diff options
Diffstat (limited to '')
159 files changed, 7094 insertions, 74 deletions
diff --git a/vorlesungen/01_0f1/0f1-handout.tex b/vorlesungen/01_0f1/0f1-handout.tex new file mode 100644 index 0000000..993f4ec --- /dev/null +++ b/vorlesungen/01_0f1/0f1-handout.tex @@ -0,0 +1,11 @@ +% +% 0f1-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/01_0f1/Makefile b/vorlesungen/01_0f1/Makefile new file mode 100644 index 0000000..054a635 --- /dev/null +++ b/vorlesungen/01_0f1/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- 0f1 +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: 0f1-handout.pdf MathSem-01-0f1.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-01-0f1.pdf: MathSem-01-0f1.tex $(SOURCES) + pdflatex MathSem-01-0f1.tex + +0f1-handout.pdf: 0f1-handout.tex $(SOURCES) + pdflatex 0f1-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-01-0f1.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-01-0f1.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-01-0f1.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-01-0f1.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/01_0f1/MathSem-01-0f1.tex b/vorlesungen/01_0f1/MathSem-01-0f1.tex new file mode 100644 index 0000000..e13603f --- /dev/null +++ b/vorlesungen/01_0f1/MathSem-01-0f1.tex @@ -0,0 +1,14 @@ +% +% MathSem-01-0f1.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/01_0f1/common.tex b/vorlesungen/01_0f1/common.tex new file mode 100644 index 0000000..3c6a194 --- /dev/null +++ b/vorlesungen/01_0f1/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\mathstrut_0F_1$]{$\mathstrut_0F_1$} +\author[F.~Dünki]{Fabian Dünki} +\date[]{2.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/01_0f1/slides.tex b/vorlesungen/01_0f1/slides.tex new file mode 100644 index 0000000..d404040 --- /dev/null +++ b/vorlesungen/01_0f1/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- 0f1 +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{0f1/test.tex} diff --git a/vorlesungen/02_parzyl/Makefile b/vorlesungen/02_parzyl/Makefile new file mode 100644 index 0000000..c27b7c9 --- /dev/null +++ b/vorlesungen/02_parzyl/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- parzyl +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: parzyl-handout.pdf MathSem-02-parzyl.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-02-parzyl.pdf: MathSem-02-parzyl.tex $(SOURCES) + pdflatex MathSem-02-parzyl.tex + +parzyl-handout.pdf: parzyl-handout.tex $(SOURCES) + pdflatex parzyl-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-02-parzyl.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-02-parzyl.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-02-parzyl.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-02-parzyl.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/02_parzyl/MathSem-02-parzyl.tex b/vorlesungen/02_parzyl/MathSem-02-parzyl.tex new file mode 100644 index 0000000..4ae611b --- /dev/null +++ b/vorlesungen/02_parzyl/MathSem-02-parzyl.tex @@ -0,0 +1,14 @@ +% +% MathSem-02-parzyl.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/02_parzyl/common.tex b/vorlesungen/02_parzyl/common.tex new file mode 100644 index 0000000..885ea19 --- /dev/null +++ b/vorlesungen/02_parzyl/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[ParZyl]{Parabolische Zylinderfunktionen} +\author[T.~S.~und~A.~K.]{Thierry Schwaller und Alain Keller} +\date[]{2.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/02_parzyl/parzyl-handout.tex b/vorlesungen/02_parzyl/parzyl-handout.tex new file mode 100644 index 0000000..5647a18 --- /dev/null +++ b/vorlesungen/02_parzyl/parzyl-handout.tex @@ -0,0 +1,11 @@ +% +% parzyl-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/02_parzyl/slides.tex b/vorlesungen/02_parzyl/slides.tex new file mode 100644 index 0000000..9258394 --- /dev/null +++ b/vorlesungen/02_parzyl/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- parzyl +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{parzyl/test.tex} diff --git a/vorlesungen/03_lambertw/Makefile b/vorlesungen/03_lambertw/Makefile new file mode 100644 index 0000000..e5ffcf0 --- /dev/null +++ b/vorlesungen/03_lambertw/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- lambertw +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: lambertw-handout.pdf MathSem-03-lambertw.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-03-lambertw.pdf: MathSem-03-lambertw.tex $(SOURCES) + pdflatex MathSem-03-lambertw.tex + +lambertw-handout.pdf: lambertw-handout.tex $(SOURCES) + pdflatex lambertw-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-03-lambertw.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-03-lambertw.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-03-lambertw.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-03-lambertw.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/03_lambertw/MathSem-03-lambertw.tex b/vorlesungen/03_lambertw/MathSem-03-lambertw.tex new file mode 100644 index 0000000..9b88b28 --- /dev/null +++ b/vorlesungen/03_lambertw/MathSem-03-lambertw.tex @@ -0,0 +1,14 @@ +% +% MathSem-03-lambertw.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/03_lambertw/common.tex b/vorlesungen/03_lambertw/common.tex new file mode 100644 index 0000000..23fb4b7 --- /dev/null +++ b/vorlesungen/03_lambertw/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Lambert $W$]{Verfolgungskurven und Lambert $W$-Funktion} +\author[D.~H.~und~Y.~K.]{David Hugentobler und Yanik Kuster} +\date[]{9.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/03_lambertw/lambertw-handout.tex b/vorlesungen/03_lambertw/lambertw-handout.tex new file mode 100644 index 0000000..2dba9a8 --- /dev/null +++ b/vorlesungen/03_lambertw/lambertw-handout.tex @@ -0,0 +1,11 @@ +% +% lambertw-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/03_lambertw/slides.tex b/vorlesungen/03_lambertw/slides.tex new file mode 100644 index 0000000..42113e2 --- /dev/null +++ b/vorlesungen/03_lambertw/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- lambertw +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{lambertw/test.tex} diff --git a/vorlesungen/04_fresnel/Makefile b/vorlesungen/04_fresnel/Makefile new file mode 100644 index 0000000..2b76cd7 --- /dev/null +++ b/vorlesungen/04_fresnel/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- fresnel +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: fresnel-handout.pdf MathSem-04-fresnel.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-04-fresnel.pdf: MathSem-04-fresnel.tex $(SOURCES) + pdflatex MathSem-04-fresnel.tex + +fresnel-handout.pdf: fresnel-handout.tex $(SOURCES) + pdflatex fresnel-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-04-fresnel.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-04-fresnel.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-04-fresnel.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-04-fresnel.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/04_fresnel/MathSem-04-fresnel.tex b/vorlesungen/04_fresnel/MathSem-04-fresnel.tex new file mode 100644 index 0000000..eae6242 --- /dev/null +++ b/vorlesungen/04_fresnel/MathSem-04-fresnel.tex @@ -0,0 +1,14 @@ +% +% MathSem-04-fresnel.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/04_fresnel/common.tex b/vorlesungen/04_fresnel/common.tex new file mode 100644 index 0000000..f4d919b --- /dev/null +++ b/vorlesungen/04_fresnel/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Klothoide]{Fresnel-Integrale und Klothoide} +\author[A.~Müller]{Prof.~Dr.~Andreas Müller} +\date[]{9.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/04_fresnel/fresnel-handout.tex b/vorlesungen/04_fresnel/fresnel-handout.tex new file mode 100644 index 0000000..fc84f67 --- /dev/null +++ b/vorlesungen/04_fresnel/fresnel-handout.tex @@ -0,0 +1,11 @@ +% +% fresnel-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/04_fresnel/slides.tex b/vorlesungen/04_fresnel/slides.tex new file mode 100644 index 0000000..a46fe9e --- /dev/null +++ b/vorlesungen/04_fresnel/slides.tex @@ -0,0 +1,10 @@ +% +% slides.tex -- fresnel +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{fresnel/integrale.tex} +\folie{fresnel/numerik.tex} +\folie{fresnel/kruemmung.tex} +\folie{fresnel/klothoide.tex} +\folie{fresnel/apfel.tex} diff --git a/vorlesungen/05_nav/Makefile b/vorlesungen/05_nav/Makefile new file mode 100644 index 0000000..8cdb5b4 --- /dev/null +++ b/vorlesungen/05_nav/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- nav +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: nav-handout.pdf MathSem-05-nav.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-05-nav.pdf: MathSem-05-nav.tex $(SOURCES) + pdflatex MathSem-05-nav.tex + +nav-handout.pdf: nav-handout.tex $(SOURCES) + pdflatex nav-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-05-nav.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-05-nav.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-05-nav.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-05-nav.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/05_nav/MathSem-05-nav.tex b/vorlesungen/05_nav/MathSem-05-nav.tex new file mode 100644 index 0000000..334865d --- /dev/null +++ b/vorlesungen/05_nav/MathSem-05-nav.tex @@ -0,0 +1,14 @@ +% +% MathSem-05-nav.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/05_nav/common.tex b/vorlesungen/05_nav/common.tex new file mode 100644 index 0000000..7aad073 --- /dev/null +++ b/vorlesungen/05_nav/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Navigation]{Sphärische Navigation} +\author[E.~E.~und~M.~K.]{Enez Erdem und Marc Kühne} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/05_nav/nav-handout.tex b/vorlesungen/05_nav/nav-handout.tex new file mode 100644 index 0000000..2cce5fa --- /dev/null +++ b/vorlesungen/05_nav/nav-handout.tex @@ -0,0 +1,11 @@ +% +% nav-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/05_nav/slides.tex b/vorlesungen/05_nav/slides.tex new file mode 100644 index 0000000..d7826b1 --- /dev/null +++ b/vorlesungen/05_nav/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- nav +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{nav/test.tex} diff --git a/vorlesungen/06_fm/Makefile b/vorlesungen/06_fm/Makefile new file mode 100644 index 0000000..12ba284 --- /dev/null +++ b/vorlesungen/06_fm/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- fm +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: fm-handout.pdf MathSem-06-fm.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-06-fm.pdf: MathSem-06-fm.tex $(SOURCES) + pdflatex MathSem-06-fm.tex + +fm-handout.pdf: fm-handout.tex $(SOURCES) + pdflatex fm-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-06-fm.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-06-fm.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-06-fm.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-06-fm.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/06_fm/MathSem-06-fm.tex b/vorlesungen/06_fm/MathSem-06-fm.tex new file mode 100644 index 0000000..6809d78 --- /dev/null +++ b/vorlesungen/06_fm/MathSem-06-fm.tex @@ -0,0 +1,14 @@ +% +% MathSem-06-fm.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/06_fm/common.tex b/vorlesungen/06_fm/common.tex new file mode 100644 index 0000000..525d6fd --- /dev/null +++ b/vorlesungen/06_fm/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[FM]{Frequenzspektrum eines frequenzmodulierten Signals} +\author[Joshua Bär]{Joshua Bär} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/06_fm/fm-handout.tex b/vorlesungen/06_fm/fm-handout.tex new file mode 100644 index 0000000..9e5a7c1 --- /dev/null +++ b/vorlesungen/06_fm/fm-handout.tex @@ -0,0 +1,11 @@ +% +% fm-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/06_fm/slides.tex b/vorlesungen/06_fm/slides.tex new file mode 100644 index 0000000..ad92b00 --- /dev/null +++ b/vorlesungen/06_fm/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- fm +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{fm/test.tex} diff --git a/vorlesungen/07_kreismembran/Makefile b/vorlesungen/07_kreismembran/Makefile new file mode 100644 index 0000000..ab1762f --- /dev/null +++ b/vorlesungen/07_kreismembran/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kreismembran +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kreismembran-handout.pdf MathSem-07-kreismembran.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-07-kreismembran.pdf: MathSem-07-kreismembran.tex $(SOURCES) + pdflatex MathSem-07-kreismembran.tex + +kreismembran-handout.pdf: kreismembran-handout.tex $(SOURCES) + pdflatex kreismembran-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-07-kreismembran.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-07-kreismembran.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-07-kreismembran.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-07-kreismembran.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex b/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex new file mode 100644 index 0000000..9f4e524 --- /dev/null +++ b/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex @@ -0,0 +1,14 @@ +% +% MathSem-07-kreismembran.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/07_kreismembran/common.tex b/vorlesungen/07_kreismembran/common.tex new file mode 100644 index 0000000..7eefaaf --- /dev/null +++ b/vorlesungen/07_kreismembran/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kreis]{Schwingungen einer kreisförmigen Membran} +\author[A.~M.~V.~und~T.~T.]{Andrea Mozzini Vellen und Tim Tönz} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/07_kreismembran/kreismembran-handout.tex b/vorlesungen/07_kreismembran/kreismembran-handout.tex new file mode 100644 index 0000000..03e14fa --- /dev/null +++ b/vorlesungen/07_kreismembran/kreismembran-handout.tex @@ -0,0 +1,11 @@ +% +% kreismembran-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/07_kreismembran/slides.tex b/vorlesungen/07_kreismembran/slides.tex new file mode 100644 index 0000000..be00745 --- /dev/null +++ b/vorlesungen/07_kreismembran/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kreismembran +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kreismembran/test.tex} diff --git a/vorlesungen/08_sturmliouville/Makefile b/vorlesungen/08_sturmliouville/Makefile new file mode 100644 index 0000000..7d777b2 --- /dev/null +++ b/vorlesungen/08_sturmliouville/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- sturmliouville +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: sturmliouville-handout.pdf MathSem-08-sturmliouville.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-08-sturmliouville.pdf: MathSem-08-sturmliouville.tex $(SOURCES) + pdflatex MathSem-08-sturmliouville.tex + +sturmliouville-handout.pdf: sturmliouville-handout.tex $(SOURCES) + pdflatex sturmliouville-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-08-sturmliouville.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-08-sturmliouville.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-08-sturmliouville.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-08-sturmliouville.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex b/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex new file mode 100644 index 0000000..ce26b7f --- /dev/null +++ b/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex @@ -0,0 +1,14 @@ +% +% MathSem-08-sturmliouville.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/08_sturmliouville/common.tex b/vorlesungen/08_sturmliouville/common.tex new file mode 100644 index 0000000..d0021eb --- /dev/null +++ b/vorlesungen/08_sturmliouville/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Titel]{Sturm-Liouville-Problem} +\author[R.~H.~und~E.~L.]{Réda Haddouche und Erik Löffler} +\date[]{23.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/08_sturmliouville/slides.tex b/vorlesungen/08_sturmliouville/slides.tex new file mode 100644 index 0000000..dcb2124 --- /dev/null +++ b/vorlesungen/08_sturmliouville/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- sturmliouville +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{sturmliouville/test.tex} diff --git a/vorlesungen/08_sturmliouville/sturmliouville-handout.tex b/vorlesungen/08_sturmliouville/sturmliouville-handout.tex new file mode 100644 index 0000000..4c8eb03 --- /dev/null +++ b/vorlesungen/08_sturmliouville/sturmliouville-handout.tex @@ -0,0 +1,11 @@ +% +% sturmliouville-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/Makefile b/vorlesungen/09_hermite/Makefile new file mode 100644 index 0000000..4e185e6 --- /dev/null +++ b/vorlesungen/09_hermite/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- hermite +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: hermite-handout.pdf MathSem-09-hermite.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-09-hermite.pdf: MathSem-09-hermite.tex $(SOURCES) + pdflatex MathSem-09-hermite.tex + +hermite-handout.pdf: hermite-handout.tex $(SOURCES) + pdflatex hermite-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-09-hermite.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-09-hermite.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-09-hermite.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-09-hermite.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/09_hermite/MathSem-09-hermite.tex b/vorlesungen/09_hermite/MathSem-09-hermite.tex new file mode 100644 index 0000000..59d9213 --- /dev/null +++ b/vorlesungen/09_hermite/MathSem-09-hermite.tex @@ -0,0 +1,14 @@ +% +% MathSem-09-hermite.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/common.tex b/vorlesungen/09_hermite/common.tex new file mode 100644 index 0000000..a4ee31f --- /dev/null +++ b/vorlesungen/09_hermite/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[QM]{Rodrigues-Formeln und harmonischer Oszillator} +\author[K.