update to current state of book

2 files changed, 178 insertions, 178 deletions

diff --git a/buch/chapters/40-eigenwerte/images/Makefile b/buch/chapters/40-eigenwerte/images/Makefile
index 54b36d5..4d882f0 100644
--- a/buch/chapters/40-eigenwerte/images/Makefile
+++ b/buch/chapters/40-eigenwerte/images/Makefile
@@ -1,44 +1,44 @@
-#
-# Makefile
-#
-# (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil
-#
-all:	sp.pdf nilpotent.pdf kernbild.pdf kombiniert.pdf \
-	wurzelapprox.pdf wurzel.pdf dimjk.pdf jknilp.pdf \
-	normalform.pdf minmax.pdf
-
-sp.pdf:	sp.tex sppaths.tex
-	pdflatex sp.tex
-
-sppaths.tex:	spbeispiel.m
-	octave spbeispiel.m
-
-nilpotent.pdf:	nilpotent.tex
-	pdflatex nilpotent.tex
-
-kernbild.pdf:	kernbild.tex bild2.jpg kern2.jpg
-	pdflatex kernbild.tex
-
-kombiniert.pdf:	kombiniert.tex kombiniert.jpg
-	pdflatex kombiniert.tex
-
-wurzelapprox.pdf:	wurzelapprox.tex wa.tex
-	pdflatex wurzelapprox.tex
-
-wa.tex:	wa.m
-	octave wa.m
-
-wurzel.pdf:	wurzel.tex
-	pdflatex wurzel.tex
-
-dimjk.pdf:	dimjk.tex
-	pdflatex dimjk.tex
-
-jknilp.pdf:	jknilp.tex
-	pdflatex jknilp.tex
-
-normalform.pdf:	normalform.tex
-	pdflatex normalform.tex
-
-minmax.pdf:	minmax.tex
-	pdflatex minmax.tex
+#

