new files

5 files changed, 247 insertions, 1 deletions

diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile
index 327fed1..4912cca 100644
--- a/buch/chapters/110-elliptisch/images/Makefile
+++ b/buch/chapters/110-elliptisch/images/Makefile
@@ -3,7 +3,7 @@
 #
 # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 #
-all:	lemniskate.pdf ellipsenumfang.pdf
+all:	lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf
 
 lemniskate.pdf:	lemniskate.tex
 	pdflatex lemniskate.tex
@@ -14,3 +14,14 @@ ellipsenumfang.pdf:	ellipsenumfang.tex ekplot.tex
 ekplot.tex:	ellipsenumfang.m
 	octave ellipsenumfang.m
 
+rechteck:	rechteck.cpp
+	g++ -O -Wall -g rechteck.cpp -o rechteck
+
+test:	rechteck
+	./rechteck
+
+unvollstaendig.pdf:	unvollstaendig.tex unvollpath.tex
+	pdflatex unvollstaendig.tex
+
+unvollpath.tex:	unvollstaendig.m
+	octave unvollstaendig.m
diff --git a/buch/chapters/110-elliptisch/images/rechteck.cpp b/buch/chapters/110-elliptisch/images/rechteck.cpp
new file mode 100644
index 0000000..6bd6a06
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/rechteck.cpp
@@ -0,0 +1,54 @@
+/*
+ * rechteck.cpp
+ *
+ * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <cmath>
+#include <cstdlib>
+#include <cstdio>
+#include <complex>
+#include <iostream>
+
+double	ast = 1;
+
+std::complex<double>	integrand(double k, const std::complex<double>& z) {
+	std::complex<double>	s = z * z;
+	std::complex<double>	eins(1);
+	std::complex<double>	result = eins / sqrt((eins - s) * (eins - k * k * s));
+	return ast * ((result.imag() < 0) ? -result : result);
+}
+
+std::complex<double>	segment(double k, const std::complex<double>& z1,
+		const std::complex<double>& z2, int n = 100) {
+	std::complex<double>	dz = z2 - z1;
+	std::complex<double>	summe(0);
+	double	h = 1. / n;
+	summe = integrand(k, z1);
+	summe += integrand(k, z2);
+	for (int i = 1; i < n; i++) {
+		double	t = i * h;
+		std::complex<double>	z = (1 - t) * z1 + t * z2;
+		summe += 2. * integrand(k, z);
+	}
+	return dz * h * summe / 2.;
+}
+
+int	main(int argc, char *argv[]) {
+	double	k = 0.5;
+	double	y = -0.0001;
+	double	xstep = -0.1;
+	ast = 1;
+	std::complex<double>	z(0, y);
+	std::complex<double>	w = segment(k, std::complex<double>(0), z);
+	std::cout << z << std::endl;
+	int	counter = 100;
+	while (counter-- > 0) {
+		std::complex<double>	znext = z + std::complex<double>(xstep);
+		std::complex<double>	incr = segment(k, z, znext);
+		w += incr;
+		std::cout << znext << " -> " << w << ", ";
+		std::cout << integrand(k, znext) << std::endl;
+		z = znext;
+	}
+	return EXIT_SUCCESS;
+}
diff --git a/buch/chapters/110-elliptisch/images/unvollstaendig.m b/buch/chapters/110-elliptisch/images/unvollstaendig.m
new file mode 100644
index 0000000..25196d0
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/unvollstaendig.m
@@ -0,0 +1,81 @@
+#