~Meili]{Kevin Meili} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/09_hermite/hermite-handout.tex b/vorlesungen/09_hermite/hermite-handout.tex new file mode 100644 index 0000000..65941da --- /dev/null +++ b/vorlesungen/09_hermite/hermite-handout.tex @@ -0,0 +1,11 @@ +% +% hermite-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/slides.tex b/vorlesungen/09_hermite/slides.tex new file mode 100644 index 0000000..d74d191 --- /dev/null +++ b/vorlesungen/09_hermite/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- hermite +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{hermite/test.tex} diff --git a/vorlesungen/10_kugel/Makefile b/vorlesungen/10_kugel/Makefile new file mode 100644 index 0000000..cd35320 --- /dev/null +++ b/vorlesungen/10_kugel/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kugel +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kugel-handout.pdf MathSem-10-kugel.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-10-kugel.pdf: MathSem-10-kugel.tex $(SOURCES) + pdflatex MathSem-10-kugel.tex + +kugel-handout.pdf: kugel-handout.tex $(SOURCES) + pdflatex kugel-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-10-kugel.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-10-kugel.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-10-kugel.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-10-kugel.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/10_kugel/MathSem-10-kugel.tex b/vorlesungen/10_kugel/MathSem-10-kugel.tex new file mode 100644 index 0000000..779ac8f --- /dev/null +++ b/vorlesungen/10_kugel/MathSem-10-kugel.tex @@ -0,0 +1,14 @@ +% +% MathSem-10-kugel.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/10_kugel/common.tex b/vorlesungen/10_kugel/common.tex new file mode 100644 index 0000000..1662568 --- /dev/null +++ b/vorlesungen/10_kugel/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kugel]{Auf- und Absteigeoperatoren und Kugelfunktionen} +\author[Naoki Pross]{Naoki Pross} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/10_kugel/kugel-handout.tex b/vorlesungen/10_kugel/kugel-handout.tex new file mode 100644 index 0000000..a7973fc --- /dev/null +++ b/vorlesungen/10_kugel/kugel-handout.tex @@ -0,0 +1,11 @@ +% +% kugel-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/10_kugel/slides.tex b/vorlesungen/10_kugel/slides.tex new file mode 100644 index 0000000..885fd87 --- /dev/null +++ b/vorlesungen/10_kugel/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kugel +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kugel/test.tex} diff --git a/vorlesungen/11_kugel2/Makefile b/vorlesungen/11_kugel2/Makefile new file mode 100644 index 0000000..8fd817c --- /dev/null +++ b/vorlesungen/11_kugel2/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kugel2 +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kugel2-handout.pdf MathSem-11-kugel2.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-11-kugel2.pdf: MathSem-11-kugel2.tex $(SOURCES) + pdflatex MathSem-11-kugel2.tex + +kugel2-handout.pdf: kugel2-handout.tex $(SOURCES) + pdflatex kugel2-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-11-kugel2.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-11-kugel2.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-11-kugel2.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-11-kugel2.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/11_kugel2/MathSem-11-kugel2.tex b/vorlesungen/11_kugel2/MathSem-11-kugel2.tex new file mode 100644 index 0000000..a474bb3 --- /dev/null +++ b/vorlesungen/11_kugel2/MathSem-11-kugel2.tex @@ -0,0 +1,14 @@ +% +% MathSem-11-kugel2.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/11_kugel2/common.tex b/vorlesungen/11_kugel2/common.tex new file mode 100644 index 0000000..002e71e --- /dev/null +++ b/vorlesungen/11_kugel2/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kugel]{Auf- und Absteigeoperatoren und Kugelfunktionen} +\author[M.~Cattaneo]{Manuel Cattaneo} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/11_kugel2/kugel2-handout.tex b/vorlesungen/11_kugel2/kugel2-handout.tex new file mode 100644 index 0000000..cb6664a --- /dev/null +++ b/vorlesungen/11_kugel2/kugel2-handout.tex @@ -0,0 +1,11 @@ +% +% kugel2-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/11_kugel2/slides.tex b/vorlesungen/11_kugel2/slides.tex new file mode 100644 index 0000000..f73034e --- /dev/null +++ b/vorlesungen/11_kugel2/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kugel2 +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kugel/test.tex} diff --git a/vorlesungen/12_dreieck/Makefile b/vorlesungen/12_dreieck/Makefile new file mode 100644 index 0000000..c790f0c --- /dev/null +++ b/vorlesungen/12_dreieck/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- dreieck +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: dreieck-handout.pdf MathSem-12-dreieck.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-12-dreieck.pdf: MathSem-12-dreieck.tex $(SOURCES) + pdflatex MathSem-12-dreieck.tex + +dreieck-handout.pdf: dreieck-handout.tex $(SOURCES) + pdflatex dreieck-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-12-dreieck.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-12-dreieck.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-12-dreieck.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-12-dreieck.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/12_dreieck/MathSem-12-dreieck.tex b/vorlesungen/12_dreieck/MathSem-12-dreieck.tex new file mode 100644 index 0000000..7dbc42a --- /dev/null +++ b/vorlesungen/12_dreieck/MathSem-12-dreieck.tex @@ -0,0 +1,14 @@ +% +% MathSem-12-dreieck.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/12_dreieck/common.tex b/vorlesungen/12_dreieck/common.tex new file mode 100644 index 0000000..9414e42 --- /dev/null +++ b/vorlesungen/12_dreieck/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Dreieckstest]{Dreieckstest} +\author[A.~Müller]{Prof. Dr. Andreas Müller} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/12_dreieck/dreieck-handout.tex b/vorlesungen/12_dreieck/dreieck-handout.tex new file mode 100644 index 0000000..010bcef --- /dev/null +++ b/vorlesungen/12_dreieck/dreieck-handout.tex @@ -0,0 +1,11 @@ +% +% dreieck-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/12_dreieck/slides.tex b/vorlesungen/12_dreieck/slides.tex new file mode 100644 index 0000000..211a105 --- /dev/null +++ b/vorlesungen/12_dreieck/slides.tex @@ -0,0 +1,8 @@ +% +% slides.tex -- dreieck +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{dreieck/stichprobe.tex} +\folie{dreieck/minmax.tex} +\folie{dreieck/ordnungsstatistik.tex} diff --git a/vorlesungen/13_ellfilter/Makefile b/vorlesungen/13_ellfilter/Makefile new file mode 100644 index 0000000..dd4395a --- /dev/null +++ b/vorlesungen/13_ellfilter/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- ellfilter +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: ellfilter-handout.pdf MathSem-13-ellfilter.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-13-ellfilter.pdf: MathSem-13-ellfilter.tex $(SOURCES) + pdflatex MathSem-13-ellfilter.tex + +ellfilter-handout.pdf: ellfilter-handout.tex $(SOURCES) + pdflatex ellfilter-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-13-ellfilter.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-13-ellfilter.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-13-ellfilter.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-13-ellfilter.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex b/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex new file mode 100644 index 0000000..82198f9 --- /dev/null +++ b/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex @@ -0,0 +1,14 @@ +% +% MathSem-13-ellfilter.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/13_ellfilter/common.tex b/vorlesungen/13_ellfilter/common.tex new file mode 100644 index 0000000..7789019 --- /dev/null +++ b/vorlesungen/13_ellfilter/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Filter]{Elliptische Filter} +\author[N.~Tobler]{Nicolas Tobler} +\date[]{3.~Juni 2022} +\newboolean{presentation} + diff --git a/vorlesungen/13_ellfilter/ellfilter-handout.tex b/vorlesungen/13_ellfilter/ellfilter-handout.tex new file mode 100644 index 0000000..c39a956 --- /dev/null +++ b/vorlesungen/13_ellfilter/ellfilter-handout.tex @@ -0,0 +1,11 @@ +% +% ellfilter-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/13_ellfilter/slides.tex b/vorlesungen/13_ellfilter/slides.tex new file mode 100644 index 0000000..44e0388 --- /dev/null +++ b/vorlesungen/13_ellfilter/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- ellfilter +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{ellfilter/test.tex} diff --git a/vorlesungen/14_kra/Makefile b/vorlesungen/14_kra/Makefile new file mode 100644 index 0000000..3bf22af --- /dev/null +++ b/vorlesungen/14_kra/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kra +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kra-handout.pdf MathSem-14-kra.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-14-kra.pdf: MathSem-14-kra.tex $(SOURCES) + pdflatex MathSem-14-kra.tex + +kra-handout.pdf: kra-handout.tex $(SOURCES) + pdflatex kra-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-14-kra.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-14-kra.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-14-kra.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-14-kra.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/14_kra/MathSem-14-kra.tex b/vorlesungen/14_kra/MathSem-14-kra.tex new file mode 100644 index 0000000..f6beb19 --- /dev/null +++ b/vorlesungen/14_kra/MathSem-14-kra.tex @@ -0,0 +1,14 @@ +% +% MathSem-14-kra.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/14_kra/common.tex b/vorlesungen/14_kra/common.tex new file mode 100644 index 0000000..0d8d23a --- /dev/null +++ b/vorlesungen/14_kra/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[KRA]{Kalman, Riccati, Abel} +\author[S.~Niederer]{Samuel Niederer} +\date[]{3.~Juni 2022} +\newboolean{presentation} + diff --git a/vorlesungen/14_kra/kra-handout.tex b/vorlesungen/14_kra/kra-handout.tex new file mode 100644 index 0000000..87dc3a6 --- /dev/null +++ b/vorlesungen/14_kra/kra-handout.tex @@ -0,0 +1,11 @@ +% +% kra-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/14_kra/slides.tex b/vorlesungen/14_kra/slides.tex new file mode 100644 index 0000000..bdd1d44 --- /dev/null +++ b/vorlesungen/14_kra/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kra +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kra/test.tex} diff --git a/vorlesungen/15_laguerre/Makefile b/vorlesungen/15_laguerre/Makefile new file mode 100644 index 0000000..4dea30b --- /dev/null +++ b/vorlesungen/15_laguerre/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- laguerre +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: laguerre-handout.pdf MathSem-15-laguerre.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-15-laguerre.pdf: MathSem-15-laguerre.tex $(SOURCES) + pdflatex MathSem-15-laguerre.tex + +laguerre-handout.pdf: laguerre-handout.tex $(SOURCES) + pdflatex laguerre-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-15-laguerre.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-15-laguerre.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-15-laguerre.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-15-laguerre.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/15_laguerre/MathSem-15-laguerre.tex b/vorlesungen/15_laguerre/MathSem-15-laguerre.tex new file mode 100644 index 0000000..3c48315 --- /dev/null +++ b/vorlesungen/15_laguerre/MathSem-15-laguerre.tex @@ -0,0 +1,14 @@ +% +% MathSem-15-laguerre.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/15_laguerre/common.tex b/vorlesungen/15_laguerre/common.tex new file mode 100644 index 0000000..5db4f95 --- /dev/null +++ b/vorlesungen/15_laguerre/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Laguerre]{Laguerre Polynome} +\author[P.~Müller]{Patrik Müller} +\date[]{3.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/15_laguerre/laguerre-handout.tex b/vorlesungen/15_laguerre/laguerre-handout.tex new file mode 100644 index 0000000..8ba2101 --- /dev/null +++ b/vorlesungen/15_laguerre/laguerre-handout.tex @@ -0,0 +1,11 @@ +% +% laguerre-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/15_laguerre/slides.tex b/vorlesungen/15_laguerre/slides.tex new file mode 100644 index 0000000..7b6b91b --- /dev/null +++ b/vorlesungen/15_laguerre/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- laguerre +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{laguerre/test.tex} diff --git a/vorlesungen/16_transfer/Makefile b/vorlesungen/16_transfer/Makefile new file mode 100644 index 0000000..bc704e5 --- /dev/null +++ b/vorlesungen/16_transfer/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- transfer +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: transfer-handout.pdf MathSem-16-transfer.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-16-transfer.pdf: MathSem-16-transfer.tex $(SOURCES) + pdflatex MathSem-16-transfer.tex + +transfer-handout.pdf: transfer-handout.tex $(SOURCES) + pdflatex transfer-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-16-transfer.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-16-transfer.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-16-transfer.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-16-transfer.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/16_transfer/MathSem-16-transfer.tex b/vorlesungen/16_transfer/MathSem-16-transfer.tex new file mode 100644 index 0000000..d975f11 --- /dev/null +++ b/vorlesungen/16_transfer/MathSem-16-transfer.tex @@ -0,0 +1,14 @@ +% +% MathSem-16-transfer.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/16_transfer/common.tex b/vorlesungen/16_transfer/common.tex new file mode 100644 index 0000000..61fc97f --- /dev/null +++ b/vorlesungen/16_transfer/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Transferfunktionen]{Transferfunktionen} +\author[Marc Benz]{Marc Benz} +\date[]{} +\newboolean{presentation} + diff --git a/vorlesungen/16_transfer/slides.tex b/vorlesungen/16_transfer/slides.tex new file mode 100644 index 0000000..bcfeb20 --- /dev/null +++ b/vorlesungen/16_transfer/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- transfer +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{transfer/test.tex} diff --git a/vorlesungen/16_transfer/transfer-handout.tex b/vorlesungen/16_transfer/transfer-handout.tex new file mode 100644 index 0000000..7e48e0b --- /dev/null +++ b/vorlesungen/16_transfer/transfer-handout.tex @@ -0,0 +1,11 @@ +% +% transfer-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/17_zeta/Makefile b/vorlesungen/17_zeta/Makefile new file mode 100644 index 0000000..ca4da07 --- /dev/null +++ b/vorlesungen/17_zeta/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- zeta +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: zeta-handout.pdf MathSem-17-zeta.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-17-zeta.pdf: MathSem-17-zeta.tex $(SOURCES) + pdflatex MathSem-17-zeta.tex + +zeta-handout.pdf: zeta-handout.tex $(SOURCES) + pdflatex zeta-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-17-zeta.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-17-zeta.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-17-zeta.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-17-zeta.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/17_zeta/MathSem-17-zeta.tex b/vorlesungen/17_zeta/MathSem-17-zeta.tex new file mode 100644 index 0000000..aa2d2dc --- /dev/null +++ b/vorlesungen/17_zeta/MathSem-17-zeta.tex @@ -0,0 +1,14 @@ +% +% MathSem-17-zeta.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/17_zeta/common.tex b/vorlesungen/17_zeta/common.tex new file mode 100644 index 0000000..a5571fb --- /dev/null +++ b/vorlesungen/17_zeta/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\zeta$]{Riemann $\zeta$-Funktion} +\author[R.~Unterer]{Raphael Unterer} +\date[]{3.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/17_zeta/slides.tex b/vorlesungen/17_zeta/slides.tex new file mode 100644 index 0000000..88ff0e7 --- /dev/null +++ b/vorlesungen/17_zeta/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{zeta/test.tex} diff --git a/vorlesungen/17_zeta/zeta-handout.tex b/vorlesungen/17_zeta/zeta-handout.tex new file mode 100644 index 0000000..73d33cd --- /dev/null +++ b/vorlesungen/17_zeta/zeta-handout.tex @@ -0,0 +1,11 @@ +% +% zeta-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/18_hermiteintegrierbar/Makefile b/vorlesungen/18_hermiteintegrierbar/Makefile new file mode 100644 index 0000000..a2dfb87 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- hermiteintegrierbar +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: hermiteintegrierbar-handout.pdf MathSem-18-hermiteintegrierbar.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-18-hermiteintegrierbar.pdf: MathSem-18-hermiteintegrierbar.tex $(SOURCES) + pdflatex MathSem-18-hermiteintegrierbar.tex + +hermiteintegrierbar-handout.pdf: hermiteintegrierbar-handout.tex $(SOURCES) + pdflatex hermiteintegrierbar-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-18-hermiteintegrierbar.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-18-hermiteintegrierbar.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-18-hermiteintegrierbar.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-18-hermiteintegrierbar.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex b/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex new file mode 100644 index 0000000..7a3a647 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex @@ -0,0 +1,14 @@ +% +% MathSem-18-hermiteintegrierbar.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/18_hermiteintegrierbar/common.tex b/vorlesungen/18_hermiteintegrierbar/common.tex new file mode 100644 index 0000000..8b1c71f --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/common.tex @@ -0,0 +1,17 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\int P(t)e^{-t^2}\,dt$]{Elementare Stammfunktion für +$\displaystyle\int P(t)e^{-t^2}\,dt$?