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diff --git a/buch/chapters/070-orthogonalitaet/images/legendre.tex b/buch/chapters/070-orthogonalitaet/images/legendre.tex new file mode 100644 index 0000000..8409da0 --- /dev/null +++ b/buch/chapters/070-orthogonalitaet/images/legendre.tex @@ -0,0 +1,99 @@ +% +% legendre.tex -- plots of legendre polynomials +% +% (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{6.5} +\input{legendrepaths.tex} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{fone}{rgb}{1,0,0} +\definecolor{ftwo}{rgb}{1.0,0,0.8} +\definecolor{fthree}{rgb}{0.8,0,1} +\definecolor{ffour}{rgb}{0,0,1} +\definecolor{ffive}{rgb}{0,0.8,1} +\definecolor{fsix}{rgb}{0,1,1} +\definecolor{fseven}{rgb}{0,0.6,0} +\definecolor{feight}{rgb}{0.2,1,0.6} +\definecolor{fnine}{rgb}{0.6,0.8,0.2} +\definecolor{ften}{rgb}{1,0.4,0} + +\def\dx{1} +\def\dy{0.25} + +\def\achsen{ + \draw[->] ({-1-(0.1/\skala)},0) -- ({1+(0.3/\skala)},0) + coordinate[label={$x$}]; + \draw[->] (0,{-(\dy)-(0.1/\skala)}) -- (0,{(\dy)+(0.3/\skala)}) + coordinate[label={right:$y$}]; + \foreach \x in {-1,-0.9,...,1.001}{ + \draw ({\dx*\x},{-0.05/\skala}) -- ({\dx*\x},{0.05/\skala}); + } + \foreach \x in {-1,-0.5,0.5,1}{ + \draw ({-0.05/\skala},{\dy*\x}) -- ({0.05/\skala},{\dy*\x}); + \node at ({\dx*\x},{-0.05/\skala}) [below] {$\mathstrut\x$}; + \node at ({-0.05/\skala},{\dy*\x}) [left] {$\mathstrut\x$}; + } +} + +\begin{scope}[yshift=0cm] + \node[color=fone] at (-0.70,{-0.9*\dy}) [right] {$n=1\mathstrut$}; + \node[color=ftwo] at (-0.90,{0.9*\dy}) [right] {$n=2\mathstrut$}; + \draw[line width=1.4pt,color=fone] \legendreone; + \draw[line width=1.4pt,color=ftwo] \legendretwo; + \achsen +\end{scope} + +\begin{scope}[yshift=-0.6cm] + \node[color=fthree] at (-0.96,{-0.9*\dy}) [right] {$n=3\mathstrut$}; + \node[color=ffour] at (-0.96,{0.9*\dy}) [right] {$n=4\mathstrut$}; + \draw[line width=1.4pt,color=fthree] \legendrethree; + \draw[line width=1.4pt,color=ffour] \legendrefour; + \achsen +\end{scope} + +\begin{scope}[yshift=-1.2cm] + \node[color=ffive] at (-0.96,{-0.9*\dy}) [right] {$n=5\mathstrut$}; + \node[color=fsix] at (-0.96,{0.9*\dy}) [right] {$n=6\mathstrut$}; + \draw[line width=1.4pt,color=ffive] \legendrefive; + \draw[line width=1.4pt,color=fsix] \legendresix; + \achsen +\end{scope} + +\begin{scope}[yshift=-1.8cm] + \node[color=fseven] at (-0.96,{-0.9*\dy}) [right] {$n=7\mathstrut$}; + \node[color=feight] at (-0.96,{0.9*\dy}) [right] {$n=8\mathstrut$}; + \draw[line width=1.4pt,color=fseven] \legendreseven; + \draw[line width=1.4pt,color=feight] \legendreeight; + \achsen +\end{scope} + +\begin{scope}[yshift=-2.4cm] + \node[color=fnine] at (-0.96,{-0.9*\dy}) [right] {$n=9\mathstrut$}; + \node[color=ften] at (-0.96,{0.9*\dy}) [right] {$n=10\mathstrut$}; + \draw[line width=1.4pt,color=fnine] \legendrenine; + \draw[line width=1.4pt,color=ften] \legendreten; + \achsen +\end{scope} + +%\draw[line width=1.4pt,color=ftwo] \legendretwo; +%\draw[line width=1.4pt,color=fthree] \legendrethree; +%\draw[line width=1.4pt,color=ffour] \legendrefour; +%\draw[line width=1.4pt,color=ffive] \legendrefive; +%\draw[line width=1.4pt,color=fsix] \legendresix; +%\draw[line width=1.4pt,color=fseven] \legendreseven; +%\draw[line width=1.4pt,color=feight] \legendreeight; +%\draw[line width=1.4pt,color=fnine] \legendrenine; +%\draw[line width=1.4pt,color=ften] \legendreten; + +\end{tikzpicture} +\end{document} + |