From 0c784258872a10b196382edf8fd3f05be97980c9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 18 Feb 2022 22:27:29 +0100 Subject: more elliptic function stuff --- buch/chapters/110-elliptisch/images/Makefile | 7 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 57192 -> 57192 bytes buch/chapters/110-elliptisch/images/sncnlimit.pdf | Bin 0 -> 24327 bytes buch/chapters/110-elliptisch/images/sncnlimit.tex | 79 +++++++++++++++++++++ 4 files changed, 85 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/110-elliptisch/images/sncnlimit.pdf create mode 100644 buch/chapters/110-elliptisch/images/sncnlimit.tex (limited to 'buch/chapters/110-elliptisch/images') diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index d1e0afe..68322b6 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -4,7 +4,8 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ - ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf + ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ + sncnlimit.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -66,3 +67,7 @@ jacobidef.pdf: jacobidef.tex jacobi12.pdf: jacobi12.tex pdflatex jacobi12.tex + +sncnlimit.pdf: sncnlimit.tex + pdflatex sncnlimit.tex + diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 8ebd501..d11bde8 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/sncnlimit.pdf b/buch/chapters/110-elliptisch/images/sncnlimit.pdf new file mode 100644 index 0000000..c721427 Binary files /dev/null and b/buch/chapters/110-elliptisch/images/sncnlimit.pdf differ diff --git a/buch/chapters/110-elliptisch/images/sncnlimit.tex b/buch/chapters/110-elliptisch/images/sncnlimit.tex new file mode 100644 index 0000000..2b284fb --- /dev/null +++ b/buch/chapters/110-elliptisch/images/sncnlimit.tex @@ -0,0 +1,79 @@ +% +% sncnlimit.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} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{2} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\pitick#1#2{ + \draw (#1,{-0.1/\skala}) -- (#1,{0.1/\skala}); + \node at (#1,{-0.1/\skala}) [below] {$\mathstrut #2$}; +} + +\def\achsen{ + \draw[->] ({-0.1/\skala},0) -- ({6.4+0.3/\skala},0) + coordinate[label=$u$]; + \pitick{3.1415}{\pi} + \pitick{2*3.1415}{2\pi} + \draw ({-0.1/\skala},1) -- ({0.1/\skala},1); + \node at ({-0.1/\skala},1) [left] {$1$}; + \node at ({-0.1/\skala},0) [left] {$0$}; +} + +\begin{scope} +\achsen +\draw[->] (0,{-1-0.1/\skala}) -- (0,{1+0.3/\skala}) + coordinate[label={right:$y$}]; +\draw[color=red!50,line width=1.4pt] + plot[domain=0:365,samples=100] ({3.1415*\x/180},{sin(\x)}); +\draw[color=red,line width=1.4pt] + plot[domain=0:6.4,samples=100] + ({\x},{(exp(\x)-exp(-\x))/(exp(\x)+exp(-\x))}); +\node[color=red] at ({1.5*3.1415},1) + [above] {$\operatorname{sn}(u,1)=\tanh u$}; +\node[color=red] at ({1.5*3.1415},{-1+0.14}) + [above] {$\operatorname{sn}(u,0)=\sin u$}; +\end{scope} + +\begin{scope}[yshift=-2.4cm] +\achsen +\draw[->] (0,{-1-0.1/\skala}) -- (0,{1+0.3/\skala}) + coordinate[label={right:$y$}]; + +\draw[color=blue!50,line width=1.4pt] + plot[domain=0:365,samples=100] ({3.1415*\x/180},{cos(\x)}); +\draw[color=blue,line width=1.4pt] + plot[domain=0:6.4,samples=100] ({\x},{2/(exp(\x)+exp(-\x))}); +\node[color=blue] at (3.1415,{-1+0.15}) + [above] {$\operatorname{cn}(u,0)=\cos u$}; +\node[color=blue] at (3.1415,{2/(exp(3.1415)+exp(-3.1415))+0.05}) + [above] {$\operatorname{sech}u$}; +\end{scope} + +\begin{scope}[yshift=-4.8cm] +\achsen +\draw[->] (0,{-0-0.1/\skala}) -- (0,{1+0.3/\skala}) + coordinate[label={right:$y$}]; +\node[color=darkgreen] at (3.1415,1) [above] {$\operatorname{dn}(u,0) = 1$}; +\draw[color=darkgreen,line width=1.4pt] + plot[domain=0:6.4,samples=100] ({\x},{2/(exp(\x)+exp(-\x))}); +\draw[color=darkgreen!50,line width=1.4pt] + (0,1) -- (6.4,1); +\node[color=darkgreen] at (3.1415,{2/(exp(3.1415)+exp(-3.1415))+0.05}) + [above] {$\operatorname{dn}(u,1)=\operatorname{sech}u$}; +\node at (0,{-0.1/\skala}) [below] {$\mathstrut 0$}; +\end{scope} + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1