} +\author[A.~Müller]{Prof. Dr. Andreas Müller} +\date[]{} +\newboolean{presentation} + diff --git a/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex b/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex new file mode 100644 index 0000000..a466024 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex @@ -0,0 +1,11 @@ +% +% hermiteintegrierbar-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/18_hermiteintegrierbar/slides.tex b/vorlesungen/18_hermiteintegrierbar/slides.tex new file mode 100644 index 0000000..cb3bbea --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/slides.tex @@ -0,0 +1,11 @@ +% +% slides.tex -- XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{hermite/normalintegrale.tex} +\folie{hermite/normalhermite.tex} +\folie{hermite/hermiteentwicklung.tex} +\folie{hermite/loesung.tex} +\folie{hermite/skalarprodukt.tex} + diff --git a/vorlesungen/slides/0f1/Makefile.inc b/vorlesungen/slides/0f1/Makefile.inc new file mode 100644 index 0000000..a37ccfc --- /dev/null +++ b/vorlesungen/slides/0f1/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapter0f1 = \ + ../slides/0f1/test.tex diff --git a/vorlesungen/slides/0f1/chapter.tex b/vorlesungen/slides/0f1/chapter.tex new file mode 100644 index 0000000..1dadad6 --- /dev/null +++ b/vorlesungen/slides/0f1/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter 0f1 +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{0f1/test.tex} diff --git a/vorlesungen/slides/0f1/test.tex b/vorlesungen/slides/0f1/test.tex new file mode 100644 index 0000000..c212802 --- /dev/null +++ b/vorlesungen/slides/0f1/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für $\mathstrut_0F_1$} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/Makefile.inc b/vorlesungen/slides/Makefile.inc index 16e3048..dc5a538 100644 --- a/vorlesungen/slides/Makefile.inc +++ b/vorlesungen/slides/Makefile.inc @@ -4,25 +4,41 @@ # (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil # include ../slides/0/Makefile.inc -#include ../slides/1/Makefile.inc -#include ../slides/2/Makefile.inc -#include ../slides/3/Makefile.inc -#include ../slides/4/Makefile.inc -#include ../slides/5/Makefile.inc -#include ../slides/6/Makefile.inc -#include ../slides/7/Makefile.inc -#include ../slides/8/Makefile.inc +include ../slides/0f1/Makefile.inc +include ../slides/dreieck/Makefile.inc +include ../slides/ellfilter/Makefile.inc +include ../slides/fm/Makefile.inc +include ../slides/fresnel/Makefile.inc +include ../slides/hermite/Makefile.inc +include ../slides/kra/Makefile.inc +include ../slides/kreismembran/Makefile.inc +include ../slides/kugel/Makefile.inc +include ../slides/laguerre/Makefile.inc +include ../slides/lambertw/Makefile.inc +include ../slides/nav/Makefile.inc +include ../slides/parzyl/Makefile.inc +include ../slides/sturmliouville/Makefile.inc +include ../slides/transfer/Makefile.inc +include ../slides/zeta/Makefile.inc slides = \ $(chapter0) \ - $(chapter1) \ - $(chapter2) \ - $(chapter3) \ - $(chapter4) \ - $(chapter5) \ - $(chapter6) \ - $(chapter7) \ - $(chapter8) + $(chapter0f1) \ + $(chapterdreieck) \ + $(chapterellfilter) \ + $(chapterfm) \ + $(chapterfresnel) \ + $(chapterhermite) \ + $(chapterkra) \ + $(chapterkreismembran) \ + $(chapterkugel) \ + $(chapterlaguerre) \ + $(chapterlambertw) \ + $(chapternav) \ + $(chapterparzyl) \ + $(chaptersturmliouville) \ + $(chaptertransfer) \ + $(chapterzeta) diff --git a/vorlesungen/slides/dreieck/Makefile.inc b/vorlesungen/slides/dreieck/Makefile.inc new file mode 100644 index 0000000..0575397 --- /dev/null +++ b/vorlesungen/slides/dreieck/Makefile.inc @@ -0,0 +1,9 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterdreieck = \ + ../slides/dreieck/minmax.tex \ + ../slides/dreieck/ordnungsstatistik.tex \ + ../slides/dreieck/test.tex diff --git a/vorlesungen/slides/dreieck/chapter.tex b/vorlesungen/slides/dreieck/chapter.tex new file mode 100644 index 0000000..2c91eb5 --- /dev/null +++ b/vorlesungen/slides/dreieck/chapter.tex @@ -0,0 +1,8 @@ +% +% chapter.tex -- slides for chapter dreieck +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{dreieck/test.tex} +\folie{dreieck/minmax.tex} +\folie{dreieck/ordnungsstatistik.tex} diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex new file mode 100644 index 0000000..9ef8d1a --- /dev/null +++ b/vorlesungen/slides/dreieck/minmax.tex @@ -0,0 +1,65 @@ +% +% minmax.tex -- Minimum und Maximum +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Minimum und Maximum} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Maximum} +Verteilungsfunktion von +\[ +Z=\operatorname{max}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&= +P(X_1\le x\wedge\dots\wedge X_n\le x) +\\ +&= +P(X_1\le x)\cdot \ldots\cdot P(X_n\le x) +\\ +&= +F_X(x)^n +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Minimum} +Verteilungsfunktion von +\[ +Z=\operatorname{min}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&=P(\overline{ +X_1\le x\wedge\dots\wedge X_n \le x +}) +\\ +&= +1-P( +X_1> x\wedge\dots\wedge X_n > x +) +\\ +&= +1-(P(X_1>x)\cdot\ldots\cdot P(X_n>x)) +\\ +&= +1-(1-F_X(x))^n +\end{align*} +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/ordnungsstatistik.tex b/vorlesungen/slides/dreieck/ordnungsstatistik.tex new file mode 100644 index 0000000..6346953 --- /dev/null +++ b/vorlesungen/slides/dreieck/ordnungsstatistik.tex @@ -0,0 +1,19 @@ +% +% ordnungsstatistik.tex -- Ordnungsstatistik +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Ordnungstatistik} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/stichprobe.tex b/vorlesungen/slides/dreieck/stichprobe.tex new file mode 100644 index 0000000..da3a20e --- /dev/null +++ b/vorlesungen/slides/dreieck/stichprobe.tex @@ -0,0 +1,60 @@ +% +% stichprobe.tex -- Stichprobe +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Stichprobe} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Zufallsvariable} +Gegeben eine Zufallsvariable $X$ mit +Verteilungsfunktion +\[ +F_X(x) += +P(X\le x) +\] +und +Wahrscheinlichkeitsdichte +\[ +\varphi_X(x) += +\frac{d}{dx} F_X(x) +\] +\end{block} +\begin{block}{Gleichverteilung} +\[ +F(x) = \begin{cases} +0&\qquad x<0\\ +x&\qquad 0\le x \le 1\\ +1&\qquad 1<x +\end{cases} +\qquad\Rightarrow\qquad +\varphi(x) += +\begin{cases} +1&\qquad 0\le x \le 1\\ +0&\qquad\text{sonst}. +\end{cases} +\] +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Stichprobe} +$n$ Zufallsvariablen $X_1,\dots,X_n$ +\begin{itemize} +\item +alle $X_i$ haben die gleiche Verteilung wie $X$ +\item +die $X_i$ sind unabhängig +\end{itemize} +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/test.tex b/vorlesungen/slides/dreieck/test.tex new file mode 100644 index 0000000..117d03d --- /dev/null +++ b/vorlesungen/slides/dreieck/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Dreieckstest} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/ellfilter/Makefile.inc b/vorlesungen/slides/ellfilter/Makefile.inc new file mode 100644 index 0000000..1ebed3c --- /dev/null +++ b/vorlesungen/slides/ellfilter/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterellfilter = \ + ../slides/ellfilter/test.tex diff --git a/vorlesungen/slides/ellfilter/chapter.tex b/vorlesungen/slides/ellfilter/chapter.tex new file mode 100644 index 0000000..92e62cd --- /dev/null +++ b/vorlesungen/slides/ellfilter/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter ellfilter +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{ellfilter/test.tex} diff --git a/vorlesungen/slides/ellfilter/test.tex b/vorlesungen/slides/ellfilter/test.tex new file mode 100644 index 0000000..1bca5f5 --- /dev/null +++ b/vorlesungen/slides/ellfilter/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Elliptische Filter} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fm/Makefile.inc b/vorlesungen/slides/fm/Makefile.inc new file mode 100644 index 0000000..13b7fe2 --- /dev/null +++ b/vorlesungen/slides/fm/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterfm = \ + ../slides/fm/test.tex diff --git a/vorlesungen/slides/fm/chapter.tex b/vorlesungen/slides/fm/chapter.tex new file mode 100644 index 0000000..684fd63 --- /dev/null +++ b/vorlesungen/slides/fm/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter fm +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{fm/test.tex} diff --git a/vorlesungen/slides/fm/test.tex b/vorlesungen/slides/fm/test.tex new file mode 100644 index 0000000..212080b --- /dev/null +++ b/vorlesungen/slides/fm/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Frequenzspektrum eines frequenzmodulierten Signals} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/Makefile b/vorlesungen/slides/fresnel/Makefile new file mode 100644 index 0000000..77ad9a2 --- /dev/null +++ b/vorlesungen/slides/fresnel/Makefile @@ -0,0 +1,9 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: eulerpath.tex + +eulerpath.tex: eulerspirale.m + octave eulerspirale.m diff --git a/vorlesungen/slides/fresnel/Makefile.inc b/vorlesungen/slides/fresnel/Makefile.inc new file mode 100644 index 0000000..b6d11f0 --- /dev/null +++ b/vorlesungen/slides/fresnel/Makefile.inc @@ -0,0 +1,11 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterfresnel = \ + ../slides/fresnel/integrale.tex \ + ../slides/fresnel/kruemmung.tex \ + ../slides/fresnel/klothoide.tex \ + ../slides/fresnel/numerik.tex \ + ../slides/fresnel/apfel.tex diff --git a/vorlesungen/slides/fresnel/apfel.jpg b/vorlesungen/slides/fresnel/apfel.jpg Binary files differnew file mode 100644 index 0000000..96b975d --- /dev/null +++ b/vorlesungen/slides/fresnel/apfel.jpg diff --git a/vorlesungen/slides/fresnel/apfel.png b/vorlesungen/slides/fresnel/apfel.png Binary files differnew file mode 100644 index 0000000..f413852 --- /dev/null +++ b/vorlesungen/slides/fresnel/apfel.png diff --git a/vorlesungen/slides/fresnel/apfel.tex b/vorlesungen/slides/fresnel/apfel.tex new file mode 100644 index 0000000..090c3d5 --- /dev/null +++ b/vorlesungen/slides/fresnel/apfel.tex @@ -0,0 +1,32 @@ +% +% apfel.tex -- Apfelschale als Klothoide +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\input{../slides/fresnel/eulerpath.tex} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Apfelschale} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\begin{scope} +\clip(-1,-1) rectangle (7,6); +\uncover<2->{ +\node at (3.1,2.2) [rotate=-3] + {\includegraphics[width=9.4cm]{../slides/fresnel/apfel.png}}; +} +\end{scope} +\draw[color=gray!50] (0,0) rectangle (4,4); +\draw[->] (-0.5,0) -- (7.5,0) coordinate[label={$C(t)$}]; +\draw[->] (0,-0.5) -- (0,6.0) coordinate[label={left:$S(t)$}]; +\uncover<3->{ +\begin{scope}[scale=8] +\draw[color=red,opacity=0.5,line width=1.4pt] \fresnela; +\end{scope} +} +\end{tikzpicture} +\end{center} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/chapter.tex b/vorlesungen/slides/fresnel/chapter.tex new file mode 100644 index 0000000..916a3a9 --- /dev/null +++ b/vorlesungen/slides/fresnel/chapter.tex @@ -0,0 +1,10 @@ +% +% chapter.tex -- slides for chapter fresnel +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{fresnel/integrale.tex} +\folie{fresnel/kruemmung.tex} +\folie{fresnel/klothoide.tex} +\folie{fresnel/numerik.tex} +\folie{fresnel/apfel.tex} diff --git a/vorlesungen/slides/fresnel/eulerpath.tex b/vorlesungen/slides/fresnel/eulerpath.tex new file mode 100644 index 0000000..ecd0b2b --- /dev/null +++ b/vorlesungen/slides/fresnel/eulerpath.tex @@ -0,0 +1,4012 @@ +\def\fresnela{ (0,0) + -- (0.0100,0.0000) + -- (0.0200,0.0000) + -- (0.0300,0.0000) + -- (0.0400,0.0000) + -- (0.0500,0.0001) + -- (0.0600,0.0001) + -- (0.0700,0.0002) + -- (0.0800,0.0003) + -- (0.0900,0.0004) + -- (0.1000,0.0005) + -- (0.1100,0.0007) + -- (0.1200,0.0009) + -- (0.1300,0.0012) + -- (0.1400,0.0014) + -- (0.1500,0.0018) + -- (0.1600,0.0021) + -- (0.1700,0.0026) + -- (0.1800,0.0031) + -- (0.1899,0.0036) + -- (0.1999,0.0042) + -- (0.2099,0.0048) + -- (0.2199,0.0056) + -- (0.2298,0.0064) + -- (0.2398,0.0072) + -- (0.2498,0.0082) + -- (0.2597,0.0092) + -- (0.2696,0.0103) + -- (0.2796,0.0115) + -- (0.2895,0.0128) + -- (0.2994,0.0141) + -- (0.3093,0.0156) + -- (0.3192,0.0171) + -- (0.3290,0.0188) + -- (0.3389,0.0205) + -- (0.3487,0.0224) + -- (0.3585,0.0244) + -- (0.3683,0.0264) + -- (0.3780,0.0286) + -- (0.3878,0.0309) + -- (0.3975,0.0334) + -- (0.4072,0.0359) + -- (0.4168,0.0386) + -- (0.4264,0.0414) + -- (0.4359,0.0443) + -- (0.4455,0.0474) + -- (0.4549,0.0506) + -- (0.4644,0.0539) + -- (0.4738,0.0574) + -- (0.4831,0.0610) + -- (0.4923,0.0647) + -- (0.5016,0.0686) + -- (0.5107,0.0727) + -- (0.5198,0.0769) + -- (0.5288,0.0812) + -- (0.5377,0.0857) + -- (0.5466,0.0904) + -- (0.5553,0.0952) + -- (0.5640,0.1001) + -- (0.5726,0.1053) + -- (0.5811,0.1105) + -- (0.5895,0.1160) + -- (0.5978,0.1216) + -- (0.6059,0.1273) + -- (0.6140,0.1333) + -- (0.6219,0.1393) + -- (0.6298,0.1456) + -- (0.6374,0.1520) + -- (0.6450,0.1585) + -- (0.6524,0.1653) + -- (0.6597,0.1721) + -- (0.6668,0.1792) + -- (0.6737,0.1864) + -- (0.6805,0.1937) + -- (0.6871,0.2012) + -- (0.6935,0.2089) + -- (0.6998,0.2167) + -- (0.7058,0.2246) + -- (0.7117,0.2327) + -- (0.7174,0.2410) + -- (0.7228,0.2493) + -- (0.7281,0.2579) + -- (0.7331,0.2665) + -- (0.7379,0.2753) + -- (0.7425,0.2841) + -- (0.7469,0.2932) + -- (0.7510,0.3023) + -- (0.7548,0.3115) + -- (0.7584,0.3208) + -- (0.7617,0.3303) + -- (0.7648,0.3398) + -- (0.7676,0.3494) + -- (0.7702,0.3590) + -- (0.7724,0.3688) + -- (0.7744,0.3786) + -- (0.7760,0.3885) + -- (0.7774,0.3984) + -- (0.7785,0.4083) + -- (0.7793,0.4183) + -- (0.7797,0.4283) + -- (0.7799,0.4383) + -- (0.7797,0.4483) + -- (0.7793,0.4582) + -- (0.7785,0.4682) + -- (0.7774,0.4782) + -- (0.7759,0.4880) + -- (0.7741,0.4979) + -- (0.7721,0.5077) + -- (0.7696,0.5174) + -- (0.7669,0.5270) + -- (0.7638,0.5365) + -- (0.7604,0.5459) + -- (0.7567,0.5552) + -- (0.7526,0.5643) + -- (0.7482,0.5733) + -- (0.7436,0.5821) + -- (0.7385,0.5908) + -- (0.7332,0.5993) + -- (0.7276,0.6075) + -- (0.7217,0.6156) + -- (0.7154,0.6234) + -- (0.7089,0.6310) + -- (0.7021,0.6383) + -- (0.6950,0.6454) + -- (0.6877,0.6522) + -- (0.6801,0.6587) + -- (0.6722,0.6648) + -- (0.6641,0.6707) + -- (0.6558,0.6763) + -- (0.6473,0.6815) + -- (0.6386,0.6863) + -- (0.6296,0.6908) + -- (0.6205,0.6950) + -- (0.6112,0.6987) + -- (0.6018,0.7021) + -- (0.5923,0.7050) + -- (0.5826,0.7076) + -- (0.5728,0.7097) + -- (0.5630,0.7114) + -- (0.5531,0.7127) + -- (0.5431,0.7135) + -- (0.5331,0.7139) + -- (0.5231,0.7139) + -- (0.5131,0.7134) + -- (0.5032,0.7125) + -- (0.4933,0.7111) + -- (0.4834,0.7093) + -- (0.4737,0.7070) + -- (0.4641,0.7043) + -- (0.4546,0.7011) + -- (0.4453,0.6975) + -- (0.4361,0.6935) + -- 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(-0.6036,-0.3945) + -- (-0.6100,-0.4022) + -- (-0.6159,-0.4103) + -- (-0.6212,-0.4188) + -- (-0.6259,-0.4276) + -- (-0.6300,-0.4367) + -- (-0.6335,-0.4461) + -- (-0.6363,-0.4557) + -- (-0.6384,-0.4655) + -- (-0.6399,-0.4754) + -- (-0.6407,-0.4853) + -- (-0.6408,-0.4953) + -- (-0.6401,-0.5053) + -- (-0.6388,-0.5152) + -- (-0.6368,-0.5250) + -- (-0.6340,-0.5346) + -- (-0.6306,-0.5440) + -- (-0.6266,-0.5532) + -- (-0.6218,-0.5620) + -- (-0.6165,-0.5704) + -- (-0.6105,-0.5784) + -- (-0.6040,-0.5860) + -- (-0.5970,-0.5931) + -- (-0.5894,-0.5996) + -- (-0.5814,-0.6056) + -- (-0.5729,-0.6110) + -- (-0.5641,-0.6157) + -- (-0.5550,-0.6197) + -- (-0.5455,-0.6230) + -- (-0.5359,-0.6256) + -- (-0.5261,-0.6275) + -- (-0.5161,-0.6286) + -- (-0.5061,-0.6289) + -- (-0.4961,-0.6285) + -- (-0.4862,-0.6273) + -- (-0.4764,-0.6254) + -- (-0.4668,-0.6226) + -- (-0.4574,-0.6192) + -- (-0.4483,-0.6150) + -- (-0.4396,-0.6101) + -- (-0.4313,-0.6045) + -- (-0.4235,-0.5983) + -- (-0.4161,-0.5915) + -- (-0.4094,-0.5842) + -- (-0.4033,-0.5763) + -- (-0.3978,-0.5679) + -- (-0.3930,-0.5591) + -- (-0.3889,-0.5500) + -- (-0.3856,-0.5406) + -- (-0.3831,-0.5309) + -- (-0.3814,-0.5210) + -- (-0.3805,-0.5111) + -- (-0.3805,-0.5011) + -- (-0.3812,-0.4911) + -- (-0.3828,-0.4812) + -- (-0.3853,-0.4715) + -- (-0.3885,-0.4621) + -- (-0.3925,-0.4529) + -- (-0.3973,-0.4441) + -- (-0.4028,-0.4358) + -- (-0.4090,-0.4279) + -- (-0.4158,-0.4207) + -- (-0.4233,-0.4140) + -- (-0.4313,-0.4080) + -- (-0.4397,-0.4027) + -- (-0.4487,-0.3982) + -- (-0.4579,-0.3944) + -- (-0.4675,-0.3915) + -- (-0.4773,-0.3895) + -- (-0.4872,-0.3883) + -- (-0.4972,-0.3880) + -- (-0.5072,-0.3886) + -- (-0.5171,-0.3900) + -- (-0.5268,-0.3924) + -- (-0.5362,-0.3956) + -- (-0.5454,-0.3996) + -- (-0.5541,-0.4045) + -- (-0.5624,-0.4101) + -- (-0.5701,-0.4165) + -- (-0.5772,-0.4235) + -- (-0.5836,-0.4312) + -- (-0.5893,-0.4394) + -- (-0.5942,-0.4481) + -- (-0.5983,-0.4572) + -- (-0.6015,-0.4667) + -- (-0.6038,-0.4764) + -- (-0.6053,-0.4863) + -- (-0.6057,-0.4963) + -- (-0.6052,-0.5063) + -- (-0.6038,-0.5162) + -- (-0.6015,-0.5259) + -- (-0.5982,-0.5354) + -- (-0.5941,-0.5445) + -- (-0.5891,-0.5531) + -- (-0.5833,-0.5613) + -- (-0.5767,-0.5688) + -- (-0.5695,-0.5757) + -- (-0.5616,-0.5818) + -- (-0.5531,-0.5872) + -- (-0.5442,-0.5917) + -- (-0.5349,-0.5952) + -- (-0.5253,-0.5979) + -- (-0.5154,-0.5996) + -- (-0.5054,-0.6003) + -- (-0.4954,-0.6001) + -- (-0.4855,-0.5988) + -- (-0.4758,-0.5966) + -- (-0.4663,-0.5933) + -- (-0.4572,-0.5892) + -- (-0.4486,-0.5842) + -- (-0.4405,-0.5783) + -- (-0.4331,-0.5716) + -- (-0.4263,-0.5642) + -- (-0.4204,-0.5562) + -- (-0.4153,-0.5476) + -- (-0.4111,-0.5385) + -- (-0.4079,-0.5290) + -- (-0.4057,-0.5193) + -- (-0.4045,-0.5094) + -- (-0.4043,-0.4994) + -- (-0.4052,-0.4894) + -- (-0.4071,-0.4796) + -- (-0.4100,-0.4700) + -- (-0.4139,-0.4608) + -- (-0.4188,-0.4521) + -- (-0.4246,-0.4439) + -- (-0.4311,-0.4364) + -- (-0.4385,-0.4296) + -- (-0.4465,-0.4237) + -- (-0.4551,-0.4186) + -- (-0.4