+# Makefile

+#

+# (c) 2020 Prof Dr Andreas Müller, Hochschule Rappersil

+#

+all:	sp.pdf nilpotent.pdf kernbild.pdf kombiniert.pdf \

+	wurzelapprox.pdf wurzel.pdf dimjk.pdf jknilp.pdf \

+	normalform.pdf minmax.pdf

+

+sp.pdf:	sp.tex sppaths.tex

+	pdflatex sp.tex

+

+sppaths.tex:	spbeispiel.m

+	octave spbeispiel.m

+

+nilpotent.pdf:	nilpotent.tex

+	pdflatex nilpotent.tex

+

+kernbild.pdf:	kernbild.tex bild2.jpg kern2.jpg

+	pdflatex kernbild.tex

+

+kombiniert.pdf:	kombiniert.tex kombiniert.jpg

+	pdflatex kombiniert.tex

+

+wurzelapprox.pdf:	wurzelapprox.tex wa.tex

+	pdflatex wurzelapprox.tex

+

+wa.tex:	wa.m

+	octave wa.m

+

+wurzel.pdf:	wurzel.tex

+	pdflatex wurzel.tex

+

+dimjk.pdf:	dimjk.tex

+	pdflatex dimjk.tex

+

+jknilp.pdf:	jknilp.tex

+	pdflatex jknilp.tex

+

+normalform.pdf:	normalform.tex

+	pdflatex normalform.tex

+

+minmax.pdf:	minmax.tex

+	pdflatex minmax.tex

diff --git a/buch/chapters/40-eigenwerte/images/minmax.tex b/buch/chapters/40-eigenwerte/images/minmax.tex
index f661d5b..cf81834 100644
--- a/buch/chapters/40-eigenwerte/images/minmax.tex
+++ b/buch/chapters/40-eigenwerte/images/minmax.tex
@@ -1,134 +1,134 @@
-%
-% minmax.tex -- minimum und maximum
-%
-% (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}{0,0.5,0}
-
-\def\mittellinie{
-	plot[domain=0:6.2832,samples=400]
-		({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))})
-}
-
-\begin{scope}
-	\fill[color=darkgreen!20]
-		plot[domain=0:6.2832,samples=360]
-			({\x},{sin(180*\x/3.1415)})
-		--
-		plot[domain=6.2832:0,samples=360]
-			({\x},{cos(180*\x/3.1415)})
-		-- cycle;
-	\foreach \x in {0.5,1,...,6}{
-		\draw[color=darkgreen]
-			({\x},{sin(180*\x/3.1415)})
-			--
-			({\x},{cos(180*\x/3.1415)});
-	}
-
-	\node[color=darkgreen] at (2,-0.8) [left] {$|f(x)-g(x)|$};
-	\draw[color=darkgreen,line width=0.3pt] (2,-0.8) -- (2.5,-0.7);
-
-	\draw[color=blue,line width=1.4pt] plot[domain=0:6.29,samples=360]
-		({\x},{sin(180*\x/3.1415)});
-	\draw[color=red,line width=1.4pt] plot[domain=0:6.29,samples=360]
-		({\x},{cos(180*\x/3.1415)});
-	\draw[color=purple!50,line width=1.4pt] \mittellinie;
-	\node[color=purple!50] at (6.2832,0.5) [right] {$\frac12(f(x)+g(x))$};
-
-	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={below:$x$}];
-	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-
-
-	\xdef\x{2}
-	\node[color=blue] at (\x,{sin(180*\x/3.1415)}) [above right] {$f(x)$};
-	\pgfmathparse{2.5*3.14159-\x}
-	\xdef\x{\pgfmathresult}
-	\node[color=red] at (\x,{cos(180*\x/3.1415)}) [above left] {$g(x)$};
-
-\end{scope}
-
-\draw[->,line width=4pt,color=gray!40] ({3.1415-1},-1.3) -- ({3.1415-2.3},-3);
-\draw[->,line width=4pt,color=gray!40] ({3.1415+1},-1.3) -- ({3.1415+2.3},-3);
-
-\node at ({3.1415-1.75},-2.15) [left] {$\frac12(f(x)+g(x))+\frac12|f(x)-g(x)|$};
-\node at ({3.1415+1.75},-2.15) [right] {$\frac12(f(x)+g(x))-\frac12|f(x)-g(x)|$};
-
-\def\s{(-0.1)}
-
-\begin{scope}[xshift=-3.4cm,yshift=-4.6cm]
-	\fill[color=darkgreen!20]
-		\mittellinie
-		--
-		plot[domain=6.2832:0,samples=400]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
-		-- cycle;
-	\foreach \x in {0.5,1,...,6}{
-		\draw[color=darkgreen]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
-			--
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
-	}
-	\draw[color=darkgreen,line width=1.4pt]
-		plot[domain=6.2832:0,samples=400]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
-
-	\node[color=darkgreen] at (2,-0.3) [left] {$|f(x)-g(x)|$};
-	\draw[color=darkgreen,line width=0.3pt] (2,-0.3) -- (2.5,0.2);
-
-	\draw[color=purple!50,line width=1.4pt] \mittellinie;
-	\pgfmathparse{0.75*3.1415+\s}
-	\xdef\x{\pgfmathresult}
-	\node[color=darkgreen] at (\x,{sin(180*\x/3.1415)}) [above right]
-		{$\max(f(x),g(x))$};
-	\node[color=purple!50] at ({1.25*3.1415},-0.7) [below]
-		{$\frac12(f(x)+g(x))$};
-	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
-	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-\end{scope}
-
-
-\begin{scope}[xshift=+3.4cm,yshift=-4.6cm]
-	\fill[color=darkgreen!20]
-		\mittellinie
-		--
-		plot[domain=6.2832:0,samples=400]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
-		-- cycle;
-	\foreach \x in {0.5,1,...,6}{
-		\draw[color=darkgreen]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})
-			--
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});
-	}
-	\draw[color=darkgreen,line width=1.4pt]
-		plot[domain=6.2832:0,samples=400]
-			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});
-
-	\node[color=darkgreen] at (3,0.3) [right] {$|f(x)-g(x)|$};
-	\draw[color=darkgreen,line width=0.3pt] (3,0.3) -- (2.5,-0.4);
-
-	\draw[color=purple!50,line width=1.4pt] \mittellinie;
-	\pgfmathparse{0.75*3.1415-\s}
-	\xdef\x{\pgfmathresult}
-	\node[color=darkgreen] at (\x,{cos(180*\x/3.1415)}) [below left]
-		{$\min(f(x),g(x))$};
-	\node[color=purple!50] at ({0.25*3.1415},0.7) [above right]
-		{$\frac12(f(x)+g(x))$};
-	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];
-	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%

+% minmax.tex -- minimum und maximum

+%

+% (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}{0,0.5,0}

+

+\def\mittellinie{

+	plot[domain=0:6.2832,samples=400]

+		({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))})

+}

+

+\begin{scope}

+	\fill[color=darkgreen!20]

+		plot[domain=0:6.2832,samples=360]

+			({\x},{sin(180*\x/3.1415)})

+		--

+		plot[domain=6.2832:0,samples=360]

+			({\x},{cos(180*\x/3.1415)})

+		-- cycle;

+	\foreach \x in {0.5,1,...,6}{

+		\draw[color=darkgreen]

+			({\x},{sin(180*\x/3.1415)})

