update to current state of book

1 files changed, 134 insertions, 134 deletions

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}

+