From 2db90bfe4b174570424c408f04000902411d8755 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 12 Apr 2021 21:51:55 +0200 Subject: update to current state of book --- buch/chapters/60-gruppen/images/sl2.tex | 292 ++++++++++++++++---------------- 1 file changed, 146 insertions(+), 146 deletions(-) (limited to 'buch/chapters/60-gruppen/images/sl2.tex') diff --git a/buch/chapters/60-gruppen/images/sl2.tex b/buch/chapters/60-gruppen/images/sl2.tex index 0e44aa9..c41308c 100644 --- a/buch/chapters/60-gruppen/images/sl2.tex +++ b/buch/chapters/60-gruppen/images/sl2.tex @@ -1,146 +1,146 @@ -% -% sl2.tex -- template for standalon tikz images -% -% (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] - -\definecolor{darkgreen}{rgb}{0,0.6,0} - -\begin{scope}[xshift=-4.5cm] - \fill[color=blue!20] - (1.4,0) -- (0,1.4) -- (-1.4,0) -- (0,-1.4) -- cycle; - \fill[color=red!40,opacity=0.5] - (1.96,0) -- (0,1) -- (-1.96,0) -- (0,-1) -- cycle; - - \begin{scope} - \clip (-2.1,-2.1) rectangle (2.3,2.3); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] - ({(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] - ({(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] - ({-(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] - ({-(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); - \end{scope} - - \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; - \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; - - \draw[->,color=blue] (0,0) -- (1.4,0); - \draw[->,color=blue] (0,0) -- (0,1.4); - - \draw[->,color=red] (0,0) -- (1.96,0); - \draw[->,color=red] (0,0) -- (0,1); - \node at (0,-3.2) - {$\displaystyle - \begin{aligned} - A&=\begin{pmatrix}1&0\\0&-1\end{pmatrix} - \\ - e^{At} - &=\begin{pmatrix}e^t&0\\0&e^{-t}\end{pmatrix} - \end{aligned} - $}; - -\end{scope} - - -\begin{scope} - \fill[color=blue!20] - (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; - \fill[color=red!40,opacity=0.5] - (33:1.4) -- (123:1.4) -- (213:1.4) -- (303:1.4) -- cycle; - - \draw[color=darkgreen] (0,0) circle[radius=1.4]; - - \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; - \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; - - \draw[->,color=blue] (0,0) -- (1.4,0); - \draw[->,color=blue] (0,0) -- (0,1.4); - - \draw[->,color=red] (0,0) -- (33:1.4); - \draw[->,color=red] (0,0) -- (123:1.4); - - \node at (0,-3.2) - {$\displaystyle - \begin{aligned} - B - &=\begin{pmatrix}0&-1\\1&0 \end{pmatrix} - \\ - e^{Bt} - &= - \begin{pmatrix} - \cos t&-\sin t\\ - \sin t& \cos t - \end{pmatrix} - \end{aligned}$}; -\end{scope} - - -\begin{scope}[xshift=4.5cm] - \fill[color=blue!20] - (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; - \def\x{0.5} - \fill[color=red!40,opacity=0.5] - ({1.4*cosh(\x)},{1.4*sinh(\x}) - -- - ({1.4*sinh(\x},{1.4*cosh(\x)}) - -- - ({-1.4*cosh(\x)},{-1.4*sinh(\x}) - -- - ({-1.4*sinh(\x},{-1.4*cosh(\x)}) - -- cycle; - - \begin{scope} - \clip (-2.1,-2.1) rectangle (2.2,2.2); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] ({1.4*cosh(\x)},{1.4*sinh(\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{1.4*cosh(\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] ({-1.4*cosh(\x)},{1.4*sinh(\x)}); - \draw[color=darkgreen] - plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{-1.4*cosh(\x)}); - \end{scope} - - \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; - \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; - - \draw[->,color=blue] (0,0) -- (1.4,0); - \draw[->,color=blue] (0,0) -- (0,1.4); - - \draw[->,color=red] (0,0) -- ({1.4*cosh(\x)},{1.4*sinh(\x)}); - \draw[->,color=red] (0,0) -- ({1.4*sinh(\x)},{1.4*cosh(\x)}); - - \node at (0,-3.2) {$\displaystyle - \begin{aligned} - C&=\begin{pmatrix}0&1\\1&0\end{pmatrix} - \\ - e^{Ct} - &= - \begin{pmatrix} - \cosh t&\sinh t\\ - \sinh t&\cosh t - \end{pmatrix} - \end{aligned} - $}; -\end{scope} - -\end{tikzpicture} -\end{document} - +% +% sl2.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\begin{scope}[xshift=-4.5cm] + \fill[color=blue!20] + (1.4,0) -- (0,1.4) -- (-1.4,0) -- (0,-1.4) -- cycle; + \fill[color=red!40,opacity=0.5] + (1.96,0) -- (0,1) -- (-1.96,0) -- (0,-1) -- cycle; + + \begin{scope} + \clip (-2.1,-2.1) rectangle (2.3,2.3); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({-(1/1.4)*exp(\x)},{(1/1.4)*exp(-\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] + ({-(1/1.4)*exp(\x)},{-(1/1.4)*exp(-\x)}); + \end{scope} + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- (1.96,0); + \draw[->,color=red] (0,0) -- (0,1); + \node at (0,-3.2) + {$\displaystyle + \begin{aligned} + A&=\begin{pmatrix}1&0\\0&-1\end{pmatrix} + \\ + e^{At} + &=\begin{pmatrix}e^t&0\\0&e^{-t}\end{pmatrix} + \end{aligned} + $}; + +\end{scope} + + +\begin{scope} + \fill[color=blue!20] + (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; + \fill[color=red!40,opacity=0.5] + (33:1.4) -- (123:1.4) -- (213:1.4) -- (303:1.4) -- cycle; + + \draw[color=darkgreen] (0,0) circle[radius=1.4]; + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- (33:1.4); + \draw[->,color=red] (0,0) -- (123:1.4); + + \node at (0,-3.2) + {$\displaystyle + \begin{aligned} + B + &=\begin{pmatrix}0&-1\\1&0 \end{pmatrix} + \\ + e^{Bt} + &= + \begin{pmatrix} + \cos t&-\sin t\\ + \sin t& \cos t + \end{pmatrix} + \end{aligned}$}; +\end{scope} + + +\begin{scope}[xshift=4.5cm] + \fill[color=blue!20] + (0:1.4) -- (90:1.4) -- (180:1.4) -- (270:1.4) -- cycle; + \def\x{0.5} + \fill[color=red!40,opacity=0.5] + ({1.4*cosh(\x)},{1.4*sinh(\x}) + -- + ({1.4*sinh(\x},{1.4*cosh(\x)}) + -- + ({-1.4*cosh(\x)},{-1.4*sinh(\x}) + -- + ({-1.4*sinh(\x},{-1.4*cosh(\x)}) + -- cycle; + + \begin{scope} + \clip (-2.1,-2.1) rectangle (2.2,2.2); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{1.4*cosh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({-1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[color=darkgreen] + plot[domain=-1:1,samples=100] ({1.4*sinh(\x)},{-1.4*cosh(\x)}); + \end{scope} + + \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; + \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; + + \draw[->,color=blue] (0,0) -- (1.4,0); + \draw[->,color=blue] (0,0) -- (0,1.4); + + \draw[->,color=red] (0,0) -- ({1.4*cosh(\x)},{1.4*sinh(\x)}); + \draw[->,color=red] (0,0) -- ({1.4*sinh(\x)},{1.4*cosh(\x)}); + + \node at (0,-3.2) {$\displaystyle + \begin{aligned} + C&=\begin{pmatrix}0&1\\1&0\end{pmatrix} + \\ + e^{Ct} + &= + \begin{pmatrix} + \cosh t&\sinh t\\ + \sinh t&\cosh t + \end{pmatrix} + \end{aligned} + $}; +\end{scope} + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1