643,-0.4145) + -- (-0.4738,-0.4114) + -- (-0.4835,-0.4094) + -- (-0.4935,-0.4084) + -- (-0.5035,-0.4085) + -- (-0.5134,-0.4097) + -- (-0.5231,-0.4119) + -- (-0.5326,-0.4152) + -- (-0.5416,-0.4196) + -- (-0.5501,-0.4249) + -- (-0.5579,-0.4311) + -- (-0.5650,-0.4381) + -- (-0.5713,-0.4459) + -- (-0.5767,-0.4543) + -- (-0.5811,-0.4633) + -- (-0.5845,-0.4727) + -- (-0.5868,-0.4824) + -- (-0.5880,-0.4923) + -- (-0.5880,-0.5023) + -- (-0.5869,-0.5122) + -- (-0.5848,-0.5220) + -- (-0.5815,-0.5314) + -- (-0.5771,-0.5404) + -- (-0.5718,-0.5489) + -- (-0.5655,-0.5567) + -- (-0.5584,-0.5637) + -- (-0.5505,-0.5698) + -- (-0.5419,-0.5750) + -- (-0.5329,-0.5791) + -- (-0.5233,-0.5822) + -- (-0.5135,-0.5841) + -- (-0.5036,-0.5849) + -- (-0.4936,-0.5845) + -- (-0.4837,-0.5830) + -- (-0.4741,-0.5803) + -- (-0.4649,-0.5764) + -- (-0.4562,-0.5715) + -- (-0.4481,-0.5656) + -- (-0.4408,-0.5588) + -- (-0.4343,-0.5512) + -- (-0.4289,-0.5428) + -- (-0.4244,-0.5338) + -- (-0.4211,-0.5244) + -- (-0.4189,-0.5147) + -- (-0.4180,-0.5047) + -- (-0.4182,-0.4947) + -- (-0.4197,-0.4848) + -- (-0.4223,-0.4752) + -- (-0.4261,-0.4660) + -- (-0.4311,-0.4573) + -- (-0.4370,-0.4492) + -- (-0.4439,-0.4420) + -- (-0.4516,-0.4357) + -- (-0.4601,-0.4303) + -- (-0.4691,-0.4261) + -- (-0.4786,-0.4230) + -- (-0.4885,-0.4211) + -- (-0.4984,-0.4205) + -- (-0.5084,-0.4211) + -- (-0.5182,-0.4230) + -- (-0.5277,-0.4261) + -- (-0.5368,-0.4304) + -- (-0.5452,-0.4358) + -- (-0.5528,-0.4422) + -- (-0.5596,-0.4495) + -- (-0.5654,-0.4576) + -- (-0.5701,-0.4665) + -- (-0.5737,-0.4758) + -- (-0.5760,-0.4855) + -- (-0.5771,-0.4955) + -- (-0.5768,-0.5054) + -- (-0.5753,-0.5153) + -- (-0.5725,-0.5249) + -- (-0.5684,-0.5341) + -- (-0.5633,-0.5426) + -- (-0.5570,-0.5504) + -- (-0.5498,-0.5573) + -- (-0.5417,-0.5632) + -- (-0.5329,-0.5680) + -- (-0.5236,-0.5716) + -- (-0.5139,-0.5739) + -- (-0.5040,-0.5749) + -- (-0.4940,-0.5746) + -- (-0.4841,-0.5730) + -- (-0.4746,-0.5700) + -- (-0.4655,-0.5658) + -- (-0.4571,-0.5604) + -- (-0.4494,-0.5540) + -- (-0.4428,-0.5466) + -- (-0.4371,-0.5383) + -- (-0.4327,-0.5294) + -- (-0.4295,-0.5199) + -- (-0.4276,-0.5101) + -- (-0.4270,-0.5001) + -- (-0.4279,-0.4902) + -- (-0.4301,-0.4804) + -- (-0.4336,-0.4711) + -- (-0.4383,-0.4623) + -- (-0.4443,-0.4542) + -- (-0.4512,-0.4471) + -- (-0.4591,-0.4410) + -- (-0.4678,-0.4360) + -- (-0.4771,-0.4323) + -- (-0.4868,-0.4299) + -- (-0.4967,-0.4289) + -- (-0.5067,-0.4293) + -- (-0.5165,-0.4311) + -- (-0.5260,-0.4343) + -- (-0.5350,-0.4387) + -- (-0.5432,-0.4444) + -- (-0.5505,-0.4512) + -- (-0.5568,-0.4590) + -- (-0.5619,-0.4676) + -- (-0.5658,-0.4768) + -- (-0.5683,-0.4864) + -- (-0.5694,-0.4964) + -- (-0.5690,-0.5064) + -- (-0.5672,-0.5162) + -- (-0.5641,-0.5257) + -- (-0.5595,-0.5346) + -- (-0.5538,-0.5427) + -- (-0.5469,-0.5500) + -- (-0.5391,-0.5562) + -- (-0.5304,-0.5611) + -- (-0.5211,-0.5648) + -- (-0.5114,-0.5670) + -- (-0.5014,-0.5678) + -- (-0.4914,-0.5671) + -- (-0.4817,-0.5650) + -- (-0.4723,-0.5615) + -- (-0.4636,-0.5566) + -- (-0.4557,-0.5504) + -- (-0.4488,-0.5432) + -- (-0.4431,-0.5350) + -- (-0.4386,-0.5261) + -- (-0.4355,-0.5166) + -- (-0.4339,-0.5067) + -- (-0.4338,-0.4968) + -- (-0.4352,-0.4869) + -- (-0.4380,-0.4773) + -- (-0.4423,-0.4682) + -- (-0.4479,-0.4600) + -- (-0.4546,-0.4526) + -- (-0.4624,-0.4464) + -- (-0.4711,-0.4414) + -- (-0.4804,-0.4378) + -- (-0.4902,-0.4357) + -- (-0.5002,-0.4351) + -- (-0.5101,-0.4360) + -- (-0.5198,-0.4384) + -- (-0.5290,-0.4423) + -- (-0.5375,-0.4476) + -- (-0.5450,-0.4541) + -- (-0.5515,-0.4618) + -- (-0.5567,-0.4703) + -- (-0.5605,-0.4795) + -- (-0.5628,-0.4892) + -- (-0.5636,-0.4992) + -- (-0.5628,-0.5092) + -- (-0.5605,-0.5189) + -- (-0.5567,-0.5281) + -- (-0.5514,-0.5366) + -- (-0.5449,-0.5442) + -- (-0.5373,-0.5506) + -- (-0.5288,-0.5558) + -- (-0.5195,-0.5595) + -- (-0.5098,-0.5617) + -- (-0.4998,-0.5624) + -- (-0.4898,-0.5614) + -- (-0.4802,-0.5589) + -- (-0.4710,-0.5549) + -- (-0.4627,-0.5494) + -- (-0.4553,-0.5427) + -- (-0.4491,-0.5348) + -- (-0.4443,-0.5261) + -- (-0.4409,-0.5167) + -- (-0.4391,-0.5069) + -- (-0.4389,-0.4969) + -- (-0.4403,-0.4870) + -- (-0.4434,-0.4775) + -- (-0.4479,-0.4686) + -- (-0.4538,-0.4605) + -- (-0.4610,-0.4536) + -- (-0.4692,-0.4479) + -- (-0.4783,-0.4437) + -- (-0.4879,-0.4410) + -- (-0.4978,-0.4399) + -- (-0.5078,-0.4405) + -- (-0.5175,-0.4427) + -- (-0.5268,-0.4465) + -- (-0.5352,-0.4518) + -- (-0.5427,-0.4584) + -- (-0.5490,-0.4662) + -- (-0.5538,-0.4749) + -- (-0.5572,-0.4844) + -- (-0.5589,-0.4942) + -- (-0.5589,-0.5042) + -- (-0.5572,-0.5140) + -- (-0.5539,-0.5235) + -- (-0.5491,-0.5322) + -- (-0.5428,-0.5400) + -- (-0.5354,-0.5466) + -- (-0.5269,-0.5518) + -- (-0.5176,-0.5556) + -- (-0.5078,-0.5576) + -- (-0.4978,-0.5580) + -- (-0.4879,-0.5567) + -- (-0.4784,-0.5537) + -- (-0.4696,-0.5491) + -- (-0.4616,-0.5430) + -- (-0.4548,-0.5357) + -- (-0.4494,-0.5273) + -- (-0.4456,-0.5181) + -- (-0.4434,-0.5083) + -- (-0.4429,-0.4984) + -- (-0.4442,-0.4884) + -- (-0.4471,-0.4789) + -- (-0.4517,-0.4700) + -- (-0.4578,-0.4621) + -- (-0.4652,-0.4554) + -- (-0.4736,-0.4500) + -- (-0.4828,-0.4462) + -- (-0.4926,-0.4442) + -- (-0.5026,-0.4438) + -- (-0.5125,-0.4453) + -- (-0.5219,-0.4484) + -- (-0.5307,-0.4532) + -- (-0.5385,-0.4595) + -- (-0.5450,-0.4671) + -- (-0.5500,-0.4757) + -- (-0.5535,-0.4851) + -- (-0.5552,-0.4949) + -- (-0.5551,-0.5049) + -- (-0.5533,-0.5147) + -- (-0.5496,-0.5240) + -- (-0.5444,-0.5325) + -- (-0.5377,-0.5400) + -- (-0.5298,-0.5460) + -- (-0.5210,-0.5506) + -- (-0.5114,-0.5535) + -- (-0.5015,-0.5546) + -- (-0.4915,-0.5538) + -- (-0.4818,-0.5513) + -- (-0.4728,-0.5470) + -- (-0.4647,-0.5412) + -- (-0.4578,-0.5339) + -- (-0.4524,-0.5256) + -- (-0.4486,-0.5163) + -- (-0.4466,-0.5066) + -- (-0.4464,-0.4966) + -- (-0.4480,-0.4867) + -- (-0.4514,-0.4774) + -- (-0.4566,-0.4688) + -- (-0.4632,-0.4613) + -- (-0.4711,-0.4552) + -- (-0.4800,-0.4507) + -- (-0.4896,-0.4479) + -- (-0.4995,-0.4470) + -- (-0.5095,-0.4479) + -- (-0.5191,-0.4507) + -- (-0.5280,-0.4552) + -- (-0.5358,-0.4614) + -- (-0.5424,-0.4689) + -- (-0.5475,-0.4775) + -- (-0.5508,-0.4869) + -- (-0.5522,-0.4968) + -- (-0.5518,-0.5068) + -- (-0.5495,-0.5165) + -- (-0.5454,-0.5256) + -- (-0.5396,-0.5337) + -- (-0.5324,-0.5406) + -- (-0.5239,-0.5460) + -- (-0.5147,-0.5496) + -- (-0.5048,-0.5514) + -- (-0.4949,-0.5513) + -- (-0.4851,-0.5493) + -- (-0.4759,-0.5454) + -- (-0.4676,-0.5398) + -- (-0.4606,-0.5327) + -- (-0.4550,-0.5244) + -- (-0.4512,-0.5152) + -- (-0.4493,-0.5054) + -- (-0.4493,-0.4954) + -- (-0.4512,-0.4856) + -- (-0.4551,-0.4764) + -- (-0.4606,-0.4681) + -- (-0.4677,-0.4611) + -- (-0.4760,-0.4555) + -- (-0.4852,-0.4518) + -- (-0.4951,-0.4499) + -- (-0.5050,-0.4500) + -- (-0.5148,-0.4520) + -- (-0.5240,-0.4560) + -- (-0.5322,-0.4617) + -- (-0.5391,-0.4689) + -- (-0.5444,-0.4773) + -- (-0.5480,-0.4866) + -- (-0.5496,-0.4965) + -- (-0.5492,-0.5065) + -- (-0.5469,-0.5162) + -- (-0.5426,-0.5252) + -- (-0.5366,-0.5332) + -- (-0.5292,-0.5398) + -- (-0.5205,-0.5448) + -- (-0.5110,-0.5479) + -- (-0.5011,-0.5491) + -- (-0.4912,-0.5482) + -- (-0.4816,-0.5454) + -- (-0.4728,-0.5406) + -- (-0.4652,-0.5342) + -- (-0.4590,-0.5264) + -- (-0.4546,-0.5174) + -- (-0.4520,-0.5078) + -- (-0.4515,-0.4978) + -- (-0.4531,-0.4879) + -- (-0.4566,-0.4786) + -- (-0.4620,-0.4702) + -- (-0.4690,-0.4631) + -- (-0.4773,-0.4575) + -- (-0.4866,-0.4538) + -- (-0.4964,-0.4521) + -- (-0.5064,-0.4525) + -- (-0.5161,-0.4549) + -- (-0.5250,-0.4593) + -- (-0.5329,-0.4654) + -- (-0.5393,-0.4731) + -- (-0.5440,-0.4819) + -- (-0.5467,-0.4915) + -- (-0.5474,-0.5015) + -- (-0.5460,-0.5113) + -- (-0.5425,-0.5207) + -- (-0.5372,-0.5291) + -- (-0.5302,-0.5362) + -- (-0.5218,-0.5417) + -- (-0.5125,-0.5453) + -- (-0.5027,-0.5469) + -- (-0.4927,-0.5463) + -- (-0.4831,-0.5436) + -- (-0.4742,-0.5390) + -- (-0.4666,-0.5326) + -- (-0.4605,-0.5247) + -- (-0.4562,-0.5157) + -- (-0.4539,-0.5060) + -- (-0.4538,-0.4960) + -- (-0.4558,-0.4862) + -- (-0.4598,-0.4771) + -- (-0.4657,-0.4690) + -- (-0.4732,-0.4624) + -- (-0.4820,-0.4576) + -- (-0.4915,-0.4548) + -- (-0.5015,-0.4541) + -- (-0.5114,-0.4556) + -- (-0.5207,-0.4591) + -- (-0.5290,-0.4646) + -- (-0.5359,-0.4718) + -- (-0.5411,-0.4803) + -- (-0.5444,-0.4898) + -- (-0.5455,-0.4997) + -- (-0.5444,-0.5096) + -- (-0.5411,-0.5191) + -- (-0.5359,-0.5276) + -- (-0.5290,-0.5347) + -- (-0.5206,-0.5402) + -- (-0.5112,-0.5437) + -- (-0.5014,-0.5450) + -- (-0.4914,-0.5441) + -- (-0.4819,-0.5411) + -- (-0.4733,-0.5360) + -- (-0.4660,-0.5292) + -- (-0.4605,-0.5209) + -- (-0.4569,-0.5116) + -- (-0.4555,-0.5017) + -- (-0.4563,-0.4918) + -- (-0.4592,-0.4822) + -- (-0.4643,-0.4736) + -- (-0.4711,-0.4664) + -- (-0.4794,-0.4608) + -- (-0.4887,-0.4573) + -- (-0.4986,-0.4559) + -- (-0.5086,-0.4568) + -- (-0.5181,-0.4599) + -- (-0.5266,-0.4650) + -- (-0.5338,-0.4719) + -- (-0.5392,-0.4803) + -- (-0.5426,-0.4897) + -- (-0.5437,-0.4996) + -- (-0.5426,-0.5095) + -- (-0.5393,-0.5189) + -- (-0.5339,-0.5273) + -- (-0.5267,-0.5343) + -- (-0.5182,-0.5394) + -- (-0.5087,-0.5425) + -- (-0.4987,-0.5433) + -- (-0.4889,-0.5418) + -- (-0.4796,-0.5381) + -- (-0.4714,-0.5323) + -- (-0.4648,-0.5249) + -- (-0.4601,-0.5161) + -- (-0.4575,-0.5064) + -- (-0.4573,-0.4965) + -- (-0.4593,-0.4867) + -- (-0.4635,-0.4777) + -- (-0.4697,-0.4698) + -- (-0.4776,-0.4637) + -- (-0.4867,-0.4595) + -- (-0.4964,-0.4576) + -- (-0.5064,-0.4580) + -- (-0.5160,-0.4607) + -- (-0.5247,-0.4656) + -- (-0.5320,-0.4724) + -- (-0.5376,-0.4807) + -- (-0.5410,-0.4900) + -- (-0.5422,-0.4999) + -- (-0.5409,-0.5098) + -- (-0.5374,-0.5192) + -- (-0.5318,-0.5274) + -- (-0.5244,-0.5341) + -- (-0.5156,-0.5389) + -- (-0.5060,-0.5414) + -- (-0.4960,-0.5416) + -- (-0.4863,-0.5394) + -- (-0.4773,-0.5350) + -- (-0.4697,-0.5285) + -- (-0.4638,-0.5205) + -- (-0.4601,-0.5112) + -- (-0.4586,-0.5014) + -- (-0.4595,-0.4914) + -- (-0.4628,-0.4820) + -- (-0.4682,-0.4737) + -- (-0.4755,-0.4668) + -- (-0.4842,-0.4620) + -- (-0.4938,-0.4593) + -- (-0.5038,-0.4591) + -- (-0.5135,-0.4613) + -- (-0.5225,-0.4657) + -- (-0.5300,-0.4722) + -- (-0.5358,-0.4804) + -- (-0.5395,-0.4896) + -- (-0.5408,-0.4995) + -- (-0.5396,-0.5094) + -- (-0.5361,-0.5188) + -- (-0.5304,-0.5270) + -- (-0.5228,-0.5335) + -- (-0.5139,-0.5380) + -- (-0.5042,-0.5402) + -- (-0.4942,-0.5400) + -- (-0.4846,-0.5373) + -- (-0.4760,-0.5323) + -- (-0.4688,-0.5254) + -- (-0.4636,-0.5169) + -- (-0.4606,-0.5074) + -- (-0.4600,-0.4975) + -- (-0.4619,-0.4877) + -- (-0.4662,-0.4787) + -- (-0.4726,-0.4710) + -- (-0.4806,-0.4651) + -- (-0.4899,-0.4615) + -- (-0.4998,-0.4602) + -- (-0.5097,-0.4615) + -- (-0.5190,-0.4651) + -- (-0.5270,-0.4710) + -- (-0.5334,-0.4787) + -- (-0.5376,-0.4877) + -- (-0.5394,-0.4976) + -- (-0.5387,-0.5075) + -- (-0.5356,-0.5170) + -- (-0.5301,-0.5253) + -- (-0.5227,-0.5320) + -- (-0.5139,-0.5367) + -- (-0.5042,-0.5390) + -- (-0.4942,-0.5387) + -- (-0.4847,-0.5360) + -- (-0.4761,-0.5309) + -- (-0.4691,-0.5238) + -- (-0.4641,-0.5151) + -- (-0.4615,-0.5055) + -- (-0.4614,-0.4955) + -- (-0.4638,-0.4859) + -- (-0.4687,-0.4772) + -- (-0.4756,-0.4700) + -- (-0.4841,-0.4648) + -- (-0.4936,-0.4619) + -- (-0.5036,-0.4616) + -- (-0.5133,-0.4638) + -- (-0.5221,-0.4685) + -- (-0.5294,-0.4753) + -- (-0.5348,-0.4837) + -- (-0.5377,-0.4932) + -- (-0.5382,-0.5032) + -- (-0.5360,-0.5129) + -- (-0.5314,-0.5218) + -- (-0.5247,-0.5291) + -- (-0.5163,-0.5345) + -- (-0.5067,-0.5375) + -- (-0.4968,-0.5379) + -- (-0.4870,-0.5357) + -- (-0.4782,-0.5311) + -- (-0.4709,-0.5243) + -- (-0.4656,-0.5158) + -- (-0.4627,-0.5063) + -- (-0.4624,-0.4963) + -- (-0.4647,-0.4866) + -- (-0.4695,-0.4779) + -- (-0.4764,-0.4707) + -- (-0.4850,-0.4656) + -- (-0.4946,-0.4629) + -- (-0.5045,-0.4628) + -- (-0.5142,-0.4653) + -- (-0.5228,-0.4703) + -- (-0.5298,-0.4775) + -- (-0.5347,-0.4862) + -- (-0.5370,-0.4958) + -- (-0.5368,-0.5058) + -- (-0.5339,-0.5153) + -- (-0.5285,-0.5238) + -- (-0.5212,-0.5305) + -- (-0.5123,-0.5350) + -- (-0.5025,-0.5369) + -- (-0.4925,-0.5362) + -- (-0.4831,-0.5329) + -- (-0.4750,-0.5271) + -- (-0.4687,-0.5194) + -- (-0.4647,-0.5103) + -- (-0.4632,-0.5004) + -- (-0.4645,-0.4905) + -- (-0.4684,-0.4813) + -- (-0.4747,-0.4736) + -- (-0.4827,-0.4677) + -- (-0.4921,-0.4643) + -- (-0.5020,-0.4636) + -- (-0.5118,-0.4655) + -- (-0.5207,-0.4700) + -- (-0.5280,-0.4768) + -- (-0.5332,-0.4853) + -- (-0.5359,-0.4949) + -- (-0.5359,-0.5049) + -- (-0.5332,-0.5145) + -- (-0.5280,-0.5229) + -- (-0.5206,-0.5297) + -- (-0.5117,-0.5341) + -- (-0.5019,-0.5360) + -- (-0.4920,-0.5351) + -- (-0.4827,-0.5315) + -- (-0.4747,-0.5255) + -- (-0.4687,-0.5176) + -- (-0.4651,-0.5083) + -- (-0.4642,-0.4983) + -- (-0.4661,-0.4886) + -- (-0.4706,-0.4797) + -- (-0.4774,-0.4724) + -- (-0.4860,-0.4672) + -- (-0.4956,-0.4647) + -- (-0.5056,-0.4649) + -- (-0.5151,-0.4678) + -- (-0.5234,-0.4733) + -- (-0.5299,-0.4809) + -- (-0.5340,-0.4900) + -- (-0.5354,-0.4999) + -- (-0.5340,-0.5097) + -- (-0.5299,-0.5188) + -- (-0.5234,-0.5264) + -- (-0.5150,-0.5318) + -- (-0.5055,-0.5347) + -- (-0.4955,-0.5348) + -- (-0.4859,-0.5322) + -- (-0.4775,-0.5269) + -- (-0.4709,-0.5194) + -- (-0.4666,-0.5104) + -- (-0.4651,-0.5006) + -- (-0.4664,-0.4907) + -- (-0.4704,-0.4816) + -- (-0.4769,-0.4740) + -- (-0.4852,-0.4685) + -- (-0.4947,-0.4657) + -- (-0.5047,-0.4656) + -- (-0.5143,-0.4684) + -- (-0.5226,-0.4738) + -- (-0.5291,-0.4814) + -- (-0.5332,-0.4904) + -- (-0.5345,-0.5003) + -- (-0.5330,-0.5102) + -- (-0.5286,-0.5191) + -- (-0.5219,-0.5265) + -- (-0.5134,-0.5317) + -- (-0.5037,-0.5341) + -- (-0.4938,-0.5337) + -- (-0.4844,-0.5305) + -- (-0.4763,-0.5247) + -- (-0.4702,-0.5168) + -- (-0.4667,-0.5074) + -- (-0.4660,-0.4975) + -- (-0.4682,-0.4878) + -- (-0.4731,-0.4791) + -- (-0.4803,-0.4723) + -- (-0.4892,-0.4678) + -- (-0.4990,-0.4661) + -- (-0.5089,-0.4673) + -- (-0.5180,-0.4713) + -- (-0.5256,-0.4779) + -- (-0.5309,-0.4863) + -- (-0.5335,-0.4959) + -- (-0.5332,-0.5059) + -- (-0.5300,-0.5153) + -- (-0.5242,-0.5234) + -- (-0.5163,-0.5294) + -- (-0.5069,-0.5329) + -- (-0.4970,-0.5334) + -- (-0.4873,-0.5310) + -- (-0.4788,-0.5259) + -- (-0.4721,-0.5184) + -- (-0.4679,-0.5094) + -- (-0.4666,-0.4995) + -- (-0.4683,-0.4897) + -- (-0.4728,-0.4808) + -- (-0.4797,-0.4736) + -- (-0.4885,-0.4688) + -- (-0.4982,-0.4669) + -- (-0.5081,-0.4679) + -- (-0.5173,-0.4718) + -- (-0.5249,-0.4782) + -- (-0.5302,-0.4866) + -- (-0.5328,-0.4962) + -- (-0.5324,-0.5062) + -- (-0.5290,-0.5156) + -- (-0.5230,-0.5235) + -- (-0.5149,-0.5293) + -- (-0.5054,-0.5324) + -- (-0.4955,-0.5325) + -- (-0.4860,-0.5296) + -- (-0.4777,-0.5240) + -- (-0.4716,-0.5162) + -- (-0.4680,-0.5069) + -- (-0.4675,-0.4969) + -- (-0.4700,-0.4873) + -- (-0.4753,-0.4788) + -- (-0.4828,-0.4723) + -- (-0.4920,-0.4685) + -- (-0.5019,-0.4676) + -- (-0.5117,-0.4697) + -- (-0.5203,-0.4747) + -- (-0.5270,-0.4821) + -- (-0.5311,-0.4911) + -- (-0.5323,-0.5010) + -- (-0.5304,-0.5108) + -- (-0.5256,-0.5196) + -- (-0.5184,-0.5264) + -- (-0.5095,-0.5308) + -- (-0.4996,-0.5321) + -- (-0.4898,-0.5305) + -- (-0.4810,-0.5258) + -- (-0.4740,-0.5187) + -- (-0.4695,-0.5098) + -- (-0.4680,-0.5000) + -- (-0.4696,-0.4901) + -- (-0.4741,-0.4813) + -- (-0.4812,-0.4742) + -- (-0.4901,-0.4697) +} + +\def\Cplotright{ (0,0) + -- ({0.0100*\dx},{0.0100*\dy}) + -- ({0.0200*\dx},{0.0200*\dy}) + -- ({0.0300*\dx},{0.0300*\dy}) + -- ({0.0400*\dx},{0.0400*\dy}) + -- ({0.0500*\dx},{0.0500*\dy}) + -- ({0.0600*\dx},{0.0600*\dy}) + -- ({0.0700*\dx},{0.0700*\dy}) + -- ({0.0800*\dx},{0.0800*\dy}) + -- ({0.0900*\dx},{0.0900*\dy}) + -- ({0.1000*\dx},{0.1000*\dy}) + -- ({0.1100*\dx},{0.1100*\dy}) + -- ({0.1200*\dx},{0.1200*\dy}) + -- ({0.1300*\dx},{0.1300*\dy}) + -- ({0.1400*\dx},{0.1400*\dy}) + -- ({0.1500*\dx},{0.1500*\dy}) + -- ({0.1600*\dx},{0.1600*\dy}) + -- ({0.1700*\dx},{0.1700*\dy}) + -- ({0.1800*\dx},{0.1800*\dy}) + -- ({0.1900*\dx},{0.1899*\dy}) + -- ({0.2000*\dx},{0.1999*\dy}) + -- ({0.2100*\dx},{0.2099*\dy}) + -- ({0.2200*\dx},{0.2199*\dy}) + -- ({0.2300*\dx},{0.2298*\dy}) + -- ({0.2400*\dx},{0.2398*\dy}) + -- ({0.2500*\dx},{0.2498*\dy}) + -- ({0.2600*\dx},{0.2597*\dy}) + -- ({0.2700*\dx},{0.2696*\dy}) + -- ({0.2800*\dx},{0.2796*\dy}) + -- ({0.2900*\dx},{0.2895*\dy}) + -- ({0.3000*\dx},{0.2994*\dy}) + -- ({0.3100*\dx},{0.3093*\dy}) + -- ({0.3200*\dx},{0.3192*\dy}) + -- ({0.3300*\dx},{0.3290*\dy}) + -- ({0.3400*\dx},{0.3389*\dy}) + -- ({0.3500*\dx},{0.3487*\dy}) + -- ({0.3600*\dx},{0.3585*\dy}) + -- ({0.3700*\dx},{0.3683*\dy}) + -- ({0.3800*\dx},{0.3780*\dy}) + -- ({0.3900*\dx},{0.3878*\dy}) + -- ({0.4000*\dx},{0.3975*\dy}) + -- ({0.4100*\dx},{0.4072*\dy}) + -- ({0.4200*\dx},{0.4168*\dy}) + -- ({0.4300*\dx},{0.4264*\dy}) + -- ({0.4400*\dx},{0.4359*\dy}) + -- ({0.4500*\dx},{0.4455*\dy}) + -- ({0.4600*\dx},{0.4549*\dy}) + -- ({0.4700*\dx},{0.4644*\dy}) + -- ({0.4800*\dx},{0.4738*\dy}) + -- ({0.4900*\dx},{0.4831*\dy}) + -- ({0.5000*\dx},{0.4923*\dy}) + -- ({0.5100*\dx},{0.5016*\dy}) + -- ({0.5200*\dx},{0.5107*\dy}) + -- ({0.5300*\dx},{0.5198*\dy}) + -- ({0.5400*\dx},{0.5288*\dy}) + -- ({0.5500*\dx},{0.5377*\dy}) + -- ({0.5600*\dx},{0.5466*\dy}) + -- ({0.5700*\dx},{0.5553*\dy}) + -- ({0.5800*\dx},{0.5640*\dy}) + -- ({0.5900*\dx},{0.5726*\dy}) + -- ({0.6000*\dx},{0.5811*\dy}) + -- ({0.6100*\dx},{0.5895*\dy}) + -- ({0.6200*\dx},{0.5978*\dy}) + -- ({0.6300*\dx},{0.6059*\dy}) + -- ({0.6400*\dx},{0.6140*\dy}) + -- ({0.6500*\dx},{0.6219*\dy}) + -- ({0.6600*\dx},{0.6298*\dy}) + -- ({0.6700*\dx},{0.6374*\dy}) + -- ({0.6800*\dx},{0.6450*\dy}) + -- ({0.6900*\dx},{0.6524*\dy}) + -- ({0.7000*\dx},{0.6597*\dy}) + -- ({0.7100*\dx},{0.6668*\dy}) + -- ({0.7200*\dx},{0.6737*\dy}) + -- ({0.7300*\dx},{0.6805*\dy}) + -- ({0.7400*\dx},{0.6871*\dy}) + -- ({0.7500*\dx},{0.6935*\dy}) + -- ({0.7600*\dx},{0.6998*\dy}) + -- ({0.7700*\dx},{0.7058*\dy}) + -- ({0.7800*\dx},{0.7117*\dy}) + -- ({0.7900*\dx},{0.7174*\dy}) + -- ({0.8000*\dx},{0.7228*\dy}) + -- ({0.8100*\dx},{0.7281*\dy}) + -- ({0.8200*\dx},{0.7331*\dy}) + -- ({0.8300*\dx},{0.7379*\dy}) + -- ({0.8400*\dx},{0.7425*\dy}) + -- ({0.8500*\dx},{0.7469*\dy}) + -- ({0.8600*\dx},{0.7510*\dy}) + -- ({0.8700*\dx},{0.7548*\dy}) + -- ({0.8800*\dx},{0.7584*\dy}) + -- ({0.8900*\dx},{0.7617*\dy}) + -- ({0.9000*\dx},{0.7648*\dy}) + -- ({0.9100*\dx},{0.7676*\dy}) + -- ({0.9200*\dx},{0.7702*\dy}) + -- ({0.9300*\dx},{0.7724*\dy}) + -- ({0.9400*\dx},{0.7744*\dy}) + -- ({0.9500*\dx},{0.7760*\dy}) + -- ({0.9600*\dx},{0.7774*\dy}) + -- ({0.9700*\dx},{0.7785*\dy}) + -- ({0.9800*\dx},{0.7793*\dy}) + -- ({0.9900*\dx},{0.7797*\dy}) + -- ({1.0000*\dx},{0.7799*\dy}) + -- ({1.0100*\dx},{0.7797*\dy}) + -- ({1.0200*\dx},{0.7793*\dy}) + -- ({1.0300*\dx},{0.7785*\dy}) + -- ({1.0400*\dx},{0.7774*\dy}) + -- ({1.0500*\dx},{0.7759*\dy}) + -- ({1.0600*\dx},{0.7741*\dy}) + -- ({1.0700*\dx},{0.7721*\dy}) + -- ({1.0800*\dx},{0.7696*\dy}) + -- ({1.0900*\dx},{0.7669*\dy}) + -- ({1.1000*\dx},{0.7638*\dy}) + -- ({1.1100*\dx},{0.7604*\dy}) + -- ({1.1200*\dx},{0.7567*\dy}) + -- ({1.1300*\dx},{0.7526*\dy}) + -- ({1.1400*\dx},{0.7482*\dy}) + -- ({1.1500*\dx},{0.7436*\dy}) + -- ({1.1600*\dx},{0.7385*\dy}) + -- ({1.1700*\dx},{0.7332*\dy}) + -- ({1.1800*\dx},{0.7276*\dy}) + -- ({1.1900*\dx},{0.7217*\dy}) + -- ({1.2000*\dx},{0.7154*\dy}) + -- ({1.2100*\dx},{0.7089*\dy}) + -- ({1.2200*\dx},{0.7021*\dy}) + -- ({1.2300*\dx},{0.6950*\dy}) + -- ({1.2400*\dx},{0.6877*\dy}) + -- ({1.2500*\dx},{0.6801*\dy}) + -- ({1.2600*\dx},{0.6722*\dy}) + -- ({1.2700*\dx},{0.6641*\dy}) + -- ({1.2800*\dx},{0.6558*\dy}) + -- ({1.2900*\dx},{0.6473*\dy}) + -- ({1.3000*\dx},{0.6386*\dy}) + -- ({1.3100*\dx},{0.6296*\dy}) + -- ({1.3200*\dx},{0.6205*\dy}) + -- ({1.3300*\dx},{0.6112*\dy}) + -- ({1.3400*\dx},{0.6018*\dy}) + -- ({1.3500*\dx},{0.5923*\dy}) + -- ({1.3600*\dx},{0.5826*\dy}) + -- ({1.3700*\dx},{0.5728*\dy}) + -- ({1.3800*\dx},{0.5630*\dy}) + -- ({1.3900*\dx},{0.5531*\dy}) + -- ({1.4000*\dx},{0.5431*\dy}) + -- ({1.4100*\dx},{0.5331*\dy}) + -- ({1.4200*\dx},{0.5231*\dy}) + -- ({1.4300*\dx},{0.5131*\dy}) + -- ({1.4400*\dx},{0.5032*\dy}) + -- ({1.4500*\dx},{0.4933*\dy}) + -- ({1.4600*\dx},{0.4834*\dy}) + -- ({1.4700*\dx},{0.4737*\dy}) + -- ({1.4800*\dx},{0.4641*\dy}) + -- ({1.4900*\dx},{0.4546*\dy}) + -- ({1.5000*\dx},{0.4453*\dy}) + -- ({1.5100*\dx},{0.4361*\dy}) + -- ({1.5200*\dx},{0.4272*\dy}) + -- ({1.5300*\dx},{0.4185*\dy}) + -- ({1.5400*\dx},{0.4100*\dy}) + -- ({1.5500*\dx},{0.4018*\dy}) + -- ({1.5600*\dx},{0.3939*\dy}) + -- ({1.5700*\dx},{0.3862*\dy}) + -- ({1.5800*\dx},{0.3790*\dy}) + -- ({1.5900*\dx},{0.3720*\dy}) + -- ({1.6000*\dx},{0.3655*\dy}) + -- ({1.6100*\dx},{0.3593*\dy}) + -- ({1.6200*\dx},{0.3535*\dy}) + -- ({1.6300*\dx},{0.3482*\dy}) + -- ({1.6400*\dx},{0.3433*\dy}) + -- ({1.6500*\dx},{0.3388*\dy}) + -- ({1.6600*\dx},{0.3348*\dy}) + -- ({1.6700*\dx},{0.3313*\dy}) + -- ({1.6800*\dx},{0.3283*\dy}) + -- ({1.6900*\dx},{0.3258*\dy}) + -- ({1.7000*\dx},{0.3238*\dy}) + -- ({1.7100*\dx},{0.3224*\dy}) + -- ({1.7200*\dx},{0.3214*\dy}) + -- ({1.7300*\dx},{0.3211*\dy}) + -- ({1.7400*\dx},{0.3212*\dy}) + -- ({1.7500*\dx},{0.3219*\dy}) + -- ({1.7600*\dx},{0.3232*\dy}) + -- ({1.7700*\dx},{0.3250*\dy}) + -- ({1.7800*\dx},{0.3273*\dy}) + -- ({1.7900*\dx},{0.3302*\dy}) + -- ({1.8000*\dx},{0.3336*\dy}) + -- ({1.8100*\dx},{0.3376*\dy}) + -- ({1.8200*\dx},{0.3420*\dy}) + -- ({1.8300*\dx},{0.3470*\dy}) + -- ({1.8400*\dx},{0.3524*\dy}) + -- ({1.8500*\dx},{0.3584*\dy}) + -- ({1.8600*\dx},{0.3648*\dy}) + -- ({1.8700*\dx},{0.3716*\dy}) + -- ({1.8800*\dx},{0.3788*\dy}) + -- ({1.8900*\dx},{0.3865*\dy}) + -- ({1.9000*\dx},{0.3945*\dy}) + -- ({1.9100*\dx},{0.4028*\dy}) + -- ({1.9200*\dx},{0.4115*\dy}) + -- ({1.9300*\dx},{0.4204*\dy}) + -- ({1.9400*\dx},{0.4296*\dy}) + -- ({1.9500*\dx},{0.4391*\dy}) + -- ({1.9600*\dx},{0.4487*\dy}) + -- ({1.9700*\dx},{0.4584*\dy}) + -- ({1.9800*\dx},{0.4683*\dy}) + -- ({1.9900*\dx},{0.4783*\dy}) + -- ({2.0000*\dx},{0.4883*\dy}) + -- ({2.0100*\dx},{0.4982*\dy}) + -- ({2.0200*\dx},{0.5082*\dy}) + -- ({2.0300*\dx},{0.5181*\dy}) + -- ({2.0400*\dx},{0.5278*\dy}) + -- ({2.0500*\dx},{0.5374*\dy}) + -- ({2.0600*\dx},{0.5468*\dy}) + -- ({2.0700*\dx},{0.5560*\dy}) + -- ({2.0800*\dx},{0.5648*\dy}) + -- ({2.0900*\dx},{0.5734*\dy}) + -- ({2.1000*\dx},{0.5816*\dy}) + -- ({2.1100*\dx},{0.5894*\dy}) + -- ({2.1200*\dx},{0.5967*\dy}) + -- ({2.1300*\dx},{0.6036*\dy}) + -- ({2.1400*\dx},{0.6100*\dy}) + -- ({2.1500*\dx},{0.6159*\dy}) + -- ({2.1600*\dx},{0.6212*\dy}) + -- ({2.1700*\dx},{0.6259*\dy}) + -- ({2.1800*\dx},{0.6300*\dy}) + -- ({2.1900*\dx},{0.6335*\dy}) + -- ({2.2000*\dx},{0.6363*\dy}) + -- ({2.2100*\dx},{0.6384*\dy}) + -- ({2.2200*\dx},{0.6399*\dy}) + -- ({2.2300*\dx},{0.6407*\dy}) + -- ({2.2400*\dx},{0.6408*\dy}) + -- ({2.2500*\dx},{0.6401*\dy}) + -- ({2.2600*\dx},{0.6388*\dy}) + -- ({2.2700*\dx},{0.6368*\dy}) + -- ({2.2800*\dx},{0.6340*\dy}) + -- ({2.2900*\dx},{0.6306*\dy}) + -- ({2.3000*\dx},{0.6266*\dy}) + -- ({2.3100*\dx},{0.6218*\dy}) + -- ({2.3200*\dx},{0.6165*\dy}) + -- ({2.3300*\dx},{0.6105*\dy}) + -- ({2.3400*\dx},{0.6040*\dy}) + -- ({2.3500*\dx},{0.5970*\dy}) + -- ({2.3600*\dx},{0.5894*\dy}) + -- ({2.3700*\dx},{0.5814*\dy}) + -- ({2.3800*\dx},{0.5729*\dy}) + -- ({2.3900*\dx},{0.5641*\dy}) + -- ({2.4000*\dx},{0.5550*\dy}) + -- ({2.4100*\dx},{0.5455*\dy}) + -- ({2.4200*\dx},{0.5359*\dy}) + -- ({2.4300*\dx},{0.5261*\dy}) + -- ({2.4400*\dx},{0.5161*\dy}) + -- ({2.4500*\dx},{0.5061*\dy}) + -- ({2.4600*\dx},{0.4961*\dy}) + -- ({2.4700*\dx},{0.4862*\dy}) + -- ({2.4800*\dx},{0.4764*\dy}) + -- ({2.4900*\dx},{0.4668*\dy}) + -- ({2.5000*\dx},{0.4574*\dy}) + -- ({2.5100*\dx},{0.4483*\dy}) + -- ({2.5200*\dx},{0.4396*\dy}) + -- ({2.5300*\dx},{0.4313*\dy}) + -- ({2.5400*\dx},{0.4235*\dy}) + -- ({2.5500*\dx},{0.4161*\dy}) + -- ({2.5600*\dx},{0.4094*\dy}) + -- ({2.5700*\dx},{0.4033*\dy}) + -- ({2.5800*\dx},{0.3978*\dy}) + -- ({2.5900*\dx},{0.3930*\dy}) + -- ({2.6000*\dx},{0.3889*\dy}) + -- ({2.6100*\dx},{0.3856*\dy}) + -- ({2.6200*\dx},{0.3831*\dy}) + -- ({2.6300*\dx},{0.3814*\dy}) + -- ({2.6400*\dx},{0.3805*\dy}) + -- ({2.6500*\dx},{0.3805*\dy}) + -- ({2.6600*\dx},{0.3812*\dy}) + -- ({2.6700*\dx},{0.3828*\dy}) + -- ({2.6800*\dx},{0.3853*\dy}) + -- ({2.6900*\dx},{0.3885*\dy}) + -- ({2.7000*\dx},{0.3925*\dy}) + -- ({2.7100*\dx},{0.3973*\dy}) + -- ({2.7200*\dx},{0.4028*\dy}) + -- ({2.7300*\dx},{0.4090*\dy}) + -- ({2.7400*\dx},{0.4158*\dy}) + -- ({2.7500*\dx},{0.4233*\dy}) + -- ({2.7600*\dx},{0.4313*\dy}) + -- ({2.7700*\dx},{0.4397*\dy}) + -- ({2.7800*\dx},{0.4487*\dy}) + -- ({2.7900*\dx},{0.4579*\dy}) + -- ({2.8000*\dx},{0.4675*\dy}) + -- ({2.8100*\dx},{0.4773*\dy}) + -- ({2.8200*\dx},{0.4872*\dy}) + -- ({2.8300*\dx},{0.4972*\dy}) + -- ({2.8400*\dx},{0.5072*\dy}) + -- ({2.8500*\dx},{0.5171*\dy}) + -- ({2.8600*\dx},{0.5268*\dy}) + -- ({2.8700*\dx},{0.5362*\dy}) + -- ({2.8800*\dx},{0.5454*\dy}) + -- ({2.8900*\dx},{0.5541*\dy}) + -- ({2.9000*\dx},{0.5624*\dy}) + -- ({2.9100*\dx},{0.5701*\dy}) + -- ({2.9200*\dx},{0.5772*\dy}) + -- ({2.9300*\dx},{0.5836*\dy}) + -- ({2.9400*\dx},{0.5893*\dy}) + -- ({2.9500*\dx},{0.5942*\dy}) + -- ({2.9600*\dx},{0.5983*\dy}) + -- ({2.9700*\dx},{0.6015*\dy}) + -- ({2.9800*\dx},{0.6038*\dy}) + -- ({2.9900*\dx},{0.6053*\dy}) + -- ({3.0000*\dx},{0.6057*\dy}) + -- ({3.0100*\dx},{0.6052*\dy}) + -- ({3.0200*\dx},{0.6038*\dy}) + -- ({3.0300*\dx},{0.6015*\dy}) + -- ({3.0400*\dx},{0.5982*\dy}) + -- ({3.0500*\dx},{0.5941*\dy}) + -- ({3.0600*\dx},{0.5891*\dy}) + -- ({3.0700*\dx},{0.5833*\dy}) + -- ({3.0800*\dx},{0.5767*\dy}) + -- ({3.0900*\dx},{0.5695*\dy}) + -- ({3.1000*\dx},{0.5616*\dy}) + -- ({3.1100*\dx},{0.5531*\dy}) + -- ({3.1200*\dx},{0.5442*\dy}) + -- ({3.1300*\dx},{0.5349*\dy}) + -- ({3.1400*\dx},{0.5253*\dy}) + -- ({3.1500*\dx},{0.5154*\dy}) + -- ({3.1600*\dx},{0.5054*\dy}) + -- ({3.1700*\dx},{0.4954*\dy}) + -- ({3.1800*\dx},{0.4855*\dy}) + -- ({3.1900*\dx},{0.4758*\dy}) + -- ({3.2000*\dx},{0.4663*\dy}) + -- ({3.2100*\dx},{0.4572*\dy}) + -- ({3.2200*\dx},{0.4486*\dy}) + -- ({3.2300*\dx},{0.4405*\dy}) + -- ({3.2400*\dx},{0.4331*\dy}) + -- ({3.2500*\dx},{0.4263*\dy}) + -- ({3.2600*\dx},{0.4204*\dy}) + -- ({3.2700*\dx},{0.4153*\dy}) + -- ({3.2800*\dx},{0.4111*\dy}) + -- ({3.2900*\dx},{0.4079*\dy}) + -- ({3.3000*\dx},{0.4057*\dy}) + -- ({3.3100*\dx},{0.4045*\dy}) + -- ({3.3200*\dx},{0.4043*\dy}) + -- ({3.3300*\dx},{0.4052*\dy}) + -- ({3.3400*\dx},{0.4071*\dy}) + -- ({3.3500*\dx},{0.4100*\dy}) + -- ({3.3600*\dx},{0.4139*\dy}) + -- ({3.3700*\dx},{0.4188*\dy}) + -- ({3.3800*\dx},{0.4246*\dy}) + -- ({3.3900*\dx},{0.4311*\dy}) + -- ({3.4000*\dx},{0.4385*\dy}) + -- ({3.4100*\dx},{0.4465*\dy}) + -- ({3.4200*\dx},{0.4551*\dy}) + -- ({3.4300*\dx},{0.4643*\dy}) + -- ({3.4400*\dx},{0.4738*\dy}) + -- ({3.4500*\dx},{0.4835*\dy}) + -- ({3.4600*\dx},{0.4935*\dy}) + -- ({3.4700*\dx},{0.5035*\dy}) + -- ({3.4800*\dx},{0.5134*\dy}) + -- ({3.4900*\dx},{0.5231*\dy}) + -- ({3.5000*\dx},{0.5326*\dy}) + -- ({3.5100*\dx},{0.5416*\dy}) + -- ({3.5200*\dx},{0.5501*\dy}) + -- ({3.5300*\dx},{0.5579*\dy}) + -- ({3.5400*\dx},{0.5650*\dy}) + -- ({3.5500*\dx},{0.5713*\dy}) + -- ({3.5600*\dx},{0.5767*\dy}) + -- ({3.5700*\dx},{0.5811*\dy}) + -- ({3.5800*\dx},{0.5845*\dy}) + -- ({3.5900*\dx},{0.5868*\dy}) + -- ({3.6000*\dx},{0.5880*\dy}) + -- ({3.6100*\dx},{0.5880*\dy}) + -- ({3.6200*\dx},{0.5869*\dy}) + -- ({3.6300*\dx},{0.5848*\dy}) + -- ({3.6400*\dx},{0.5815*\dy}) + -- ({3.6500*\dx},{0.5771*\dy}) + -- ({3.6600*\dx},{0.5718*\dy}) + -- ({3.6700*\dx},{0.5655*\dy}) + -- ({3.6800*\dx},{0.5584*\dy}) + -- ({3.6900*\dx},{0.5505*\dy}) + -- ({3.7000*\dx},{0.5419*\dy}) + -- ({3.7100*\dx},{0.5329*\dy}) + -- ({3.7200*\dx},{0.5233*\dy}) + -- ({3.7300*\dx},{0.5135*\dy}) + -- ({3.7400*\dx},{0.5036*\dy}) + -- ({3.7500*\dx},{0.4936*\dy}) + -- ({3.7600*\dx},{0.4837*\dy}) + -- ({3.7700*\dx},{0.4741*\dy}) + -- ({3.7800*\dx},{0.4649*\dy}) + -- ({3.7900*\dx},{0.4562*\dy}) + -- ({3.8000*\dx},{0.4481*\dy}) + -- ({3.8100*\dx},{0.4408*\dy}) + -- ({3.8200*\dx},{0.4343*\dy}) + -- ({3.8300*\dx},{0.4289*\dy}) + -- ({3.8400*\dx},{0.4244*\dy}) + -- ({3.8500*\dx},{0.4211*\dy}) + -- ({3.8600*\dx},{0.4189*\dy}) + -- ({3.8700*\dx},{0.4180*\dy}) + -- ({3.8800*\dx},{0.4182*\dy}) + -- ({3.8900*\dx},{0.4197*\dy}) + -- ({3.9000*\dx},{0.4223*\dy}) + -- ({3.9100*\dx},{0.4261*\dy}) + -- ({3.9200*\dx},{0.4311*\dy}) + -- ({3.9300*\dx},{0.4370*\dy}) + -- ({3.9400*\dx},{0.4439*\dy}) + -- ({3.9500*\dx},{0.4516*\dy}) + -- ({3.9600*\dx},{0.4601*\dy}) + -- ({3.9700*\dx},{0.4691*\dy}) + -- ({3.9800*\dx},{0.4786*\dy}) + -- ({3.9900*\dx},{0.4885*\dy}) + -- ({4.0000*\dx},{0.4984*\dy}) + -- ({4.0100*\dx},{0.5084*\dy}) + -- ({4.0200*\dx},{0.5182*\dy}) + -- ({4.0300*\dx},{0.5277*\dy}) + -- ({4.0400*\dx},{0.5368*\dy}) + -- ({4.0500*\dx},{0.5452*\dy}) + -- ({4.0600*\dx},{0.5528*\dy}) + -- ({4.0700*\dx},{0.5596*\dy}) + -- ({4.0800*\dx},{0.5654*\dy}) + -- ({4.0900*\dx},{0.5701*\dy}) + -- ({4.1000*\dx},{0.5737*\dy}) + -- ({4.1100*\dx},{0.5760*\dy}) + -- ({4.1200*\dx},{0.5771*\dy}) + -- ({4.1300*\dx},{0.5768*\dy}) + -- ({4.1400*\dx},{0.5753*\dy}) + -- ({4.1500*\dx},{0.5725*\dy}) + -- ({4.1600*\dx},{0.5684*\dy}) + -- ({4.1700*\dx},{0.5633*\dy}) + -- ({4.1800*\dx},{0.5570*\dy}) + -- ({4.1900*\dx},{0.5498*\dy}) + -- ({4.2000*\dx},{0.5417*\dy}) + -- ({4.2100*\dx},{0.5329*\dy}) + -- ({4.2200*\dx},{0.5236*\dy}) + -- ({4.2300*\dx},{0.5139*\dy}) + -- ({4.2400*\dx},{0.5040*\dy}) + -- ({4.2500*\dx},{0.4940*\dy}) + -- ({4.2600*\dx},{0.4841*\dy}) + -- ({4.2700*\dx},{0.4746*\dy}) + -- ({4.2800*\dx},{0.4655*\dy}) + -- ({4.2900*\dx},{0.4571*\dy}) + -- ({4.3000*\dx},{0.4494*\dy}) + -- ({4.3100*\dx},{0.4428*\dy}) + -- ({4.3200*\dx},{0.4371*\dy}) + -- ({4.3300*\dx},{0.4327*\dy}) + -- ({4.3400*\dx},{0.4295*\dy}) + -- ({4.3500*\dx},{0.4276*\dy}) + -- ({4.3600*\dx},{0.4270*\dy}) + -- ({4.3700*\dx},{0.4279*\dy}) + -- ({4.3800*\dx},{0.4301*\dy}) + -- ({4.3900*\dx},{0.4336*\dy}) + -- ({4.4000*\dx},{0.4383*\dy}) + -- ({4.4100*\dx},{0.4443*\dy}) + -- ({4.4200*\dx},{0.4512*\dy}) + -- ({4.4300*\dx},{0.4591*\dy}) + -- ({4.4400*\dx},{0.4678*\dy}) + -- ({4.4500*\dx},{0.4771*\dy}) + -- ({4.4600*\dx},{0.4868*\dy}) + -- ({4.4700*\dx},{0.4967*\dy}) + -- ({4.4800*\dx},{0.5067*\dy}) + -- ({4.4900*\dx},{0.5165*\dy}) + -- ({4.5000*\dx},{0.5260*\dy}) + -- ({4.5100*\dx},{0.5350*\dy}) + -- ({4.5200*\dx},{0.5432*\dy}) + -- ({4.5300*\dx},{0.5505*\dy}) + -- ({4.5400*\dx},{0.5568*\dy}) + -- ({4.5500*\dx},{0.5619*\dy}) + -- ({4.5600*\dx},{0.5658*\dy}) + -- ({4.5700*\dx},{0.5683*\dy}) + -- ({4.5800*\dx},{0.5694*\dy}) + -- ({4.5900*\dx},{0.5690*\dy}) + -- ({4.6000*\dx},{0.5672*\dy}) + -- ({4.6100*\dx},{0.5641*\dy}) + -- ({4.6200*\dx},{0.5595*\dy}) + -- ({4.6300*\dx},{0.5538*\dy}) + -- ({4.6400*\dx},{0.5469*\dy}) + -- ({4.6500*\dx},{0.5391*\dy}) + -- ({4.6600*\dx},{0.5304*\dy}) + -- ({4.6700*\dx},{0.5211*\dy}) + -- ({4.6800*\dx},{0.5114*\dy}) + -- ({4.6900*\dx},{0.5014*\dy}) + -- ({4.7000*\dx},{0.4914*\dy}) + -- ({4.7100*\dx},{0.4817*\dy}) + -- ({4.7200*\dx},{0.4723*\dy}) + -- ({4.7300*\dx},{0.4636*\dy}) + -- ({4.7400*\dx},{0.4557*\dy}) + -- ({4.7500*\dx},{0.4488*\dy}) + -- ({4.7600*\dx},{0.4431*\dy}) + -- ({4.7700*\dx},{0.4386*\dy}) + -- ({4.7800*\dx},{0.4355*\dy}) + -- ({4.7900*\dx},{0.4339*\dy}) + -- ({4.8000*\dx},{0.4338*\dy}) + -- ({4.8100*\dx},{0.4352*\dy}) + -- ({4.8200*\dx},{0.4380*\dy}) + -- ({4.8300*\dx},{0.4423*\dy}) + -- ({4.8400*\dx},{0.4479*\dy}) + -- ({4.8500*\dx},{0.4546*\dy}) + -- ({4.8600*\dx},{0.4624*\dy}) + -- ({4.8700*\dx},{0.4711*\dy}) + -- ({4.8800*\dx},{0.4804*\dy}) + -- ({4.8900*\dx},{0.4902*\dy}) + -- ({4.9000*\dx},{0.5002*\dy}) + -- ({4.9100*\dx},{0.5101*\dy}) + -- ({4.9200*\dx},{0.5198*\dy}) + -- ({4.9300*\dx},{0.5290*\dy}) + -- ({4.9400*\dx},{0.5375*\dy}) + -- ({4.9500*\dx},{0.5450*\dy}) + -- ({4.9600*\dx},{0.5515*\dy}) + -- ({4.9700*\dx},{0.5567*\dy}) + -- ({4.9800*\dx},{0.5605*\dy}) + -- ({4.9900*\dx},{0.5628*\dy}) +} + +\def\Cplotleft{ (0,0) + -- ({-0.0100*\dx},{-0.0100*\dy}) + -- ({-0.0200*\dx},{-0.0200*\dy}) + -- ({-0.0300*\dx},{-0.0300*\dy}) + -- ({-0.0400*\dx},{-0.0400*\dy}) + -- ({-0.0500*\dx},{-0.0500*\dy}) + -- ({-0.0600*\dx},{-0.0600*\dy}) + -- ({-0.0700*\dx},{-0.0700*\dy}) + -- ({-0.0800*\dx},{-0.0800*\dy}) + -- ({-0.0900*\dx},{-0.0900*\dy}) + -- ({-0.1000*\dx},{-0.1000*\dy}) + -- ({-0.1100*\dx},{-0.1100*\dy}) + -- ({-0.1200*\dx},{-0.1200*\dy}) + -- ({-0.1300*\dx},{-0.1300*\dy}) + -- ({-0.1400*\dx},{-0.1400*\dy}) + -- ({-0.1500*\dx},{-0.1500*\dy}) + -- ({-0.1600*\dx},{-0.1600*\dy}) + -- ({-0.1700*\dx},{-0.1700*\dy}) + -- ({-0.1800*\dx},{-0.1800*\dy}) + -- ({-0.1900*\dx},{-0.1899*\dy}) + -- ({-0.2000*\dx},{-0.1999*\dy}) + -- ({-0.2100*\dx},{-0.2099*\dy}) + -- ({-0.2200*\dx},{-0.2199*\dy}) + -- ({-0.2300*\dx},{-0.2298*\dy}) + -- ({-0.2400*\dx},{-0.2398*\dy}) + -- ({-0.2500*\dx},{-0.2498*\dy}) + -- ({-0.2600*\dx},{-0.2597*\dy}) + -- ({-0.2700*\dx},{-0.2696*\dy}) + -- ({-0.2800*\dx},{-0.2796*\dy}) + -- ({-0.2900*\dx},{-0.2895*\dy}) + -- ({-0.3000*\dx},{-0.2994*\dy}) + -- ({-0.3100*\dx},{-0.3093*\dy}) + -- ({-0.3200*\dx},{-0.3192*\dy}) + -- ({-0.3300*\dx},{-0.3290*\dy}) + -- ({-0.3400*\dx},{-0.3389*\dy}) + -- ({-0.3500*\dx},{-0.3487*\dy}) + -- ({-0.3600*\dx},{-0.3585*\dy}) + -- ({-0.3700*\dx},{-0.3683*\dy}) + -- ({-0.3800*\dx},{-0.3780*\dy}) + -- ({-0.3900*\dx},{-0.3878*\dy}) + -- ({-0.4000*\dx},{-0.3975*\dy}) + -- ({-0.4100*\dx},{-0.4072*\dy}) + -- ({-0.4200*\dx},{-0.4168*\dy}) + -- ({-0.4300*\dx},{-0.4264*\dy}) + -- ({-0.4400*\dx},{-0.4359*\dy}) + -- ({-0.4500*\dx},{-0.4455*\dy}) + -- ({-0.4600*\dx},{-0.4549*\dy}) + -- ({-0.4700*\dx},{-0.4644*\dy}) + -- ({-0.4800*\dx},{-0.4738*\dy}) + -- ({-0.4900*\dx},{-0.4831*\dy}) + -- ({-0.5000*\dx},{-0.4923*\dy}) + -- ({-0.5100*\dx},{-0.5016*\dy}) + -- ({-0.5200*\dx},{-0.5107*\dy}) + -- ({-0.5300*\dx},{-0.5198*\dy}) + -- ({-0.5400*\dx},{-0.5288*\dy}) + -- ({-0.5500*\dx},{-0.5377*\dy}) + -- ({-0.5600*\dx},{-0.5466*\dy}) + -- ({-0.5700*\dx},{-0.5553*\dy}) + -- ({-0.5800*\dx},{-0.5640*\dy}) + -- ({-0.5900*\dx},{-0.5726*\dy}) + -- ({-0.6000*\dx},{-0.5811*\dy}) + -- ({-0.6100*\dx},{-0.5895*\dy}) + -- ({-0.6200*\dx},{-0.5978*\dy}) + -- ({-0.6300*\dx},{-0.6059*\dy}) + -- ({-0.6400*\dx},{-0.6140*\dy}) + -- ({-0.6500*\dx},{-0.6219*\dy}) + -- ({-0.6600*\dx},{-0.6298*\dy}) + -- ({-0.6700*\dx},{-0.6374*\dy}) + -- ({-0.6800*\dx},{-0.6450*\dy}) + -- ({-0.6900*\dx},{-0.6524*\dy}) + -- ({-0.7000*\dx},{-0.6597*\dy}) + -- ({-0.7100*\dx},{-0.6668*\dy}) + -- ({-0.7200*\dx},{-0.6737*\dy}) + -- ({-0.7300*\dx},{-0.6805*\dy}) + -- ({-0.7400*\dx},{-0.6871*\dy}) + -- ({-0.7500*\dx},{-0.6935*\dy}) + -- ({-0.7600*\dx},{-0.6998*\dy}) + -- ({-0.7700*\dx},{-0.7058*\dy}) + -- ({-0.7800*\dx},{-0.7117*\dy}) + -- ({-0.7900*\dx},{-0.7174*\dy}) + -- ({-0.8000*\dx},{-0.7228*\dy}) + -- ({-0.8100*\dx},{-0.7281*\dy}) + -- ({-0.8200*\dx},{-0.7331*\dy}) + -- ({-0.8300*\dx},{-0.7379*\dy}) + -- ({-0.8400*\dx},{-0.7425*\dy}) + -- ({-0.8500*\dx},{-0.7469*\dy}) + -- ({-0.8600*\dx},{-0.7510*\dy}) + -- ({-0.8700*\dx},{-0.7548*\dy}) + -- ({-0.8800*\dx},{-0.7584*\dy}) + -- ({-0.8900*\dx},{-0.7617*\dy}) + -- ({-0.9000*\dx},{-0.7648*\dy}) + -- ({-0.9100*\dx},{-0.7676*\dy}) + -- ({-0.9200*\dx},{-0.7702*\dy}) + -- ({-0.9300*\dx},{-0.7724*\dy}) + -- ({-0.9400*\dx},{-0.7744*\dy}) + -- ({-0.9500*\dx},{-0.7760*\dy}) + -- ({-0.9600*\dx},{-0.7774*\dy}) + -- ({-0.9700*\dx},{-0.7785*\dy}) + -- ({-0.9800*\dx},{-0.7793*\dy}) + -- ({-0.9900*\dx},{-0.7797*\dy}) + -- ({-1.0000*\dx},{-0.7799*\dy}) + -- ({-1.0100*\dx},{-0.7797*\dy}) + -- ({-1.0200*\dx},{-0.7793*\dy}) + -- ({-1.0300*\dx},{-0.7785*\dy}) + -- ({-1.0400*\dx},{-0.7774*\dy}) + -- ({-1.0500*\dx},{-0.7759*\dy}) + -- ({-1.0600*\dx},{-0.7741*\dy}) + -- ({-1.0700*\dx},{-0.7721*\dy}) + -- ({-1.0800*\dx},{-0.7696*\dy}) + -- ({-1.0900*\dx},{-0.7669*\dy}) + -- ({-1.1000*\dx},{-0.7638*\dy}) + -- ({-1.1100*\dx},{-0.7604*\dy}) + -- ({-1.1200*\dx},{-0.7567*\dy}) + -- ({-1.1300*\dx},{-0.7526*\dy}) + -- ({-1.1400*\dx},{-0.7482*\dy}) + -- ({-1.1500*\dx},{-0.7436*\dy}) + -- ({-1.1600*\dx},{-0.7385*\dy}) + -- ({-1.1700*\dx},