]; + +\draw[->] (0,0) -- (-150:1.5); +\node at (-150:1.0) [below] {$\varrho$}; + +\begin{scope} +\clip (-4,-3) rectangle (4,3); +\draw[color=red, line width=1.4pt] + (-3,0.5) + .. controls (-4,-0.5) and (-3,-2) .. + (-2,-2) + .. controls (-1,-2) and (-1,-1.5) .. + (0,-1.5) + .. controls (1.0,-1.5) and (1.0,-3) .. + (2,-3) + .. controls (5,-3) and (3,5) .. + (-1,2); +\end{scope} + +\node[color=red] at (3.2,-1.5) {$\gamma$}; + +\coordinate (Z) at (1,0.5); + +\fill[color=white] (Z) circle[radius=0.05]; +\draw (Z) circle[radius=0.05]; +\node at (Z) [above] {$z$}; + +\draw[->] (0,-3.1) -- (0,3.3) coordinate[label={left:$\operatorname{Im}z$}]; +\draw[->] (-4.1,0) -- (4.3,0) coordinate[label={$\operatorname{Re}z$}]; + +\end{tikzpicture} +\end{document} + |