aboutsummaryrefslogtreecommitdiffstats
path: root/buch/chapters/110-elliptisch/images
diff options
context:
space:
mode:
authorAndreas Müller <andreas.mueller@ost.ch>2022-02-18 22:27:29 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2022-02-18 22:27:29 +0100
commit0c784258872a10b196382edf8fd3f05be97980c9 (patch)
tree376434831c740008ced3ee6d098440b618cf0128 /buch/chapters/110-elliptisch/images
parentMerge branch 'master' of github.com:AndreasFMueller/SeminarSpezielleFunktionen (diff)
downloadSeminarSpezielleFunktionen-0c784258872a10b196382edf8fd3f05be97980c9.tar.gz
SeminarSpezielleFunktionen-0c784258872a10b196382edf8fd3f05be97980c9.zip
more elliptic function stuff
Diffstat (limited to 'buch/chapters/110-elliptisch/images')
-rw-r--r--buch/chapters/110-elliptisch/images/Makefile7
-rw-r--r--buch/chapters/110-elliptisch/images/jacobiplots.pdfbin57192 -> 57192 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/sncnlimit.pdfbin0 -> 24327 bytes
-rw-r--r--buch/chapters/110-elliptisch/images/sncnlimit.tex79
4 files changed, 85 insertions, 1 deletions
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
--- a/buch/chapters/110-elliptisch/images/jacobiplots.pdf
+++ b/buch/chapters/110-elliptisch/images/jacobiplots.pdf
Binary files 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
--- /dev/null
+++ b/buch/chapters/110-elliptisch/images/sncnlimit.pdf
Binary files 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}
+