{-0.7332*\dy}) + -- ({-1.1800*\dx},{-0.7276*\dy}) + -- ({-1.1900*\dx},{-0.7217*\dy}) + -- ({-1.2000*\dx},{-0.7154*\dy}) + -- ({-1.2100*\dx},{-0.7089*\dy}) + -- ({-1.2200*\dx},{-0.7021*\dy}) + -- ({-1.2300*\dx},{-0.6950*\dy}) + -- ({-1.2400*\dx},{-0.6877*\dy}) + -- ({-1.2500*\dx},{-0.6801*\dy}) + -- ({-1.2600*\dx},{-0.6722*\dy}) + -- ({-1.2700*\dx},{-0.6641*\dy}) + -- ({-1.2800*\dx},{-0.6558*\dy}) + -- ({-1.2900*\dx},{-0.6473*\dy}) + -- ({-1.3000*\dx},{-0.6386*\dy}) + -- ({-1.3100*\dx},{-0.6296*\dy}) + -- ({-1.3200*\dx},{-0.6205*\dy}) + -- ({-1.3300*\dx},{-0.6112*\dy}) + -- ({-1.3400*\dx},{-0.6018*\dy}) + -- ({-1.3500*\dx},{-0.5923*\dy}) + -- ({-1.3600*\dx},{-0.5826*\dy}) + -- ({-1.3700*\dx},{-0.5728*\dy}) + -- ({-1.3800*\dx},{-0.5630*\dy}) + -- ({-1.3900*\dx},{-0.5531*\dy}) + -- ({-1.4000*\dx},{-0.5431*\dy}) + -- ({-1.4100*\dx},{-0.5331*\dy}) + -- ({-1.4200*\dx},{-0.5231*\dy}) + -- ({-1.4300*\dx},{-0.5131*\dy}) + -- ({-1.4400*\dx},{-0.5032*\dy}) + -- ({-1.4500*\dx},{-0.4933*\dy}) + -- ({-1.4600*\dx},{-0.4834*\dy}) + -- ({-1.4700*\dx},{-0.4737*\dy}) + -- ({-1.4800*\dx},{-0.4641*\dy}) + -- ({-1.4900*\dx},{-0.4546*\dy}) + -- ({-1.5000*\dx},{-0.4453*\dy}) + -- ({-1.5100*\dx},{-0.4361*\dy}) + -- ({-1.5200*\dx},{-0.4272*\dy}) + -- ({-1.5300*\dx},{-0.4185*\dy}) + -- ({-1.5400*\dx},{-0.4100*\dy}) + -- ({-1.5500*\dx},{-0.4018*\dy}) + -- ({-1.5600*\dx},{-0.3939*\dy}) + -- ({-1.5700*\dx},{-0.3862*\dy}) + -- ({-1.5800*\dx},{-0.3790*\dy}) + -- ({-1.5900*\dx},{-0.3720*\dy}) + -- ({-1.6000*\dx},{-0.3655*\dy}) + -- ({-1.6100*\dx},{-0.3593*\dy}) + -- ({-1.6200*\dx},{-0.3535*\dy}) + -- ({-1.6300*\dx},{-0.3482*\dy}) + -- ({-1.6400*\dx},{-0.3433*\dy}) + -- ({-1.6500*\dx},{-0.3388*\dy}) + -- ({-1.6600*\dx},{-0.3348*\dy}) + -- ({-1.6700*\dx},{-0.3313*\dy}) + -- ({-1.6800*\dx},{-0.3283*\dy}) + -- ({-1.6900*\dx},{-0.3258*\dy}) + -- ({-1.7000*\dx},{-0.3238*\dy}) + -- ({-1.7100*\dx},{-0.3224*\dy}) + -- ({-1.7200*\dx},{-0.3214*\dy}) + -- ({-1.7300*\dx},{-0.3211*\dy}) + -- ({-1.7400*\dx},{-0.3212*\dy}) + -- ({-1.7500*\dx},{-0.3219*\dy}) + -- ({-1.7600*\dx},{-0.3232*\dy}) + -- ({-1.7700*\dx},{-0.3250*\dy}) + -- ({-1.7800*\dx},{-0.3273*\dy}) + -- ({-1.7900*\dx},{-0.3302*\dy}) + -- ({-1.8000*\dx},{-0.3336*\dy}) + -- ({-1.8100*\dx},{-0.3376*\dy}) + -- ({-1.8200*\dx},{-0.3420*\dy}) + -- ({-1.8300*\dx},{-0.3470*\dy}) + -- ({-1.8400*\dx},{-0.3524*\dy}) + -- ({-1.8500*\dx},{-0.3584*\dy}) + -- ({-1.8600*\dx},{-0.3648*\dy}) + -- ({-1.8700*\dx},{-0.3716*\dy}) + -- ({-1.8800*\dx},{-0.3788*\dy}) + -- ({-1.8900*\dx},{-0.3865*\dy}) + -- ({-1.9000*\dx},{-0.3945*\dy}) + -- ({-1.9100*\dx},{-0.4028*\dy}) + -- ({-1.9200*\dx},{-0.4115*\dy}) + -- ({-1.9300*\dx},{-0.4204*\dy}) + -- ({-1.9400*\dx},{-0.4296*\dy}) + -- ({-1.9500*\dx},{-0.4391*\dy}) + -- ({-1.9600*\dx},{-0.4487*\dy}) + -- ({-1.9700*\dx},{-0.4584*\dy}) + -- ({-1.9800*\dx},{-0.4683*\dy}) + -- ({-1.9900*\dx},{-0.4783*\dy}) + -- ({-2.0000*\dx},{-0.4883*\dy}) + -- ({-2.0100*\dx},{-0.4982*\dy}) + -- ({-2.0200*\dx},{-0.5082*\dy}) + -- ({-2.0300*\dx},{-0.5181*\dy}) + -- ({-2.0400*\dx},{-0.5278*\dy}) + -- ({-2.0500*\dx},{-0.5374*\dy}) + -- ({-2.0600*\dx},{-0.5468*\dy}) + -- ({-2.0700*\dx},{-0.5560*\dy}) + -- ({-2.0800*\dx},{-0.5648*\dy}) + -- ({-2.0900*\dx},{-0.5734*\dy}) + -- ({-2.1000*\dx},{-0.5816*\dy}) + -- ({-2.1100*\dx},{-0.5894*\dy}) + -- ({-2.1200*\dx},{-0.5967*\dy}) + -- ({-2.1300*\dx},{-0.6036*\dy}) + -- ({-2.1400*\dx},{-0.6100*\dy}) + -- ({-2.1500*\dx},{-0.6159*\dy}) + -- ({-2.1600*\dx},{-0.6212*\dy}) + -- ({-2.1700*\dx},{-0.6259*\dy}) + -- ({-2.1800*\dx},{-0.6300*\dy}) + -- ({-2.1900*\dx},{-0.6335*\dy}) + -- ({-2.2000*\dx},{-0.6363*\dy}) + -- ({-2.2100*\dx},{-0.6384*\dy}) + -- ({-2.2200*\dx},{-0.6399*\dy}) + -- ({-2.2300*\dx},{-0.6407*\dy}) + -- ({-2.2400*\dx},{-0.6408*\dy}) + -- ({-2.2500*\dx},{-0.6401*\dy}) + -- ({-2.2600*\dx},{-0.6388*\dy}) + -- ({-2.2700*\dx},{-0.6368*\dy}) + -- ({-2.2800*\dx},{-0.6340*\dy}) + -- ({-2.2900*\dx},{-0.6306*\dy}) + -- ({-2.3000*\dx},{-0.6266*\dy}) + -- ({-2.3100*\dx},{-0.6218*\dy}) + -- ({-2.3200*\dx},{-0.6165*\dy}) + -- ({-2.3300*\dx},{-0.6105*\dy}) + -- ({-2.3400*\dx},{-0.6040*\dy}) + -- ({-2.3500*\dx},{-0.5970*\dy}) + -- ({-2.3600*\dx},{-0.5894*\dy}) + -- ({-2.3700*\dx},{-0.5814*\dy}) + -- ({-2.3800*\dx},{-0.5729*\dy}) + -- ({-2.3900*\dx},{-0.5641*\dy}) + -- ({-2.4000*\dx},{-0.5550*\dy}) + -- ({-2.4100*\dx},{-0.5455*\dy}) + -- ({-2.4200*\dx},{-0.5359*\dy}) + -- ({-2.4300*\dx},{-0.5261*\dy}) + -- ({-2.4400*\dx},{-0.5161*\dy}) + -- ({-2.4500*\dx},{-0.5061*\dy}) + -- ({-2.4600*\dx},{-0.4961*\dy}) + -- ({-2.4700*\dx},{-0.4862*\dy}) + -- ({-2.4800*\dx},{-0.4764*\dy}) + -- ({-2.4900*\dx},{-0.4668*\dy}) + -- ({-2.5000*\dx},{-0.4574*\dy}) + -- ({-2.5100*\dx},{-0.4483*\dy}) + -- ({-2.5200*\dx},{-0.4396*\dy}) + -- ({-2.5300*\dx},{-0.4313*\dy}) + -- ({-2.5400*\dx},{-0.4235*\dy}) + -- ({-2.5500*\dx},{-0.4161*\dy}) + -- ({-2.5600*\dx},{-0.4094*\dy}) + -- ({-2.5700*\dx},{-0.4033*\dy}) + -- ({-2.5800*\dx},{-0.3978*\dy}) + -- ({-2.5900*\dx},{-0.3930*\dy}) + -- ({-2.6000*\dx},{-0.3889*\dy}) + -- ({-2.6100*\dx},{-0.3856*\dy}) + -- ({-2.6200*\dx},{-0.3831*\dy}) + -- ({-2.6300*\dx},{-0.3814*\dy}) + -- ({-2.6400*\dx},{-0.3805*\dy}) + -- ({-2.6500*\dx},{-0.3805*\dy}) + -- ({-2.6600*\dx},{-0.3812*\dy}) + -- ({-2.6700*\dx},{-0.3828*\dy}) + -- ({-2.6800*\dx},{-0.3853*\dy}) + -- ({-2.6900*\dx},{-0.3885*\dy}) + -- ({-2.7000*\dx},{-0.3925*\dy}) + -- ({-2.7100*\dx},{-0.3973*\dy}) + -- ({-2.7200*\dx},{-0.4028*\dy}) + -- ({-2.7300*\dx},{-0.4090*\dy}) + -- ({-2.7400*\dx},{-0.4158*\dy}) + -- ({-2.7500*\dx},{-0.4233*\dy}) + -- ({-2.7600*\dx},{-0.4313*\dy}) + -- ({-2.7700*\dx},{-0.4397*\dy}) + -- ({-2.7800*\dx},{-0.4487*\dy}) + -- ({-2.7900*\dx},{-0.4579*\dy}) + -- ({-2.8000*\dx},{-0.4675*\dy}) + -- ({-2.8100*\dx},{-0.4773*\dy}) + -- ({-2.8200*\dx},{-0.4872*\dy}) + -- ({-2.8300*\dx},{-0.4972*\dy}) + -- ({-2.8400*\dx},{-0.5072*\dy}) + -- ({-2.8500*\dx},{-0.5171*\dy}) + -- ({-2.8600*\dx},{-0.5268*\dy}) + -- ({-2.8700*\dx},{-0.5362*\dy}) + -- ({-2.8800*\dx},{-0.5454*\dy}) + -- ({-2.8900*\dx},{-0.5541*\dy}) + -- ({-2.9000*\dx},{-0.5624*\dy}) + -- ({-2.9100*\dx},{-0.5701*\dy}) + -- ({-2.9200*\dx},{-0.5772*\dy}) + -- ({-2.9300*\dx},{-0.5836*\dy}) + -- ({-2.9400*\dx},{-0.5893*\dy}) + -- ({-2.9500*\dx},{-0.5942*\dy}) + -- ({-2.9600*\dx},{-0.5983*\dy}) + -- ({-2.9700*\dx},{-0.6015*\dy}) + -- ({-2.9800*\dx},{-0.6038*\dy}) + -- ({-2.9900*\dx},{-0.6053*\dy}) + -- ({-3.0000*\dx},{-0.6057*\dy}) + -- ({-3.0100*\dx},{-0.6052*\dy}) + -- ({-3.0200*\dx},{-0.6038*\dy}) + -- ({-3.0300*\dx},{-0.6015*\dy}) + -- ({-3.0400*\dx},{-0.5982*\dy}) + -- ({-3.0500*\dx},{-0.5941*\dy}) + -- ({-3.0600*\dx},{-0.5891*\dy}) + -- ({-3.0700*\dx},{-0.5833*\dy}) + -- ({-3.0800*\dx},{-0.5767*\dy}) + -- ({-3.0900*\dx},{-0.5695*\dy}) + -- ({-3.1000*\dx},{-0.5616*\dy}) + -- ({-3.1100*\dx},{-0.5531*\dy}) + -- ({-3.1200*\dx},{-0.5442*\dy}) + -- ({-3.1300*\dx},{-0.5349*\dy}) + -- ({-3.1400*\dx},{-0.5253*\dy}) + -- ({-3.1500*\dx},{-0.5154*\dy}) + -- ({-3.1600*\dx},{-0.5054*\dy}) + -- ({-3.1700*\dx},{-0.4954*\dy}) + -- ({-3.1800*\dx},{-0.4855*\dy}) + -- ({-3.1900*\dx},{-0.4758*\dy}) + -- ({-3.2000*\dx},{-0.4663*\dy}) + -- ({-3.2100*\dx},{-0.4572*\dy}) + -- ({-3.2200*\dx},{-0.4486*\dy}) + -- ({-3.2300*\dx},{-0.4405*\dy}) + -- ({-3.2400*\dx},{-0.4331*\dy}) + -- ({-3.2500*\dx},{-0.4263*\dy}) + -- ({-3.2600*\dx},{-0.4204*\dy}) + -- ({-3.2700*\dx},{-0.4153*\dy}) + -- ({-3.2800*\dx},{-0.4111*\dy}) + -- ({-3.2900*\dx},{-0.4079*\dy}) + -- ({-3.3000*\dx},{-0.4057*\dy}) + -- ({-3.3100*\dx},{-0.4045*\dy}) + -- ({-3.3200*\dx},{-0.4043*\dy}) + -- ({-3.3300*\dx},{-0.4052*\dy}) + -- ({-3.3400*\dx},{-0.4071*\dy}) + -- ({-3.3500*\dx},{-0.4100*\dy}) + -- ({-3.3600*\dx},{-0.4139*\dy}) + -- ({-3.3700*\dx},{-0.4188*\dy}) + -- ({-3.3800*\dx},{-0.4246*\dy}) + -- ({-3.3900*\dx},{-0.4311*\dy}) + -- ({-3.4000*\dx},{-0.4385*\dy}) + -- ({-3.4100*\dx},{-0.4465*\dy}) + -- ({-3.4200*\dx},{-0.4551*\dy}) + -- ({-3.4300*\dx},{-0.4643*\dy}) + -- ({-3.4400*\dx},{-0.4738*\dy}) + -- ({-3.4500*\dx},{-0.4835*\dy}) + -- ({-3.4600*\dx},{-0.4935*\dy}) + -- ({-3.4700*\dx},{-0.5035*\dy}) + -- ({-3.4800*\dx},{-0.5134*\dy}) + -- ({-3.4900*\dx},{-0.5231*\dy}) + -- ({-3.5000*\dx},{-0.5326*\dy}) + -- ({-3.5100*\dx},{-0.5416*\dy}) + -- ({-3.5200*\dx},{-0.5501*\dy}) + -- ({-3.5300*\dx},{-0.5579*\dy}) + -- ({-3.5400*\dx},{-0.5650*\dy}) + -- ({-3.5500*\dx},{-0.5713*\dy}) + -- ({-3.5600*\dx},{-0.5767*\dy}) + -- ({-3.5700*\dx},{-0.5811*\dy}) + -- ({-3.5800*\dx},{-0.5845*\dy}) + -- ({-3.5900*\dx},{-0.5868*\dy}) + -- ({-3.6000*\dx},{-0.5880*\dy}) + -- ({-3.6100*\dx},{-0.5880*\dy}) + -- ({-3.6200*\dx},{-0.5869*\dy}) + -- ({-3.6300*\dx},{-0.5848*\dy}) + -- ({-3.6400*\dx},{-0.5815*\dy}) + -- ({-3.6500*\dx},{-0.5771*\dy}) + -- ({-3.6600*\dx},{-0.5718*\dy}) + -- ({-3.6700*\dx},{-0.5655*\dy}) + -- ({-3.6800*\dx},{-0.5584*\dy}) + -- ({-3.6900*\dx},{-0.5505*\dy}) + -- ({-3.7000*\dx},{-0.5419*\dy}) + -- ({-3.7100*\dx},{-0.5329*\dy}) + -- ({-3.7200*\dx},{-0.5233*\dy}) + -- ({-3.7300*\dx},{-0.5135*\dy}) + -- ({-3.7400*\dx},{-0.5036*\dy}) + -- ({-3.7500*\dx},{-0.4936*\dy}) + -- ({-3.7600*\dx},{-0.4837*\dy}) + -- ({-3.7700*\dx},{-0.4741*\dy}) + -- ({-3.7800*\dx},{-0.4649*\dy}) + -- ({-3.7900*\dx},{-0.4562*\dy}) + -- ({-3.8000*\dx},{-0.4481*\dy}) + -- ({-3.8100*\dx},{-0.4408*\dy}) + -- ({-3.8200*\dx},{-0.4343*\dy}) + -- ({-3.8300*\dx},{-0.4289*\dy}) + -- ({-3.8400*\dx},{-0.4244*\dy}) + -- ({-3.8500*\dx},{-0.4211*\dy}) + -- ({-3.8600*\dx},{-0.4189*\dy}) + -- ({-3.8700*\dx},{-0.4180*\dy}) + -- ({-3.8800*\dx},{-0.4182*\dy}) + -- ({-3.8900*\dx},{-0.4197*\dy}) + -- ({-3.9000*\dx},{-0.4223*\dy}) + -- ({-3.9100*\dx},{-0.4261*\dy}) + -- ({-3.9200*\dx},{-0.4311*\dy}) + -- ({-3.9300*\dx},{-0.4370*\dy}) + -- ({-3.9400*\dx},{-0.4439*\dy}) + -- ({-3.9500*\dx},{-0.4516*\dy}) + -- ({-3.9600*\dx},{-0.4601*\dy}) + -- ({-3.9700*\dx},{-0.4691*\dy}) + -- ({-3.9800*\dx},{-0.4786*\dy}) + -- ({-3.9900*\dx},{-0.4885*\dy}) + -- ({-4.0000*\dx},{-0.4984*\dy}) + -- ({-4.0100*\dx},{-0.5084*\dy}) + -- ({-4.0200*\dx},{-0.5182*\dy}) + -- ({-4.0300*\dx},{-0.5277*\dy}) + -- ({-4.0400*\dx},{-0.5368*\dy}) + -- ({-4.0500*\dx},{-0.5452*\dy}) + -- ({-4.0600*\dx},{-0.5528*\dy}) + -- ({-4.0700*\dx},{-0.5596*\dy}) + -- ({-4.0800*\dx},{-0.5654*\dy}) + -- ({-4.0900*\dx},{-0.5701*\dy}) + -- ({-4.1000*\dx},{-0.5737*\dy}) + -- ({-4.1100*\dx},{-0.5760*\dy}) + -- ({-4.1200*\dx},{-0.5771*\dy}) + -- ({-4.1300*\dx},{-0.5768*\dy}) + -- ({-4.1400*\dx},{-0.5753*\dy}) + -- ({-4.1500*\dx},{-0.5725*\dy}) + -- ({-4.1600*\dx},{-0.5684*\dy}) + -- ({-4.1700*\dx},{-0.5633*\dy}) + -- ({-4.1800*\dx},{-0.5570*\dy}) + -- ({-4.1900*\dx},{-0.5498*\dy}) + -- ({-4.2000*\dx},{-0.5417*\dy}) + -- ({-4.2100*\dx},{-0.5329*\dy}) + -- ({-4.2200*\dx},{-0.5236*\dy}) + -- ({-4.2300*\dx},{-0.5139*\dy}) + -- ({-4.2400*\dx},{-0.5040*\dy}) + -- ({-4.2500*\dx},{-0.4940*\dy}) + -- ({-4.2600*\dx},{-0.4841*\dy}) + -- ({-4.2700*\dx},{-0.4746*\dy}) + -- ({-4.2800*\dx},{-0.4655*\dy}) + -- ({-4.2900*\dx},{-0.4571*\dy}) + -- ({-4.3000*\dx},{-0.4494*\dy}) + -- ({-4.3100*\dx},{-0.4428*\dy}) + -- ({-4.3200*\dx},{-0.4371*\dy}) + -- ({-4.3300*\dx},{-0.4327*\dy}) + -- ({-4.3400*\dx},{-0.4295*\dy}) + -- ({-4.3500*\dx},{-0.4276*\dy}) + -- ({-4.3600*\dx},{-0.4270*\dy}) + -- ({-4.3700*\dx},{-0.4279*\dy}) + -- ({-4.3800*\dx},{-0.4301*\dy}) + -- ({-4.3900*\dx},{-0.4336*\dy}) + -- ({-4.4000*\dx},{-0.4383*\dy}) + -- ({-4.4100*\dx},{-0.4443*\dy}) + -- ({-4.4200*\dx},{-0.4512*\dy}) + -- ({-4.4300*\dx},{-0.4591*\dy}) + -- ({-4.4400*\dx},{-0.4678*\dy}) + -- ({-4.4500*\dx},{-0.4771*\dy}) + -- ({-4.4600*\dx},{-0.4868*\dy}) + -- ({-4.4700*\dx},{-0.4967*\dy}) + -- ({-4.4800*\dx},{-0.5067*\dy}) + -- ({-4.4900*\dx},{-0.5165*\dy}) + -- ({-4.5000*\dx},{-0.5260*\dy}) + -- ({-4.5100*\dx},{-0.5350*\dy}) + -- ({-4.5200*\dx},{-0.5432*\dy}) + -- ({-4.5300*\dx},{-0.5505*\dy}) + -- ({-4.5400*\dx},{-0.5568*\dy}) + -- ({-4.5500*\dx},{-0.5619*\dy}) + -- ({-4.5600*\dx},{-0.5658*\dy}) + -- ({-4.5700*\dx},{-0.5683*\dy}) + -- ({-4.5800*\dx},{-0.5694*\dy}) + -- ({-4.5900*\dx},{-0.5690*\dy}) + -- ({-4.6000*\dx},{-0.5672*\dy}) + -- ({-4.6100*\dx},{-0.5641*\dy}) + -- ({-4.6200*\dx},{-0.5595*\dy}) + -- ({-4.6300*\dx},{-0.5538*\dy}) + -- ({-4.6400*\dx},{-0.5469*\dy}) + -- ({-4.6500*\dx},{-0.5391*\dy}) + -- ({-4.6600*\dx},{-0.5304*\dy}) + -- ({-4.6700*\dx},{-0.5211*\dy}) + -- ({-4.6800*\dx},{-0.5114*\dy}) + -- ({-4.6900*\dx},{-0.5014*\dy}) + -- ({-4.7000*\dx},{-0.4914*\dy}) + -- ({-4.7100*\dx},{-0.4817*\dy}) + -- ({-4.7200*\dx},{-0.4723*\dy}) + -- ({-4.7300*\dx},{-0.4636*\dy}) + -- ({-4.7400*\dx},{-0.4557*\dy}) + -- ({-4.7500*\dx},{-0.4488*\dy}) + -- ({-4.7600*\dx},{-0.4431*\dy}) + -- ({-4.7700*\dx},{-0.4386*\dy}) + -- ({-4.7800*\dx},{-0.4355*\dy}) + -- ({-4.7900*\dx},{-0.4339*\dy}) + -- ({-4.8000*\dx},{-0.4338*\dy}) + -- ({-4.8100*\dx},{-0.4352*\dy}) + -- ({-4.8200*\dx},{-0.4380*\dy}) + -- ({-4.8300*\dx},{-0.4423*\dy}) + -- ({-4.8400*\dx},{-0.4479*\dy}) + -- ({-4.8500*\dx},{-0.4546*\dy}) + -- ({-4.8600*\dx},{-0.4624*\dy}) + -- ({-4.8700*\dx},{-0.4711*\dy}) + -- ({-4.8800*\dx},{-0.4804*\dy}) + -- ({-4.8900*\dx},{-0.4902*\dy}) + -- ({-4.9000*\dx},{-0.5002*\dy}) + -- ({-4.9100*\dx},{-0.5101*\dy}) + -- ({-4.9200*\dx},{-0.5198*\dy}) + -- ({-4.9300*\dx},{-0.5290*\dy}) + -- ({-4.9400*\dx},{-0.5375*\dy}) + -- ({-4.9500*\dx},{-0.5450*\dy}) + -- ({-4.9600*\dx},{-0.5515*\dy}) + -- ({-4.9700*\dx},{-0.5567*\dy}) + -- ({-4.9800*\dx},{-0.5605*\dy}) + -- ({-4.9900*\dx},{-0.5628*\dy}) +} + +\def\Splotright{ (0,0) + -- ({0.0100*\dx},{0.0000*\dy}) + -- ({0.0200*\dx},{0.0000*\dy}) + -- ({0.0300*\dx},{0.0000*\dy}) + -- ({0.0400*\dx},{0.0000*\dy}) + -- ({0.0500*\dx},{0.0001*\dy}) + -- ({0.0600*\dx},{0.0001*\dy}) + -- ({0.0700*\dx},{0.0002*\dy}) + -- ({0.0800*\dx},{0.0003*\dy}) + -- ({0.0900*\dx},{0.0004*\dy}) + -- ({0.1000*\dx},{0.0005*\dy}) + -- ({0.1100*\dx},{0.0007*\dy}) + -- ({0.1200*\dx},{0.0009*\dy}) + -- ({0.1300*\dx},{0.0012*\dy}) + -- ({0.1400*\dx},{0.0014*\dy}) + -- ({0.1500*\dx},{0.0018*\dy}) + -- ({0.1600*\dx},{0.0021*\dy}) + -- ({0.1700*\dx},{0.0026*\dy}) + -- ({0.1800*\dx},{0.0031*\dy}) + -- ({0.1900*\dx},{0.0036*\dy}) + -- ({0.2000*\dx},{0.0042*\dy}) + -- ({0.2100*\dx},{0.0048*\dy}) + -- ({0.2200*\dx},{0.0056*\dy}) + -- ({0.2300*\dx},{0.0064*\dy}) + -- ({0.2400*\dx},{0.0072*\dy}) + -- ({0.2500*\dx},{0.0082*\dy}) + -- ({0.2600*\dx},{0.0092*\dy}) + -- ({0.2700*\dx},{0.0103*\dy}) + -- ({0.2800*\dx},{0.0115*\dy}) + -- ({0.2900*\dx},{0.0128*\dy}) + -- ({0.3000*\dx},{0.0141*\dy}) + -- ({0.3100*\dx},{0.0156*\dy}) + -- ({0.3200*\dx},{0.0171*\dy}) + -- ({0.3300*\dx},{0.0188*\dy}) + -- ({0.3400*\dx},{0.0205*\dy}) + -- ({0.3500*\dx},{0.0224*\dy}) + -- ({0.3600*\dx},{0.0244*\dy}) + -- ({0.3700*\dx},{0.0264*\dy}) + -- ({0.3800*\dx},{0.0286*\dy}) + -- ({0.3900*\dx},{0.0309*\dy}) + -- ({0.4000*\dx},{0.0334*\dy}) + -- ({0.4100*\dx},{0.0359*\dy}) + -- ({0.4200*\dx},{0.0386*\dy}) + -- ({0.4300*\dx},{0.0414*\dy}) + -- ({0.4400*\dx},{0.0443*\dy}) + -- ({0.4500*\dx},{0.0474*\dy}) + -- ({0.4600*\dx},{0.0506*\dy}) + -- ({0.4700*\dx},{0.0539*\dy}) + -- ({0.4800*\dx},{0.0574*\dy}) + -- ({0.4900*\dx},{0.0610*\dy}) + -- ({0.5000*\dx},{0.0647*\dy}) + -- ({0.5100*\dx},{0.0686*\dy}) + -- ({0.5200*\dx},{0.0727*\dy}) + -- ({0.5300*\dx},{0.0769*\dy}) + -- ({0.5400*\dx},{0.0812*\dy}) + -- ({0.5500*\dx},{0.0857*\dy}) + -- ({0.5600*\dx},{0.0904*\dy}) + -- ({0.5700*\dx},{0.0952*\dy}) + -- ({0.5800*\dx},{0.1001*\dy}) + -- ({0.5900*\dx},{0.1053*\dy}) + -- ({0.6000*\dx},{0.1105*\dy}) + -- ({0.6100*\dx},{0.1160*\dy}) + -- ({0.6200*\dx},{0.1216*\dy}) + -- ({0.6300*\dx},{0.1273*\dy}) + -- ({0.6400*\dx},{0.1333*\dy}) + -- ({0.6500*\dx},{0.1393*\dy}) + -- ({0.6600*\dx},{0.1456*\dy}) + -- ({0.6700*\dx},{0.1520*\dy}) + -- ({0.6800*\dx},{0.1585*\dy}) + -- ({0.6900*\dx},{0.1653*\dy}) + -- ({0.7000*\dx},{0.1721*\dy}) + -- ({0.7100*\dx},{0.1792*\dy}) + -- ({0.7200*\dx},{0.1864*\dy}) + -- ({0.7300*\dx},{0.1937*\dy}) + -- ({0.7400*\dx},{0.2012*\dy}) + -- ({0.7500*\dx},{0.2089*\dy}) + -- ({0.7600*\dx},{0.2167*\dy}) + -- ({0.7700*\dx},{0.2246*\dy}) + -- ({0.7800*\dx},{0.2327*\dy}) + -- ({0.7900*\dx},{0.2410*\dy}) + -- ({0.8000*\dx},{0.2493*\dy}) + -- ({0.8100*\dx},{0.2579*\dy}) + -- ({0.8200*\dx},{0.2665*\dy}) + -- ({0.8300*\dx},{0.2753*\dy}) + -- ({0.8400*\dx},{0.2841*\dy}) + -- ({0.8500*\dx},{0.2932*\dy}) + -- ({0.8600*\dx},{0.3023*\dy}) + -- ({0.8700*\dx},{0.3115*\dy}) + -- ({0.8800*\dx},{0.3208*\dy}) + -- ({0.8900*\dx},{0.3303*\dy}) + -- ({0.9000*\dx},{0.3398*\dy}) + -- ({0.9100*\dx},{0.3494*\dy}) + -- ({0.9200*\dx},{0.3590*\dy}) + -- ({0.9300*\dx},{0.3688*\dy}) + -- ({0.9400*\dx},{0.3786*\dy}) + -- ({0.9500*\dx},{0.3885*\dy}) + -- ({0.9600*\dx},{0.3984*\dy}) + -- ({0.9700*\dx},{0.4083*\dy}) + -- ({0.9800*\dx},{0.4183*\dy}) + -- ({0.9900*\dx},{0.4283*\dy}) + -- ({1.0000*\dx},{0.4383*\dy}) + -- ({1.0100*\dx},{0.4483*\dy}) + -- ({1.0200*\dx},{0.4582*\dy}) + -- ({1.0300*\dx},{0.4682*\dy}) + -- ({1.0400*\dx},{0.4782*\dy}) + -- ({1.0500*\dx},{0.4880*\dy}) + -- ({1.0600*\dx},{0.4979*\dy}) + -- ({1.0700*\dx},{0.5077*\dy}) + -- ({1.0800*\dx},{0.5174*\dy}) + -- ({1.0900*\dx},{0.5270*\dy}) + -- ({1.1000*\dx},{0.5365*\dy}) + -- ({1.1100*\dx},{0.5459*\dy}) + -- ({1.1200*\dx},{0.5552*\dy}) + -- ({1.1300*\dx},{0.5643*\dy}) + -- ({1.1400*\dx},{0.5733*\dy}) + -- ({1.1500*\dx},{0.5821*\dy}) + -- ({1.1600*\dx},{0.5908*\dy}) + -- ({1.1700*\dx},{0.5993*\dy}) + -- ({1.1800*\dx},{0.6075*\dy}) + -- ({1.1900*\dx},{0.6156*\dy}) + -- ({1.2000*\dx},{0.6234*\dy}) + -- ({1.2100*\dx},{0.6310*\dy}) + -- ({1.2200*\dx},{0.6383*\dy}) + -- ({1.2300*\dx},{0.6454*\dy}) + -- ({1.2400*\dx},{0.6522*\dy}) + -- ({1.2500*\dx},{0.6587*\dy}) + -- ({1.2600*\dx},{0.6648*\dy}) + -- ({1.2700*\dx},{0.6707*\dy}) + -- ({1.2800*\dx},{0.6763*\dy}) + -- ({1.2900*\dx},{0.6815*\dy}) + -- ({1.3000*\dx},{0.6863*\dy}) + -- ({1.3100*\dx},{0.6908*\dy}) + -- ({1.3200*\dx},{0.6950*\dy}) + -- ({1.3300*\dx},{0.6987*\dy}) + -- ({1.3400*\dx},{0.7021*\dy}) + -- ({1.3500*\dx},{0.7050*\dy}) + -- ({1.3600*\dx},{0.7076*\dy}) + -- ({1.3700*\dx},{0.7097*\dy}) + -- ({1.3800*\dx},{0.7114*\dy}) + -- ({1.3900*\dx},{0.7127*\dy}) + -- ({1.4000*\dx},{0.7135*\dy}) + -- ({1.4100*\dx},{0.7139*\dy}) + -- ({1.4200*\dx},{0.7139*\dy}) + -- ({1.4300*\dx},{0.7134*\dy}) + -- ({1.4400*\dx},{0.7125*\dy}) + -- ({1.4500*\dx},{0.7111*\dy}) + -- ({1.4600*\dx},{0.7093*\dy}) + -- ({1.4700*\dx},{0.7070*\dy}) + -- ({1.4800*\dx},{0.7043*\dy}) + -- ({1.4900*\dx},{0.7011*\dy}) + -- ({1.5000*\dx},{0.6975*\dy}) + -- ({1.5100*\dx},{0.6935*\dy}) + -- ({1.5200*\dx},{0.6890*\dy}) + -- ({1.5300*\dx},{0.6841*\dy}) + -- ({1.5400*\dx},{0.6788*\dy}) + -- ({1.5500*\dx},{0.6731*\dy}) + -- ({1.5600*\dx},{0.6670*\dy}) + -- ({1.5700*\dx},{0.6605*\dy}) + -- ({1.5800*\dx},{0.6536*\dy}) + -- ({1.5900*\dx},{0.6464*\dy}) + -- ({1.6000*\dx},{0.6389*\dy}) + -- ({1.6100*\dx},{0.6310*\dy}) + -- ({1.6200*\dx},{0.6229*\dy}) + -- ({1.6300*\dx},{0.6144*\dy}) + -- ({1.6400*\dx},{0.6057*\dy}) + -- ({1.6500*\dx},{0.5968*\dy}) + -- ({1.6600*\dx},{0.5876*\dy}) + -- ({1.6700*\dx},{0.5782*\dy}) + -- ({1.6800*\dx},{0.5687*\dy}) + -- ({1.6900*\dx},{0.5590*\dy}) + -- ({1.7000*\dx},{0.5492*\dy}) + -- ({1.7100*\dx},{0.5393*\dy}) + -- ({1.7200*\dx},{0.5293*\dy}) + -- ({1.7300*\dx},{0.5194*\dy}) + -- ({1.7400*\dx},{0.5094*\dy}) + -- ({1.7500*\dx},{0.4994*\dy}) + -- ({1.7600*\dx},{0.4895*\dy}) + -- ({1.7700*\dx},{0.4796*\dy}) + -- ({1.7800*\dx},{0.4699*\dy}) + -- ({1.7900*\dx},{0.4603*\dy}) + -- ({1.8000*\dx},{0.4509*\dy}) + -- ({1.8100*\dx},{0.4418*\dy}) + -- ({1.8200*\dx},{0.4328*\dy}) + -- ({1.8300*\dx},{0.4241*\dy}) + -- ({1.8400*\dx},{0.4157*\dy}) + -- ({1.8500*\dx},{0.4077*\dy}) + -- ({1.8600*\dx},{0.4000*\dy}) + -- ({1.8700*\dx},{0.3927*\dy}) + -- ({1.8800*\dx},{0.3858*\dy}) + -- ({1.8900*\dx},{0.3793*\dy}) + -- ({1.9000*\dx},{0.3733*\dy}) + -- ({1.9100*\dx},{0.3678*\dy}) + -- ({1.9200*\dx},{0.3629*\dy}) + -- ({1.9300*\dx},{0.3584*\dy}) + -- ({1.9400*\dx},{0.3545*\dy}) + -- ({1.9500*\dx},{0.3511*\dy}) + -- ({1.9600*\dx},{0.3484*\dy}) + -- ({1.9700*\dx},{0.3462*\dy}) + -- ({1.9800*\dx},{0.3447*\dy}) + -- ({1.9900*\dx},{0.3437*\dy}) + -- ({2.0000*\dx},{0.3434*\dy}) + -- ({2.0100*\dx},{0.3437*\dy}) + -- ({2.0200*\dx},{0.3447*\dy}) + -- ({2.0300*\dx},{0.3462*\dy}) + -- ({2.0400*\dx},{0.3484*\dy}) + -- ({2.0500*\dx},{0.3513*\dy}) + -- ({2.0600*\dx},{0.3547*\dy}) + -- ({2.0700*\dx},{0.3587*\dy}) + -- ({2.0800*\dx},{0.3633*\dy}) + -- ({2.0900*\dx},{0.3685*\dy}) + -- ({2.1000*\dx},{0.3743*\dy}) + -- ({2.1100*\dx},{0.3805*\dy}) + -- ({2.1200*\dx},{0.3873*\dy}) + -- ({2.1300*\dx},{0.3945*\dy}) + -- ({2.1400*\dx},{0.4022*\dy}) + -- ({2.1500*\dx},{0.4103*\dy}) + -- ({2.1600*\dx},{0.4188*\dy}) + -- ({2.1700*\dx},{0.4276*\dy}) + -- ({2.1800*\dx},{0.4367*\dy}) + -- ({2.1900*\dx},{0.4461*\dy}) + -- ({2.2000*\dx},{0.4557*\dy}) + -- ({2.2100*\dx},{0.4655*\dy}) + -- ({2.2200*\dx},{0.4754*\dy}) + -- ({2.2300*\dx},{0.4853*\dy}) + -- ({2.2400*\dx},{0.4953*\dy}) + -- ({2.2500*\dx},{0.5053*\dy}) + -- ({2.2600*\dx},{0.5152*\dy}) + -- ({2.2700*\dx},{0.5250*\dy}) + -- ({2.2800*\dx},{0.5346*\dy}) + -- ({2.2900*\dx},{0.5440*\dy}) + -- ({2.3000*\dx},{0.5532*\dy}) + -- ({2.3100*\dx},{0.5620*\dy}) + -- ({2.3200*\dx},{0.5704*\dy}) + -- ({2.3300*\dx},{0.5784*\dy}) + -- ({2.3400*\dx},{0.5860*\dy}) + -- ({2.3500*\dx},{0.5931*\dy}) + -- ({2.3600*\dx},{0.5996*\dy}) + -- ({2.3700*\dx},{0.6056*\dy}) + -- ({2.3800*\dx},{0.6110*\dy}) + -- ({2.3900*\dx},{0.6157*\dy}) + -- ({2.4000*\dx},{0.6197*\dy}) + -- ({2.4100*\dx},{0.6230*\dy}) + -- ({2.4200*\dx},{0.6256*\dy}) + -- ({2.4300*\dx},{0.6275*\dy}) + -- ({2.4400*\dx},{0.6286*\dy}) + -- ({2.4500*\dx},{0.6289*\dy}) + -- ({2.4600*\dx},{0.6285*\dy}) + -- ({2.4700*\dx},{0.6273*\dy}) + -- ({2.4800*\dx},{0.6254*\dy}) + -- ({2.4900*\dx},{0.6226*\dy}) + -- ({2.5000*\dx},{0.6192*\dy}) + -- ({2.5100*\dx},{0.6150*\dy}) + -- ({2.5200*\dx},{0.6101*\dy}) + -- ({2.5300*\dx},{0.6045*\dy}) + -- ({2.5400*\dx},{0.5983*\dy}) + -- ({2.5500*\dx},{0.5915*\dy}) + -- ({2.5600*\dx},{0.5842*\dy}) + -- ({2.5700*\dx},{0.5763*\dy}) + -- ({2.5800*\dx},{0.5679*\dy}) + -- ({2.5900*\dx},{0.5591*\dy}) + -- ({2.6000*\dx},{0.5500*\dy}) + -- ({2.6100*\dx},{0.5406*\dy}) + -- ({2.6200*\dx},{0.5309*\dy}) + -- ({2.6300*\dx},{0.5210*\dy}) + -- ({2.6400*\dx},{0.5111*\dy}) + -- ({2.6500*\dx},{0.5011*\dy}) + -- ({2.6600*\dx},{0.4911*\dy}) + -- ({2.6700*\dx},{0.4812*\dy}) + -- ({2.6800*\dx},{0.4715*\dy}) + -- ({2.6900*\dx},{0.4621*\dy}) + -- ({2.7000*\dx},{0.4529*\dy}) + -- ({2.7100*\dx},{0.4441*\dy}) + -- ({2.7200*\dx},{0.4358*\dy}) + -- ({2.7300*\dx},{0.4279*\dy}) + -- ({2.7400*\dx},{0.4207*\dy}) + -- ({2.7500*\dx},{0.4140*\dy}) + -- ({2.7600*\dx},{0.4080*\dy}) + -- ({2.7700*\dx},{0.4027*\dy}) + -- ({2.7800*\dx},{0.3982*\dy}) + -- ({2.7900*\dx},{0.3944*\dy}) + -- ({2.8000*\dx},{0.3915*\dy}) + -- ({2.8100*\dx},{0.3895*\dy}) + -- ({2.8200*\dx},{0.3883*\dy}) + -- ({2.8300*\dx},{0.3880*\dy}) + -- ({2.8400*\dx},{0.3886*\dy}) + -- ({2.8500*\dx},{0.3900*\dy}) + -- ({2.8600*\dx},{0.3924*\dy}) + -- ({2.8700*\dx},{0.3956*\dy}) + -- ({2.8800*\dx},{0.3996*\dy}) + -- ({2.8900*\dx},{0.4045*\dy}) + -- ({2.9000*\dx},{0.4101*\dy}) + -- ({2.9100*\dx},{0.4165*\dy}) + -- ({2.9200*\dx},{0.4235*\dy}) + -- ({2.9300*\dx},{0.4312*\dy}) + -- ({2.9400*\dx},{0.4394*\dy}) + -- ({2.9500*\dx},{0.4481*\dy}) + -- ({2.9600*\dx},{0.4572*\dy}) + -- ({2.9700*\dx},{0.4667*\dy}) + -- ({2.9800*\dx},{0.4764*\dy}) + -- ({2.9900*\dx},{0.4863*\dy}) + -- ({3.0000*\dx},{0.4963*\dy}) + -- ({3.0100*\dx},{0.5063*\dy}) + -- ({3.0200*\dx},{0.5162*\dy}) + -- ({3.0300*\dx},{0.5259*\dy}) + -- ({3.0400*\dx},{0.5354*\dy}) + -- ({3.0500*\dx},{0.5445*\dy}) + -- ({3.0600*\dx},{0.5531*\dy}) + -- ({3.0700*\dx},{0.5613*\dy}) + -- ({3.0800*\dx},{0.5688*\dy}) + -- ({3.0900*\dx},{0.5757*\dy}) + -- ({3.1000*\dx},{0.5818*\dy}) + -- ({3.1100*\dx},{0.5872*\dy}) + -- ({3.1200*\dx},{0.5917*\dy}) + -- ({3.1300*\dx},{0.5952*\dy}) + -- ({3.1400*\dx},{0.5979*\dy}) + -- ({3.1500*\dx},{0.5996*\dy}) + -- ({3.1600*\dx},{0.6003*\dy}) + -- ({3.1700*\dx},{0.6001*\dy}) + -- ({3.1800*\dx},{0.5988*\dy}) + -- ({3.1900*\dx},{0.5966*\dy}) + -- ({3.2000*\dx},{0.5933*\dy}) + -- ({3.2100*\dx},{0.5892*\dy}) + -- ({3.2200*\dx},{0.5842*\dy}) + -- ({3.2300*\dx},{0.5783*\dy}) + -- ({3.2400*\dx},{0.5716*\dy}) + -- ({3.2500*\dx},{0.5642*\dy}) + -- ({3.2600*\dx},{0.5562*\dy}) + -- ({3.2700*\dx},{0.5476*\dy}) + -- ({3.2800*\dx},{0.5385*\dy}) + -- ({3.2900*\dx},{0.5290*\dy}) + -- ({3.3000*\dx},{0.5193*\dy}) + -- ({3.3100*\dx},{0.5094*\dy}) + -- ({3.3200*\dx},{0.4994*\dy}) + -- ({3.3300*\dx},{0.4894*\dy}) + -- ({3.3400*\dx},{0.4796*\dy}) + -- ({3.3500*\dx},{0.4700*\dy}) + -- ({3.3600*\dx},{0.4608*\dy}) + -- ({3.3700*\dx},{0.4521*\dy}) + -- ({3.3800*\dx},{0.4439*\dy}) + -- ({3.3900*\dx},{0.4364*\dy}) + -- ({3.4000*\dx},{0.4296*\dy}) + -- ({3.4100*\dx},{0.4237*\dy}) + -- ({3.4200*\dx},{0.4186*\dy}) + -- ({3.4300*\dx},{0.4145*\dy}) + -- ({3.4400*\dx},{0.4114*\dy}) + -- ({3.4500*\dx},{0.4094*\dy}) + -- ({3.4600*\dx},{0.4084*\dy}) + -- ({3.4700*\dx},{0.4085*\dy}) + -- ({3.4800*\dx},{0.4097*\dy}) + -- ({3.4900*\dx},{0.4119*\dy}) + -- ({3.5000*\dx},{0.4152*\dy}) + -- ({3.5100*\dx},{0.4196*\dy}) + -- ({3.5200*\dx},{0.4249*\dy}) + -- ({3.5300*\dx},{0.4311*\dy}) + -- ({3.5400*\dx},{0.4381*\dy}) + -- ({3.5500*\dx},{0.4459*\dy}) + -- ({3.5600*\dx},{0.4543*\dy}) + -- ({3.5700*\dx},{0.4633*\dy}) + -- ({3.5800*\dx},{0.4727*\dy}) + -- ({3.5900*\dx},{0.4824*\dy}) + -- ({3.6000*\dx},{0.4923*\dy}) + -- ({3.6100*\dx},{0.5023*\dy}) + -- ({3.6200*\dx},{0.5122*\dy}) + -- ({3.6300*\dx},{0.5220*\dy}) + -- ({3.6400*\dx},{0.5314*\dy}) + -- ({3.6500*\dx},{0.5404*\dy}) + -- ({3.6600*\dx},{0.5489*\dy}) + -- ({3.6700*\dx},{0.5567*\dy}) + -- ({3.6800*\dx},{0.5637*\dy}) + -- ({3.6900*\dx},{0.5698*\dy}) + -- ({3.7000*\dx},{0.5750*\dy}) + -- ({3.7100*\dx},{0.5791*\dy}) + -- ({3.7200*\dx},{0.5822*\dy}) + -- ({3.7300*\dx},{0.5841*\dy}) + -- ({3.7400*\dx},{0.5849*\dy}) + -- ({3.7500*\dx},{0.5845*\dy}) + -- ({3.7600*\dx},{0.5830*\dy}) + -- ({3.7700*\dx},{0.5803*\dy}) + -- ({3.7800*\dx},{0.5764*\dy}) + -- ({3.7900*\dx},{0.5715*\dy}) + -- ({3.8000*\dx},{0.5656*\dy}) + -- ({3.8100*\dx},{0.5588*\dy}) + -- ({3.8200*\dx},{0.5512*\dy}) + -- ({3.8300*\dx},{0.5428*\dy}) + -- ({3.8400*\dx},{0.5338*\dy}) + -- ({3.8500*\dx},{0.5244*\dy}) + -- ({3.8600*\dx},{0.5147*\dy}) + -- ({3.8700*\dx},{0.5047*\dy}) + -- ({3.8800*\dx},{0.4947*\dy}) + -- ({3.8900*\dx},{0.4848*\dy}) + -- ({3.9000*\dx},{0.4752*\dy}) + -- ({3.9100*\dx},{0.4660*\dy}) + -- ({3.9200*\dx},{0.4573*\dy}) + -- ({3.9300*\dx},{0.4492*\dy}) + -- ({3.9400*\dx},{0.4420*\dy}) + -- ({3.9500*\dx},{0.4357*\dy}) + -- ({3.9600*\dx},{0.4303*\dy}) + -- ({3.9700*\dx},{0.4261*\dy}) + -- ({3.9800*\dx},{0.4230*\dy}) + -- ({3.9900*\dx},{0.4211*\dy}) + -- ({4.0000*\dx},{0.4205*\dy}) + -- ({4.0100*\dx},{0.4211*\dy}) + -- ({4.0200*\dx},{0.4230*\dy}) + -- ({4.0300*\dx},{0.4261*\dy}) + -- ({4.0400*\dx},{0.4304*\dy}) + -- ({4.0500*\dx},{0.4358*\dy}) + -- ({4.0600*\dx},{0.4422*\dy}) + -- ({4.0700*\dx},{0.4495*\dy}) + -- ({4.0800*\dx},{0.4576*\dy}) + -- ({4.0900*\dx},{0.4665*\dy}) + -- ({4.1000*\dx},{0.4758*\dy}) + -- ({4.1100*\dx},{0.4855*\dy}) + -- ({4.1200*\dx},{0.4955*\dy}) + -- ({4.1300*\dx},{0.5054*\dy}) + -- ({4.1400*\dx},{0.5153*\dy}) + -- ({4.1500*\dx},{0.5249*\dy}) + -- ({4.1600*\dx},{0.5341*\dy}) + -- ({4.1700*\dx},{0.5426*\dy}) + -- ({4.1800*\dx},{0.5504*\dy}) + -- ({4.1900*\dx},{0.5573*\dy}) + -- ({4.2000*\dx},{0.5632*\dy}) + -- ({4.2100*\dx},{0.5680*\dy}) + -- ({4.2200*\dx},{0.5716*\dy}) + -- ({4.2300*\dx},{0.5739*\dy}) + -- ({4.2400*\dx},{0.5749*\dy}) + -- ({4.2500*\dx},{0.5746*\dy}) + -- ({4.2600*\dx},{0.5730*\dy}) + -- ({4.2700*\dx},{0.5700*\dy}) + -- ({4.2800*\dx},{0.5658*\dy}) + -- ({4.2900*\dx},{0.5604*\dy}) + -- ({4.3000*\dx},{0.5540*\dy}) + -- ({4.3100*\dx},{0.5466*\dy}) + -- ({4.3200*\dx},{0.5383*\dy}) + -- ({4.3300*\dx},{0.5294*\dy}) + -- ({4.3400*\dx},{0.5199*\dy}) + -- ({4.3500*\dx},{0.5101*\dy}) + -- ({4.3600*\dx},{0.5001*\dy}) + -- ({4.3700*\dx},{0.4902*\dy}) + -- ({4.3800*\dx},{0.4804*\dy}) + -- ({4.3900*\dx},{0.4711*\dy}) + -- ({4.4000*\dx},{0.4623*\dy}) + -- ({4.4100*\dx},{0.4542*\dy}) + -- ({4.4200*\dx},{0.4471*\dy}) + -- ({4.4300*\dx},{0.4410*\dy}) + -- ({4.4400*\dx},{0.4360*\dy}) + -- ({4.4500*\dx},{0.4323*\dy}) + -- ({4.4600*\dx},{0.4299*\dy}) + -- ({4.4700*\dx},{0.4289*\dy}) + -- ({4.4800*\dx},{0.4293*\dy}) + -- ({4.4900*\dx},{0.4311*\dy}) + -- ({4.5000*\dx},{0.4343*\dy}) + -- ({4.5100*\dx},{0.4387*\dy}) + -- ({4.5200*\dx},{0.4444*\dy}) + -- ({4.5300*\dx},{0.4512*\dy}) + -- ({4.5400*\dx},{0.4590*\dy}) + -- ({4.5500*\dx},{0.4676*\dy}) + -- ({4.5600*\dx},{0.4768*\dy}) + -- ({4.5700*\dx},{0.4864*\dy}) + -- ({4.5800*\dx},{0.4964*\dy}) + -- ({4.5900*\dx},{0.5064*\dy}) + -- ({4.6000*\dx},{0.5162*\dy}) + -- ({4.6100*\dx},{0.5257*\dy}) + -- ({4.6200*\dx},{0.5346*\dy}) + -- ({4.6300*\dx},{0.5427*\dy}) + -- ({4.6400*\dx},{0.5500*\dy}) + -- ({4.6500*\dx},{0.5562*\dy}) + -- ({4.6600*\dx},{0.5611*\dy}) + -- ({4.6700*\dx},{0.5648*\dy}) + -- ({4.6800*\dx},{0.5670*\dy}) + -- ({4.6900*\dx},{0.5678*\dy}) + -- ({4.7000*\dx},{0.5671*\dy}) + -- ({4.7100*\dx},{0.5650*\dy}) + -- ({4.7200*\dx},{0.5615*\dy}) + -- ({4.7300*\dx},{0.5566*\dy}) + -- ({4.7400*\dx},{0.5504*\dy}) + -- ({4.7500*\dx},{0.5432*\dy}) + -- ({4.7600*\dx},{0.5350*\dy}) + -- ({4.7700*\dx},{0.5261*\dy}) + -- ({4.7800*\dx},{0.5166*\dy}) + -- ({4.7900*\dx},{0.5067*\dy}) + -- ({4.8000*\dx},{0.4968*\dy}) + -- ({4.8100*\dx},{0.4869*\dy}) + -- ({4.8200*\dx},{0.4773*\dy}) + -- ({4.8300*\dx},{0.4682*\dy}) + -- ({4.8400*\dx},{0.4600*\dy}) + -- ({4.8500*\dx},{0.4526*\dy}) + -- ({4.8600*\dx},{0.4464*\dy}) + -- ({4.8700*\dx},{0.4414*\dy}) + -- ({4.8800*\dx},{0.4378*\dy}) + -- ({4.8900*\dx},{0.4357*\dy}) + -- ({4.9000*\dx},{0.4351*\dy}) + -- ({4.9100*\dx},{0.4360*\dy}) + -- ({4.9200*\dx},{0.4384*\dy}) + -- ({4.9300*\dx},{0.4423*\dy}) + -- ({4.9400*\dx},{0.4476*\dy}) + -- ({4.9500*\dx},{0.4541*\dy}) + -- ({4.9600*\dx},{0.4618*\dy}) + -- ({4.9700*\dx},{0.4703*\dy}) + -- ({4.9800*\dx},{0.4795*\dy}) + -- ({4.9900*\dx},{0.4892*\dy}) +} + +\def\Splotleft{ (0,0) + -- ({-0.0100*\dx},{-0.0000*\dy}) + -- ({-0.0200*\dx},{-0.0000*\dy}) + -- ({-0.0300*\dx},{-0.0000*\dy}) + -- ({-0.0400*\dx},{-0.0000*\dy}) + -- ({-0.0500*\dx},{-0.0001*\dy}) + -- ({-0.0600*\dx},{-0.0001*\dy}) + -- ({-0.0700*\dx},{-0.0002*\dy}) + -- ({-0.0800*\dx},{-0.0003*\dy}) + -- ({-0.0900*\dx},{-0.0004*\dy}) + -- ({-0.1000*\dx},{-0.0005*\dy}) + -- ({-0.1100*\dx},{-0.0007*\dy}) + -- ({-0.1200*\dx},{-0.0009*\dy}) + -- ({-0.1300*\dx},{-0.0012*\dy}) + -- ({-0.1400*\dx},{-0.0014*\dy}) + -- ({-0.1500*\dx},{-0.0018*\dy}) + -- ({-0.1600*\dx},{-0.0021*\dy}) + -- ({-0.1700*\dx},{-0.0026*\dy}) + -- ({-0.1800*\dx},{-0.0031*\dy}) + -- ({-0.1900*\dx},{-0.0036*\dy}) + -- ({-0.2000*\dx},{-0.0042*\dy}) + -- ({-0.2100*\dx},{-0.0048*\dy}) + -- ({-0.2200*\dx},{-0.0056*\dy}) + -- ({-0.2300*\dx},{-0.0064*\dy}) + -- ({-0.2400*\dx},{-0.0072*\dy}) + -- ({-0.2500*\dx},{-0.0082*\dy}) + -- ({-0.2600*\dx},{-0.0092*\dy}) + -- ({-0.2700*\dx},{-0.0103*\dy}) + -- ({-0.2800*\dx},{-0.0115*\dy}) + -- ({-0.2900*\dx},{-0.0128*\dy}) + -- ({-0.3000*\dx},{-0.0141*\dy}) + -- ({-0.3100*\dx},{-0.0156*\dy}) + -- ({-0.3200*\dx},{-0.0171*\dy}) + -- ({-0.3300*\dx},{-0.0188*\dy}) + -- ({-0.3400*\dx},{-0.0205*\dy}) + -- ({-0.3500*\dx},{-0.0224*\dy}) + -- ({-0.3600*\dx},{-0.0244*\dy}) + -- ({-0.3700*\dx},{-0.0264*\dy}) + -- ({-0.3800*\dx},{-0.0286*\dy}) + -- ({-0.3900*\dx},{-0.0309*\dy}) + -- ({-0.4000*\dx},{-0.0334*\dy}) + -- ({-0.4100*\dx},{-0.0359*\dy}) + -- ({-0.4200*\dx},{-0.0386*\dy}) + -- ({-0.4300*\dx},{-0.0414*\dy}) + -- ({-0.4400*\dx},{-0.0443*\dy}) + -- ({-0.4500*\dx},{-0.0474*\dy}) + -- ({-0.4600*\dx},{-0.0506*\dy}) + -- ({-0.4700*\dx},{-0.0539*\dy}) + -- ({-0.4800*\dx},{-0.0574*\dy}) + -- ({-0.4900*\dx},{-0.0610*\dy}) + -- ({-0.5000*\dx},{-0.0647*\dy}) + -- ({-0.5100*\dx},{-0.0686*\dy}) + -- ({-0.5200*\dx},{-0.0727*\dy}) + -- ({-0.5300*\dx},{-0.0769*\dy}) + -- ({-0.5400*\dx},{-0.0812*\dy}) + -- ({-0.5500*\dx},{-0.0857*\dy}) + -- ({-0.5600*\dx},{-0.0904*\dy}) + -- ({-0.5700*\dx},{-0.0952*\dy}) + -- ({-0.5800*\dx},{-0.1001*\dy}) + -- ({-0.5900*\dx},{-0.1053*\dy}) + -- ({-0.6000*\dx},{-0.1105*\dy}) + -- ({-0.6100*\dx},{-0.1160*\dy}) + -- ({-0.6200*\dx},{-0.1216*\dy}) + -- ({-0.6300*\dx},{-0.1273*\dy}) + -- ({-0.6400*\dx},{-0.1333*\dy}) + -- ({-0.6500*\dx},{-0.1393*\dy}) + -- ({-0.6600*\dx},{-0.1456*\dy}) + -- ({-0.6700*\dx},{-0.1520*\dy}) + -- ({-0.6800*\dx},{-0.1585*\dy}) + -- ({-0.6900*\dx},{-0.1653*\dy}) + -- ({-0.7000*\dx},{-0.1721*\dy}) + -- ({-0.7100*\dx},{-0.1792*\dy}) + -- ({-0.7200*\dx},{-0.1864*\dy}) + -- ({-0.7300*\dx},{-0.1937*\dy}) + -- ({-0.7400*\dx},{-0.2012*\dy}) + -- ({-0.7500*\dx},{-0.2089*\dy}) + -- ({-0.7600*\dx},{-0.2167*\dy}) + -- ({-0.7700*\dx},{-0.2246*\dy}) + -- ({-0.7800*\dx},{-0.2327*\dy}) + -- ({-0.7900*\dx},{-0.2410*\dy}) + -- ({-0.8000*\dx},{-0.2493*\dy}) + -- ({-0.8100*\dx},{-0.2579*\dy}) + -- ({-0.8200*\dx},{-0.2665*\dy}) + -- ({-0.8300*\dx},{-0.2753*\dy}) + -- ({-0.8400*\dx},{-0.2841*\dy}) + -- ({-0.8500*\dx},{-0.2932*\dy}) + -- ({-0.8600*\dx},{-0.3023*\dy}) + -- ({-0.8700*\dx},{-0.3115*\dy}) + -- ({-0.8800*\dx},{-0.3208*\dy}) + -- ({-0.8900*\dx},{-0.3303*\dy}) + -- ({-0.9000*\dx},{-0.3398*\dy}) + -- ({-0.9100*\dx},{-0.3494*\dy}) + -- ({-0.9200*\dx},{-0.3590*\dy}) + -- ({-0.9300*\dx},{-0.3688*\dy}) + -- ({-0.9400*\dx},{-0.3786*\dy}) + -- ({-0.9500*\dx},{-0.3885*\dy}) + -- ({-0.9600*\dx},{-0.3984*\dy}) + -- ({-0.9700*\dx},{-0.4083*\dy}) + -- ({-0.9800*\dx},{-0.4183*\dy}) + -- ({-0.9900*\dx},{-0.4283*\dy}) + -- ({-1.0000*\dx},{-0.4383*\dy}) + -- ({-1.0100*\dx},{-0.4483*\dy}) + -- ({-1.0200*\dx},{-0.4582*\dy}) + -- ({-1.0300*\dx},{-0.4682*\dy}) + -- ({-1.0400*\dx},{-0.4782*\dy}) + -- ({-1.0500*\dx},{-0.4880*\dy}) + -- ({-1.0600*\dx},{-0.4979*\dy}) + -- ({-1.0700*\dx},{-0.5077*\dy}) + -- ({-1.0800*\dx},{-0.5174*\dy}) + -- ({-1.0900*\dx},{-0.5270*\dy}) + -- ({-1.1000*\dx},{-0.5365*\dy}) + -- ({-1.1100*\dx},{-0.5459*\dy}) + -- ({-1.1200*\dx},{-0.5552*\dy}) + -- ({-1.1300*\dx},{-0.5643*\dy}) + -- ({-1.1400*\dx},{-0.5733*\dy}) + -- ({-1.1500*\dx},{-0.5821*\dy}) + -- ({-1.1600*\dx},{-0.5908*\dy}) + -- ({-1.1700*\dx},{-0.5993*\dy}) + -- ({-1.1800*\dx},{-0.6075*\dy}) + -- ({-1.1900*\dx},{-0.6156*\dy}) + -- ({-1.2000*\dx},{-0.6234*\dy}) + -- ({-1.2100*\dx},{-0.6310*\dy}) + -- ({-1.2200*\dx},{-0.6383*\dy}) + -- ({-1.2300*\dx},{-0.6454*\dy}) + -- ({-1.2400*\dx},{-0.6522*\dy}) + -- ({-1.2500*\dx},{-0.6587*\dy}) + -- ({-1.2600*\dx},{-0.6648*\dy}) + -- ({-1.2700*\dx},{-0.6707*\dy}) + -- ({-1.2800*\dx},{-0.6763*\dy}) + -- ({-1.2900*\dx},{-0.6815*\dy}) + -- ({-1.3000*\dx},{-0.6863*\dy}) + -- ({-1.3100*\dx},{-0.6908*\dy}) + -- ({-1.3200*\dx},{-0.6950*\dy}) + -- ({-1.3300*\dx},{-0.6987*\dy}) + -- ({-1.3400*\dx},{-0.7021*\dy}) + -- ({-1.3500*\dx},{-0.7050*\dy}) + -- ({-1.3600*\dx},{-0.7076*\dy}) + -- ({-1.3700*\dx},{-0.7097*\dy}) + -- ({-1.3800*\dx},{-0.7114*\dy}) + -- ({-1.3900*\dx},{-0.7127*\dy}) + -- ({-1.4000*\dx},{-0.7135*\dy}) + -- ({-1.4100*\dx},{-0.7139*\dy}) + -- ({-1.4200*\dx},{-0.7139*\dy}) + -- ({-1.4300*\dx},{-0.7134*\dy}) + -- ({-1.4400*\dx},{-0.7125*\dy}) + -- ({-1.4500*\dx},{-0.7111*\dy}) + -- ({-1.4600*\dx},{-0.7093*\dy}) + -- ({-1.4700*\dx},{-0.7070*\dy}) + -- ({-1.4800*\dx},{-0.7043*\dy}) + -- ({-1.4900*\dx},{-0.7011*\dy}) + -- ({-1.5000*\dx},{-0.6975*\dy}) + -- ({-1.5100*\dx},{-0.6935*\dy}) + -- ({-1.5200*\dx},{-0.6890*\dy}) + -- ({-1.5300*\dx},{-0.6841*\dy}) + -- ({-1.5400*\dx},{-0.6788*\dy}) + -- ({-1.5500*\dx},{-0.6731*\dy}) + -- ({-1.5600*\dx},{-0.6670*\dy}) + -- ({-1.5700*\dx},{-0.6605*\dy}) + -- ({-1.5800*\dx},{-0.6536*\dy}) + -- ({-1.5900*\dx},{-0.6464*\dy}) + -- ({-1.6000*\dx},{-0.6389*\dy}) + -- ({-1.6100*\dx},{-0.6310*\dy}) + -- ({-1.6200*\dx},{-0.6229*\dy}) + -- ({-1.6300*\dx},{-0.6144*\dy}) + -- ({-1.6400*\dx},{-0.6057*\dy}) + -- ({-1.6500*\dx},{-0.5968*\dy}) + -- ({-1.6600*\dx},