+			--

+			({\x},{cos(180*\x/3.1415)});

+	}

+

+	\node[color=darkgreen] at (2,-0.8) [left] {$|f(x)-g(x)|$};

+	\draw[color=darkgreen,line width=0.3pt] (2,-0.8) -- (2.5,-0.7);

+

+	\draw[color=blue,line width=1.4pt] plot[domain=0:6.29,samples=360]

+		({\x},{sin(180*\x/3.1415)});

+	\draw[color=red,line width=1.4pt] plot[domain=0:6.29,samples=360]

+		({\x},{cos(180*\x/3.1415)});

+	\draw[color=purple!50,line width=1.4pt] \mittellinie;

+	\node[color=purple!50] at (6.2832,0.5) [right] {$\frac12(f(x)+g(x))$};

+

+	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={below:$x$}];

+	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];

+

+

+	\xdef\x{2}

+	\node[color=blue] at (\x,{sin(180*\x/3.1415)}) [above right] {$f(x)$};

+	\pgfmathparse{2.5*3.14159-\x}

+	\xdef\x{\pgfmathresult}

+	\node[color=red] at (\x,{cos(180*\x/3.1415)}) [above left] {$g(x)$};

+

+\end{scope}

+

+\draw[->,line width=4pt,color=gray!40] ({3.1415-1},-1.3) -- ({3.1415-2.3},-3);

+\draw[->,line width=4pt,color=gray!40] ({3.1415+1},-1.3) -- ({3.1415+2.3},-3);

+

+\node at ({3.1415-1.75},-2.15) [left] {$\frac12(f(x)+g(x))+\frac12|f(x)-g(x)|$};

+\node at ({3.1415+1.75},-2.15) [right] {$\frac12(f(x)+g(x))-\frac12|f(x)-g(x)|$};

+

+\def\s{(-0.1)}

+

+\begin{scope}[xshift=-3.4cm,yshift=-4.6cm]

+	\fill[color=darkgreen!20]

+		\mittellinie

+		--

+		plot[domain=6.2832:0,samples=400]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})

+		-- cycle;

+	\foreach \x in {0.5,1,...,6}{

+		\draw[color=darkgreen]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})

+			--

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});

+	}

+	\draw[color=darkgreen,line width=1.4pt]

+		plot[domain=6.2832:0,samples=400]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)+abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});

+

+	\node[color=darkgreen] at (2,-0.3) [left] {$|f(x)-g(x)|$};

+	\draw[color=darkgreen,line width=0.3pt] (2,-0.3) -- (2.5,0.2);

+

+	\draw[color=purple!50,line width=1.4pt] \mittellinie;

+	\pgfmathparse{0.75*3.1415+\s}

+	\xdef\x{\pgfmathresult}

+	\node[color=darkgreen] at (\x,{sin(180*\x/3.1415)}) [above right]

+		{$\max(f(x),g(x))$};

+	\node[color=purple!50] at ({1.25*3.1415},-0.7) [below]

+		{$\frac12(f(x)+g(x))$};

+	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];

+	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];

+\end{scope}

+

+

+\begin{scope}[xshift=+3.4cm,yshift=-4.6cm]

+	\fill[color=darkgreen!20]

+		\mittellinie

+		--

+		plot[domain=6.2832:0,samples=400]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})

+		-- cycle;

+	\foreach \x in {0.5,1,...,6}{

+		\draw[color=darkgreen]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))})

+			--

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159))});

+	}

+	\draw[color=darkgreen,line width=1.4pt]

+		plot[domain=6.2832:0,samples=400]

+			({\x},{0.5*(sin(180*\x/3.14159)+cos(180*\x/3.14159)-abs(sin(180*\x/3.14159)-cos(180*\x/3.14159)))});

+

+	\node[color=darkgreen] at (3,0.3) [right] {$|f(x)-g(x)|$};

+	\draw[color=darkgreen,line width=0.3pt] (3,0.3) -- (2.5,-0.4);

+

+	\draw[color=purple!50,line width=1.4pt] \mittellinie;

+	\pgfmathparse{0.75*3.1415-\s}

+	\xdef\x{\pgfmathresult}

+	\node[color=darkgreen] at (\x,{cos(180*\x/3.1415)}) [below left]

+		{$\min(f(x),g(x))$};

+	\node[color=purple!50] at ({0.25*3.1415},0.7) [above right]

+		{$\frac12(f(x)+g(x))$};

+	\draw[->] (-0.1,0) -- (6.5,0) coordinate[label={$x$}];

+	\draw[->] (0,-1.1) -- (0,1.3) coordinate[label={right:$y$}];

+\end{scope}

+

+\end{tikzpicture}

+\end{document}

+