+# unvollstaendig.m
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global N;
+N = 200;
+global n;
+n = 5;
+
+function retval = integrand_f(t, k)
+	retval = 1 / sqrt((1 - t^2) * (1 - k^2 * t^2));
+endfunction
+
+function retval = integrand_e(t, k)
+	retval = sqrt((1-k^2*t^2)/(1-t^2));
+endfunction
+
+function retval = integrand_pi(n, t, k)
+	retval = 1 / ((1-n*t^2) * sqrt((1-k^2*t^2)*(1-t^2)));
+endfunction
+
+function retval = elliptisch1(f, name, k)
+	global N;
+	global n;
+	s = 0;
+	fprintf(f, "\\def\\ell%s{ (0,0)", name);
+	delta = 1 / N;
+	for x = (0:delta:(1-delta))
+		h = delta / n;
+		for t = (x+h/2:h:x+delta)
+			s = s + integrand_f(t, k) * h;
+		endfor
+		fprintf(f, "\n    -- ({\\dx*%.4f},{\\dy*%.4f})", x + delta, s);
+	endfor
+	fprintf(f, "}\n");
+endfunction
+
+function retval = elliptisch2(f, name, k)
+	global N;
+	global n;
+	s = 0;
+	fprintf(f, "\\def\\ell%s{ (0,0)", name);
+	delta = 1 / N;
+	for x = (0:delta:(1-delta))
+		h = delta / n;
+		for t = (x+h/2:h:x+delta)
+			s = s + integrand_e(t, k) * h;
+		endfor
+		fprintf(f, "\n    -- ({\\dx*%.4f},{\\dy*%.4f})", x + delta, s);
+	endfor
+	fprintf(f, "\n}\n");
+endfunction
+
+fn = fopen("unvollpath.tex", "w");
+
+elliptisch1(fn, "Fzero", 0.0);
+elliptisch1(fn, "Fone", 0.1);
+elliptisch1(fn, "Ftwo", 0.2);
+elliptisch1(fn, "Fthree", 0.3);
+elliptisch1(fn, "Ffour", 0.4);
+elliptisch1(fn, "Ffive", 0.5);
+elliptisch1(fn, "Fsix", 0.6);
+elliptisch1(fn, "Fseven", 0.7);
+elliptisch1(fn, "Feight", 0.8);
+elliptisch1(fn, "Fnine", 0.9);
+elliptisch1(fn, "Ften", 1.0);
+
+elliptisch2(fn, "Ezero", 0.0);
+elliptisch2(fn, "Eone", 0.1);
+elliptisch2(fn, "Etwo", 0.2);
+elliptisch2(fn, "Ethree", 0.3);
+elliptisch2(fn, "Efour", 0.4);
+elliptisch2(fn, "Efive", 0.5);
+elliptisch2(fn, "Esix", 0.6);
+elliptisch2(fn, "Eseven", 0.7);
+elliptisch2(fn, "Eeight", 0.8);
+elliptisch2(fn, "Enine", 0.9);
+elliptisch2(fn, "Eten", 1.0);
+
+fclose(fn);
diff --git a/buch/chapters/110-elliptisch/images/unvollstaendig.pdf b/buch/chapters/110-elliptisch/images/unvollstaendig.pdf
new file mode 100644
index 0000000..4da2c0c
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/unvollstaendig.pdf
diff --git a/buch/chapters/110-elliptisch/images/unvollstaendig.tex b/buch/chapters/110-elliptisch/images/unvollstaendig.tex
new file mode 100644
index 0000000..1a1af13
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/unvollstaendig.tex
@@ -0,0 +1,100 @@
+%
+% unvollstaendig.tex -- Plots der unvollständigen elliptischen integrale
+%
+% (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}
+\input{unvollpath.tex}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\pgfkeys{/pgf/number format/.cd, fixed, fixed zerofill, precision=1}
+
+\def\dx{12.8}
+\def\dy{6}
+
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{blau}{rgb}{0.3,0.3,1}
+
+\begin{scope}
+\begin{scope}
+\clip (-0.1,-0.1) rectangle ({\dx+0.0},{10.1});
+
+\fill[color=darkgreen!10] \ellEzero -- (\dx,{1.571*\dy}) -- (\dx,0) -- cycle;
+\fill[color=red!10] \ellEzero -- (\dx,{1.571*\dy}) -- (\dx,10.1) -- (0,10.2) -- cycle;
+
+\node[color=red] at ({0.6*\dx},{1.3*\dy}) [scale=2] {$F(x,k)$};
+\node[color=darkgreen] at ({0.6*\dx},{0.3*\dy}) [scale=2] {$E(x,k)$};
+
+
+\draw[color=red!0!blau,line width=1.0pt] \ellFzero;
+\draw[color=red!10!blau,line width=1.0pt] \ellFone;
+\draw[color=red!20!blau,line width=1.0pt] \ellFtwo;
+\draw[color=red!30!blau,line width=1.0pt] \ellFthree;
+\draw[color=red!40!blau,line width=1.0pt] \ellFfour;
+\draw[color=red!50!blau,line width=1.0pt] \ellFfive;
+\draw[color=red!60!blau,line width=1.0pt] \ellFsix;
+\draw[color=red!70!blau,line width=1.0pt] \ellFseven;
+\draw[color=red!80!blau,line width=1.0pt] \ellFeight;
+\draw[color=red!90!blau,line width=1.0pt] \ellFnine;
+\draw[color=red!100!blau,line width=1.0pt] \ellFten;
+
+\draw[color=darkgreen!100!blau,line width=1.0pt] \ellEten;
+\draw[color=darkgreen!90!blau,line width=1.0pt] \ellEnine;
+\draw[color=darkgreen!80!blau,line width=1.0pt] \ellEeight;
+\draw[color=darkgreen!70!blau,line width=1.0pt] \ellEseven;
+\draw[color=darkgreen!60!blau,line width=1.0pt] \ellEsix;
+\draw[color=darkgreen!50!blau,line width=1.0pt] \ellEfive;
+\draw[color=darkgreen!40!blau,line width=1.0pt] \ellEfour;
+\draw[color=darkgreen!30!blau,line width=1.0pt] \ellEthree;
+\draw[color=darkgreen!20!blau,line width=1.0pt] \ellEtwo;
+\draw[color=darkgreen!10!blau,line width=1.0pt] \ellEone;
+\draw[color=darkgreen!0!blau,line width=1.0pt] \ellEzero;
+
+\end{scope}
+
+\draw[line width=0.2pt] (\dx,0) -- (\dx,10.1);
+
+\begin{scope}
+	\clip ({0.7*\dx},0) rectangle (\dx,10.1);
+	\draw[color=white,line width=0.5pt] \ellEzero -- (\dx,{1.571*\dy});
+\end{scope}
+
+\draw[->] ({-0.1},0) -- ({\dx+0.3},0) coordinate[label={$x$}];
+\foreach \x in {0,0.2,...,1.0}{
+	\draw ({\x*\dx},-0.1) -- ({\x*\dx},0.1);
+	\node at ({\x*\dx},0) [below] {$\pgfmathprintnumber{\x}$};
+}
+\draw[->] (0,{-0.1}) -- (0,{10.3}) coordinate[label={right:$y$}];
+\foreach \y in {0.5,1,1.5}{
+	%\draw[line width=0.2pt] (0,{\y*\dy}) -- (\dx,{\y*\dy});
+	\draw (-0.1,{\y*\dy}) -- (0.1,{\y*\dy});
+	\node at (0,{\y*\dy}) [left] {$\pgfmathprintnumber{\y}$};
+}
+\foreach \c in {0,10,...,100}{
+	\pgfmathparse{\c/100}
+	\xdef\k{\pgfmathresult}
+	\node[color=red!\c!blau] at ({0.02*\dx},{0.95*\dy+0.04*\c})
+		[right] {$k=\pgfmathprintnumber{\k}$};
+}
+\foreach \c in {0,10,...,100}{
+	\pgfmathparse{\c/100}
+	\xdef\k{\pgfmathresult}
+	\node[color=darkgreen!\c!blau] at ({0.98*\dx},{0.75*\dy-0.04*\c})
+		[left] {$k=\pgfmathprintnumber{\k}$};
+}
+
+\draw ({\dx-0.1},{1.571*\dy}) -- ({\dx+0.1},{1.571*\dy});
+\node at (\dx,{1.571*\dy}) [right] {$\frac{\pi}2$};
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+