{-0.5876*\dy}) + -- ({-1.6700*\dx},{-0.5782*\dy}) + -- ({-1.6800*\dx},{-0.5687*\dy}) + -- ({-1.6900*\dx},{-0.5590*\dy}) + -- ({-1.7000*\dx},{-0.5492*\dy}) + -- ({-1.7100*\dx},{-0.5393*\dy}) + -- ({-1.7200*\dx},{-0.5293*\dy}) + -- ({-1.7300*\dx},{-0.5194*\dy}) + -- ({-1.7400*\dx},{-0.5094*\dy}) + -- ({-1.7500*\dx},{-0.4994*\dy}) + -- ({-1.7600*\dx},{-0.4895*\dy}) + -- ({-1.7700*\dx},{-0.4796*\dy}) + -- ({-1.7800*\dx},{-0.4699*\dy}) + -- ({-1.7900*\dx},{-0.4603*\dy}) + -- ({-1.8000*\dx},{-0.4509*\dy}) + -- ({-1.8100*\dx},{-0.4418*\dy}) + -- ({-1.8200*\dx},{-0.4328*\dy}) + -- ({-1.8300*\dx},{-0.4241*\dy}) + -- ({-1.8400*\dx},{-0.4157*\dy}) + -- ({-1.8500*\dx},{-0.4077*\dy}) + -- ({-1.8600*\dx},{-0.4000*\dy}) + -- ({-1.8700*\dx},{-0.3927*\dy}) + -- ({-1.8800*\dx},{-0.3858*\dy}) + -- ({-1.8900*\dx},{-0.3793*\dy}) + -- ({-1.9000*\dx},{-0.3733*\dy}) + -- ({-1.9100*\dx},{-0.3678*\dy}) + -- ({-1.9200*\dx},{-0.3629*\dy}) + -- ({-1.9300*\dx},{-0.3584*\dy}) + -- ({-1.9400*\dx},{-0.3545*\dy}) + -- ({-1.9500*\dx},{-0.3511*\dy}) + -- ({-1.9600*\dx},{-0.3484*\dy}) + -- ({-1.9700*\dx},{-0.3462*\dy}) + -- ({-1.9800*\dx},{-0.3447*\dy}) + -- ({-1.9900*\dx},{-0.3437*\dy}) + -- ({-2.0000*\dx},{-0.3434*\dy}) + -- ({-2.0100*\dx},{-0.3437*\dy}) + -- ({-2.0200*\dx},{-0.3447*\dy}) + -- ({-2.0300*\dx},{-0.3462*\dy}) + -- ({-2.0400*\dx},{-0.3484*\dy}) + -- ({-2.0500*\dx},{-0.3513*\dy}) + -- ({-2.0600*\dx},{-0.3547*\dy}) + -- ({-2.0700*\dx},{-0.3587*\dy}) + -- ({-2.0800*\dx},{-0.3633*\dy}) + -- ({-2.0900*\dx},{-0.3685*\dy}) + -- ({-2.1000*\dx},{-0.3743*\dy}) + -- ({-2.1100*\dx},{-0.3805*\dy}) + -- ({-2.1200*\dx},{-0.3873*\dy}) + -- ({-2.1300*\dx},{-0.3945*\dy}) + -- ({-2.1400*\dx},{-0.4022*\dy}) + -- ({-2.1500*\dx},{-0.4103*\dy}) + -- ({-2.1600*\dx},{-0.4188*\dy}) + -- ({-2.1700*\dx},{-0.4276*\dy}) + -- ({-2.1800*\dx},{-0.4367*\dy}) + -- ({-2.1900*\dx},{-0.4461*\dy}) + -- ({-2.2000*\dx},{-0.4557*\dy}) + -- ({-2.2100*\dx},{-0.4655*\dy}) + -- ({-2.2200*\dx},{-0.4754*\dy}) + -- ({-2.2300*\dx},{-0.4853*\dy}) + -- ({-2.2400*\dx},{-0.4953*\dy}) + -- ({-2.2500*\dx},{-0.5053*\dy}) + -- ({-2.2600*\dx},{-0.5152*\dy}) + -- ({-2.2700*\dx},{-0.5250*\dy}) + -- ({-2.2800*\dx},{-0.5346*\dy}) + -- ({-2.2900*\dx},{-0.5440*\dy}) + -- ({-2.3000*\dx},{-0.5532*\dy}) + -- ({-2.3100*\dx},{-0.5620*\dy}) + -- ({-2.3200*\dx},{-0.5704*\dy}) + -- ({-2.3300*\dx},{-0.5784*\dy}) + -- ({-2.3400*\dx},{-0.5860*\dy}) + -- ({-2.3500*\dx},{-0.5931*\dy}) + -- ({-2.3600*\dx},{-0.5996*\dy}) + -- ({-2.3700*\dx},{-0.6056*\dy}) + -- ({-2.3800*\dx},{-0.6110*\dy}) + -- ({-2.3900*\dx},{-0.6157*\dy}) + -- ({-2.4000*\dx},{-0.6197*\dy}) + -- ({-2.4100*\dx},{-0.6230*\dy}) + -- ({-2.4200*\dx},{-0.6256*\dy}) + -- ({-2.4300*\dx},{-0.6275*\dy}) + -- ({-2.4400*\dx},{-0.6286*\dy}) + -- ({-2.4500*\dx},{-0.6289*\dy}) + -- ({-2.4600*\dx},{-0.6285*\dy}) + -- ({-2.4700*\dx},{-0.6273*\dy}) + -- ({-2.4800*\dx},{-0.6254*\dy}) + -- ({-2.4900*\dx},{-0.6226*\dy}) + -- ({-2.5000*\dx},{-0.6192*\dy}) + -- ({-2.5100*\dx},{-0.6150*\dy}) + -- ({-2.5200*\dx},{-0.6101*\dy}) + -- ({-2.5300*\dx},{-0.6045*\dy}) + -- ({-2.5400*\dx},{-0.5983*\dy}) + -- ({-2.5500*\dx},{-0.5915*\dy}) + -- ({-2.5600*\dx},{-0.5842*\dy}) + -- ({-2.5700*\dx},{-0.5763*\dy}) + -- ({-2.5800*\dx},{-0.5679*\dy}) + -- ({-2.5900*\dx},{-0.5591*\dy}) + -- ({-2.6000*\dx},{-0.5500*\dy}) + -- ({-2.6100*\dx},{-0.5406*\dy}) + -- ({-2.6200*\dx},{-0.5309*\dy}) + -- ({-2.6300*\dx},{-0.5210*\dy}) + -- ({-2.6400*\dx},{-0.5111*\dy}) + -- ({-2.6500*\dx},{-0.5011*\dy}) + -- ({-2.6600*\dx},{-0.4911*\dy}) + -- ({-2.6700*\dx},{-0.4812*\dy}) + -- ({-2.6800*\dx},{-0.4715*\dy}) + -- ({-2.6900*\dx},{-0.4621*\dy}) + -- ({-2.7000*\dx},{-0.4529*\dy}) + -- ({-2.7100*\dx},{-0.4441*\dy}) + -- ({-2.7200*\dx},{-0.4358*\dy}) + -- ({-2.7300*\dx},{-0.4279*\dy}) + -- ({-2.7400*\dx},{-0.4207*\dy}) + -- ({-2.7500*\dx},{-0.4140*\dy}) + -- ({-2.7600*\dx},{-0.4080*\dy}) + -- ({-2.7700*\dx},{-0.4027*\dy}) + -- ({-2.7800*\dx},{-0.3982*\dy}) + -- ({-2.7900*\dx},{-0.3944*\dy}) + -- ({-2.8000*\dx},{-0.3915*\dy}) + -- ({-2.8100*\dx},{-0.3895*\dy}) + -- ({-2.8200*\dx},{-0.3883*\dy}) + -- ({-2.8300*\dx},{-0.3880*\dy}) + -- ({-2.8400*\dx},{-0.3886*\dy}) + -- ({-2.8500*\dx},{-0.3900*\dy}) + -- ({-2.8600*\dx},{-0.3924*\dy}) + -- ({-2.8700*\dx},{-0.3956*\dy}) + -- ({-2.8800*\dx},{-0.3996*\dy}) + -- ({-2.8900*\dx},{-0.4045*\dy}) + -- ({-2.9000*\dx},{-0.4101*\dy}) + -- ({-2.9100*\dx},{-0.4165*\dy}) + -- ({-2.9200*\dx},{-0.4235*\dy}) + -- ({-2.9300*\dx},{-0.4312*\dy}) + -- ({-2.9400*\dx},{-0.4394*\dy}) + -- ({-2.9500*\dx},{-0.4481*\dy}) + -- ({-2.9600*\dx},{-0.4572*\dy}) + -- ({-2.9700*\dx},{-0.4667*\dy}) + -- ({-2.9800*\dx},{-0.4764*\dy}) + -- ({-2.9900*\dx},{-0.4863*\dy}) + -- ({-3.0000*\dx},{-0.4963*\dy}) + -- ({-3.0100*\dx},{-0.5063*\dy}) + -- ({-3.0200*\dx},{-0.5162*\dy}) + -- ({-3.0300*\dx},{-0.5259*\dy}) + -- ({-3.0400*\dx},{-0.5354*\dy}) + -- ({-3.0500*\dx},{-0.5445*\dy}) + -- ({-3.0600*\dx},{-0.5531*\dy}) + -- ({-3.0700*\dx},{-0.5613*\dy}) + -- ({-3.0800*\dx},{-0.5688*\dy}) + -- ({-3.0900*\dx},{-0.5757*\dy}) + -- ({-3.1000*\dx},{-0.5818*\dy}) + -- ({-3.1100*\dx},{-0.5872*\dy}) + -- ({-3.1200*\dx},{-0.5917*\dy}) + -- ({-3.1300*\dx},{-0.5952*\dy}) + -- ({-3.1400*\dx},{-0.5979*\dy}) + -- ({-3.1500*\dx},{-0.5996*\dy}) + -- ({-3.1600*\dx},{-0.6003*\dy}) + -- ({-3.1700*\dx},{-0.6001*\dy}) + -- ({-3.1800*\dx},{-0.5988*\dy}) + -- ({-3.1900*\dx},{-0.5966*\dy}) + -- ({-3.2000*\dx},{-0.5933*\dy}) + -- ({-3.2100*\dx},{-0.5892*\dy}) + -- ({-3.2200*\dx},{-0.5842*\dy}) + -- ({-3.2300*\dx},{-0.5783*\dy}) + -- ({-3.2400*\dx},{-0.5716*\dy}) + -- ({-3.2500*\dx},{-0.5642*\dy}) + -- ({-3.2600*\dx},{-0.5562*\dy}) + -- ({-3.2700*\dx},{-0.5476*\dy}) + -- ({-3.2800*\dx},{-0.5385*\dy}) + -- ({-3.2900*\dx},{-0.5290*\dy}) + -- ({-3.3000*\dx},{-0.5193*\dy}) + -- ({-3.3100*\dx},{-0.5094*\dy}) + -- ({-3.3200*\dx},{-0.4994*\dy}) + -- ({-3.3300*\dx},{-0.4894*\dy}) + -- ({-3.3400*\dx},{-0.4796*\dy}) + -- ({-3.3500*\dx},{-0.4700*\dy}) + -- ({-3.3600*\dx},{-0.4608*\dy}) + -- ({-3.3700*\dx},{-0.4521*\dy}) + -- ({-3.3800*\dx},{-0.4439*\dy}) + -- ({-3.3900*\dx},{-0.4364*\dy}) + -- ({-3.4000*\dx},{-0.4296*\dy}) + -- ({-3.4100*\dx},{-0.4237*\dy}) + -- ({-3.4200*\dx},{-0.4186*\dy}) + -- ({-3.4300*\dx},{-0.4145*\dy}) + -- ({-3.4400*\dx},{-0.4114*\dy}) + -- ({-3.4500*\dx},{-0.4094*\dy}) + -- ({-3.4600*\dx},{-0.4084*\dy}) + -- ({-3.4700*\dx},{-0.4085*\dy}) + -- ({-3.4800*\dx},{-0.4097*\dy}) + -- ({-3.4900*\dx},{-0.4119*\dy}) + -- ({-3.5000*\dx},{-0.4152*\dy}) + -- ({-3.5100*\dx},{-0.4196*\dy}) + -- ({-3.5200*\dx},{-0.4249*\dy}) + -- ({-3.5300*\dx},{-0.4311*\dy}) + -- ({-3.5400*\dx},{-0.4381*\dy}) + -- ({-3.5500*\dx},{-0.4459*\dy}) + -- ({-3.5600*\dx},{-0.4543*\dy}) + -- ({-3.5700*\dx},{-0.4633*\dy}) + -- ({-3.5800*\dx},{-0.4727*\dy}) + -- ({-3.5900*\dx},{-0.4824*\dy}) + -- ({-3.6000*\dx},{-0.4923*\dy}) + -- ({-3.6100*\dx},{-0.5023*\dy}) + -- ({-3.6200*\dx},{-0.5122*\dy}) + -- ({-3.6300*\dx},{-0.5220*\dy}) + -- ({-3.6400*\dx},{-0.5314*\dy}) + -- ({-3.6500*\dx},{-0.5404*\dy}) + -- ({-3.6600*\dx},{-0.5489*\dy}) + -- ({-3.6700*\dx},{-0.5567*\dy}) + -- ({-3.6800*\dx},{-0.5637*\dy}) + -- ({-3.6900*\dx},{-0.5698*\dy}) + -- ({-3.7000*\dx},{-0.5750*\dy}) + -- ({-3.7100*\dx},{-0.5791*\dy}) + -- ({-3.7200*\dx},{-0.5822*\dy}) + -- ({-3.7300*\dx},{-0.5841*\dy}) + -- ({-3.7400*\dx},{-0.5849*\dy}) + -- ({-3.7500*\dx},{-0.5845*\dy}) + -- ({-3.7600*\dx},{-0.5830*\dy}) + -- ({-3.7700*\dx},{-0.5803*\dy}) + -- ({-3.7800*\dx},{-0.5764*\dy}) + -- ({-3.7900*\dx},{-0.5715*\dy}) + -- ({-3.8000*\dx},{-0.5656*\dy}) + -- ({-3.8100*\dx},{-0.5588*\dy}) + -- ({-3.8200*\dx},{-0.5512*\dy}) + -- ({-3.8300*\dx},{-0.5428*\dy}) + -- ({-3.8400*\dx},{-0.5338*\dy}) + -- ({-3.8500*\dx},{-0.5244*\dy}) + -- ({-3.8600*\dx},{-0.5147*\dy}) + -- ({-3.8700*\dx},{-0.5047*\dy}) + -- ({-3.8800*\dx},{-0.4947*\dy}) + -- ({-3.8900*\dx},{-0.4848*\dy}) + -- ({-3.9000*\dx},{-0.4752*\dy}) + -- ({-3.9100*\dx},{-0.4660*\dy}) + -- ({-3.9200*\dx},{-0.4573*\dy}) + -- ({-3.9300*\dx},{-0.4492*\dy}) + -- ({-3.9400*\dx},{-0.4420*\dy}) + -- ({-3.9500*\dx},{-0.4357*\dy}) + -- ({-3.9600*\dx},{-0.4303*\dy}) + -- ({-3.9700*\dx},{-0.4261*\dy}) + -- ({-3.9800*\dx},{-0.4230*\dy}) + -- ({-3.9900*\dx},{-0.4211*\dy}) + -- ({-4.0000*\dx},{-0.4205*\dy}) + -- ({-4.0100*\dx},{-0.4211*\dy}) + -- ({-4.0200*\dx},{-0.4230*\dy}) + -- ({-4.0300*\dx},{-0.4261*\dy}) + -- ({-4.0400*\dx},{-0.4304*\dy}) + -- ({-4.0500*\dx},{-0.4358*\dy}) + -- ({-4.0600*\dx},{-0.4422*\dy}) + -- ({-4.0700*\dx},{-0.4495*\dy}) + -- ({-4.0800*\dx},{-0.4576*\dy}) + -- ({-4.0900*\dx},{-0.4665*\dy}) + -- ({-4.1000*\dx},{-0.4758*\dy}) + -- ({-4.1100*\dx},{-0.4855*\dy}) + -- ({-4.1200*\dx},{-0.4955*\dy}) + -- ({-4.1300*\dx},{-0.5054*\dy}) + -- ({-4.1400*\dx},{-0.5153*\dy}) + -- ({-4.1500*\dx},{-0.5249*\dy}) + -- ({-4.1600*\dx},{-0.5341*\dy}) + -- ({-4.1700*\dx},{-0.5426*\dy}) + -- ({-4.1800*\dx},{-0.5504*\dy}) + -- ({-4.1900*\dx},{-0.5573*\dy}) + -- ({-4.2000*\dx},{-0.5632*\dy}) + -- ({-4.2100*\dx},{-0.5680*\dy}) + -- ({-4.2200*\dx},{-0.5716*\dy}) + -- ({-4.2300*\dx},{-0.5739*\dy}) + -- ({-4.2400*\dx},{-0.5749*\dy}) + -- ({-4.2500*\dx},{-0.5746*\dy}) + -- ({-4.2600*\dx},{-0.5730*\dy}) + -- ({-4.2700*\dx},{-0.5700*\dy}) + -- ({-4.2800*\dx},{-0.5658*\dy}) + -- ({-4.2900*\dx},{-0.5604*\dy}) + -- ({-4.3000*\dx},{-0.5540*\dy}) + -- ({-4.3100*\dx},{-0.5466*\dy}) + -- ({-4.3200*\dx},{-0.5383*\dy}) + -- ({-4.3300*\dx},{-0.5294*\dy}) + -- ({-4.3400*\dx},{-0.5199*\dy}) + -- ({-4.3500*\dx},{-0.5101*\dy}) + -- ({-4.3600*\dx},{-0.5001*\dy}) + -- ({-4.3700*\dx},{-0.4902*\dy}) + -- ({-4.3800*\dx},{-0.4804*\dy}) + -- ({-4.3900*\dx},{-0.4711*\dy}) + -- ({-4.4000*\dx},{-0.4623*\dy}) + -- ({-4.4100*\dx},{-0.4542*\dy}) + -- ({-4.4200*\dx},{-0.4471*\dy}) + -- ({-4.4300*\dx},{-0.4410*\dy}) + -- ({-4.4400*\dx},{-0.4360*\dy}) + -- ({-4.4500*\dx},{-0.4323*\dy}) + -- ({-4.4600*\dx},{-0.4299*\dy}) + -- ({-4.4700*\dx},{-0.4289*\dy}) + -- ({-4.4800*\dx},{-0.4293*\dy}) + -- ({-4.4900*\dx},{-0.4311*\dy}) + -- ({-4.5000*\dx},{-0.4343*\dy}) + -- ({-4.5100*\dx},{-0.4387*\dy}) + -- ({-4.5200*\dx},{-0.4444*\dy}) + -- ({-4.5300*\dx},{-0.4512*\dy}) + -- ({-4.5400*\dx},{-0.4590*\dy}) + -- ({-4.5500*\dx},{-0.4676*\dy}) + -- ({-4.5600*\dx},{-0.4768*\dy}) + -- ({-4.5700*\dx},{-0.4864*\dy}) + -- ({-4.5800*\dx},{-0.4964*\dy}) + -- ({-4.5900*\dx},{-0.5064*\dy}) + -- ({-4.6000*\dx},{-0.5162*\dy}) + -- ({-4.6100*\dx},{-0.5257*\dy}) + -- ({-4.6200*\dx},{-0.5346*\dy}) + -- ({-4.6300*\dx},{-0.5427*\dy}) + -- ({-4.6400*\dx},{-0.5500*\dy}) + -- ({-4.6500*\dx},{-0.5562*\dy}) + -- ({-4.6600*\dx},{-0.5611*\dy}) + -- ({-4.6700*\dx},{-0.5648*\dy}) + -- ({-4.6800*\dx},{-0.5670*\dy}) + -- ({-4.6900*\dx},{-0.5678*\dy}) + -- ({-4.7000*\dx},{-0.5671*\dy}) + -- ({-4.7100*\dx},{-0.5650*\dy}) + -- ({-4.7200*\dx},{-0.5615*\dy}) + -- ({-4.7300*\dx},{-0.5566*\dy}) + -- ({-4.7400*\dx},{-0.5504*\dy}) + -- ({-4.7500*\dx},{-0.5432*\dy}) + -- ({-4.7600*\dx},{-0.5350*\dy}) + -- ({-4.7700*\dx},{-0.5261*\dy}) + -- ({-4.7800*\dx},{-0.5166*\dy}) + -- ({-4.7900*\dx},{-0.5067*\dy}) + -- ({-4.8000*\dx},{-0.4968*\dy}) + -- ({-4.8100*\dx},{-0.4869*\dy}) + -- ({-4.8200*\dx},{-0.4773*\dy}) + -- ({-4.8300*\dx},{-0.4682*\dy}) + -- ({-4.8400*\dx},{-0.4600*\dy}) + -- ({-4.8500*\dx},{-0.4526*\dy}) + -- ({-4.8600*\dx},{-0.4464*\dy}) + -- ({-4.8700*\dx},{-0.4414*\dy}) + -- ({-4.8800*\dx},{-0.4378*\dy}) + -- ({-4.8900*\dx},{-0.4357*\dy}) + -- ({-4.9000*\dx},{-0.4351*\dy}) + -- ({-4.9100*\dx},{-0.4360*\dy}) + -- ({-4.9200*\dx},{-0.4384*\dy}) + -- ({-4.9300*\dx},{-0.4423*\dy}) + -- ({-4.9400*\dx},{-0.4476*\dy}) + -- ({-4.9500*\dx},{-0.4541*\dy}) + -- ({-4.9600*\dx},{-0.4618*\dy}) + -- ({-4.9700*\dx},{-0.4703*\dy}) + -- ({-4.9800*\dx},{-0.4795*\dy}) + -- ({-4.9900*\dx},{-0.4892*\dy}) +} + diff --git a/vorlesungen/slides/fresnel/eulerspirale.m b/vorlesungen/slides/fresnel/eulerspirale.m new file mode 100644 index 0000000..84e3696 --- /dev/null +++ b/vorlesungen/slides/fresnel/eulerspirale.m @@ -0,0 +1,61 @@ +# +# eulerspirale.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +# +global n; +n = 1000; +global tmax; +tmax = 10; +global N; +N = round(n*5/tmax); + +function retval = f(x, t) + x = pi * t^2 / 2; + retval = [ cos(x); sin(x) ]; +endfunction + +x0 = [ 0; 0 ]; +t = tmax * (0:n) / n; + +c = lsode(@f, x0, t); + +fn = fopen("eulerpath.tex", "w"); + +fprintf(fn, "\\def\\fresnela{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\fresnelb{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fclose(fn); diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex new file mode 100644 index 0000000..906aec1 --- /dev/null +++ b/vorlesungen/slides/fresnel/integrale.tex @@ -0,0 +1,119 @@ +% +% integrale.tex -- Definition der Fresnel Integrale +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\input{../slides/fresnel/eulerpath.tex} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Fresnel-Integrale} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Definition} +Fresnel-Integrale: +\begin{align*} +\color{red}S(t) +&= +\int_0^t \sin\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau +\\ +\color{blue}C(t) +&= +\int_0^t \cos\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau +\end{align*} +\uncover<3->{% +Können nicht in geschlossener Form ausgewertet werden. +} +\end{block} +\uncover<4->{% +\begin{block}{Euler-Spirale} +\[ +\gamma_a(t) += +\begin{pmatrix} +C_a(t)\\S_a(t) +\end{pmatrix} += +\begin{pmatrix} +\displaystyle +\int_0^t \cos (a\tau^2)\,d\tau\\[8pt] +\displaystyle +\int_0^t \sin (a\tau^2)\,d\tau +\end{pmatrix} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\ifthenelse{\boolean{presentation}}{ +\only<2-4>{% +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=1] +\def\dx{0.6} +\def\dy{1.5} + +\begin{scope} + \draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy}); + \draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy}); + \draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}]; + \draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$S(t)$}]; + \draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy}); + \node at (-0.1,{0.5*\dy}) [left] {$\frac12$}; + \draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy}); + \node at (0.1,{-0.5*\dy}) [right] {$-\frac12$}; + \draw[color=red,line width=1.4pt] \Splotright; + \draw[color=red,line width=1.4pt] \Splotleft; +\end{scope} + +\begin{scope}[yshift=-3.4cm] + \draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy}); + \draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy}); + \draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}]; + \draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$C(t)$}]; + \draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy}); + \node at (-0.1,{0.5*\dy}) [left] {$\frac12$}; + \draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy}); + \node at (0.1,{-0.5*\dy}) [right] {$-\frac12$}; + \draw[color=blue,line width=1.4pt] \Cplotright; + \draw[color=blue,line width=1.4pt] \Cplotleft; +\end{scope} + +\end{tikzpicture} +\end{center} +}}{} +\uncover<5->{% +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=3.5] + +\draw[color=gray!50] (-0.5,-0.5) rectangle (0.5,0.5); + +\draw[->] (-0.8,0) -- (0.9,0) coordinate[label={$\color{blue}C(t)$}]; +\draw[->] (0,-0.8) -- (0,0.9) coordinate[label={right:$\color{red}S(t)$}]; + +\draw[color=darkgreen,line width=1.0pt] \fresnela; +\draw[color=darkgreen,line width=1.0pt] \fresnelb; + +\fill[color=orange] (0.5,0.5) circle[radius=0.02]; +\fill[color=orange] (-0.5,-0.5) circle[radius=0.02]; + +\draw (0.5,-0.02) -- (0.5,0.02); +\node at (0.5,-0.02) [below right] {$\frac12$}; + +\draw (-0.5,-0.02) -- (-0.5,0.02); +\node at (-0.5,0.02) [above left] {$-\frac12$}; + +\draw (-0.01,0.5) -- (0.02,0.5); +\node at (-0.02,0.5) [above left] {$\frac12$}; + +\draw (-0.02,-0.5) -- (0.02,-0.5); +\node at (0.02,-0.5) [below right] {$-\frac12$}; + +\end{tikzpicture} +\end{center} +} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/klothoide.tex b/vorlesungen/slides/fresnel/klothoide.tex new file mode 100644 index 0000000..bf43644 --- /dev/null +++ b/vorlesungen/slides/fresnel/klothoide.tex @@ -0,0 +1,68 @@ +% +% klothoide.tex -- Klothoide +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Klothoide} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Krümmung der Euler-Spirale} +\begin{align*} +\frac{d}{dt}\gamma_1(t) +&= +\dot{\gamma}_1(t) += +\begin{pmatrix} +\cos t^2\\ +\sin t^2 +\end{pmatrix} +\intertext{\uncover<2->{Bogenlänge:}} +\uncover<2->{ +|\dot{\gamma}_1(t)| +&= +\sqrt{\cos^2 t^2 + \sin^2 t^2} += +1 +} +\intertext{\uncover<3->{Polarwinkel:}} +\uncover<3->{ +\varphi&=t^2 +\intertext{\uncover<4->{Krümmung:}} +\uncover<4->{ +\frac{d\varphi}{dt} +&= +2t +} +} +\end{align*} +\uncover<5->{% +$\Rightarrow$ Krümmung ist proportional zur Bogenlänge +} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<6->{% +\begin{block}{Definition} +Eine Kurve, deren Krümmung proportional zur Bogenlänge ist, heisst +{\em Klothoide} +\end{block}} +\uncover<7->{% +\begin{block}{Anwendung} +\begin{itemize} +\item<8-> +Strassenbau: Um mit konstanter Geschwindigkeit auf einer +Klothoide zu fahren, muss man das Lenkrad mit konstanter Geschwindigkeit +drehen +\item<9-> +Apfel + Sparschäler +\end{itemize} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/kruemmung.tex b/vorlesungen/slides/fresnel/kruemmung.tex new file mode 100644 index 0000000..06f6b9b --- /dev/null +++ b/vorlesungen/slides/fresnel/kruemmung.tex @@ -0,0 +1,91 @@ +% +% kruemmung.tex -- Kruemmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Krümmung einer Kurve} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Krümmungsradius} +Bogen und Radius: +\[ +s=r\cdot\Delta\varphi +\uncover<2->{ +\quad +\Rightarrow +\quad +r += +\frac{s}{\Delta\varphi} +} +\] +\end{block} +\vspace*{-12pt} +\uncover<3->{ +\begin{block}{Krümmung} +Je grösser der Krümmungsradius, desto kleiner die Krümmung: +\[ +\kappa = \frac{1}{r} +\] +\end{block}} +\vspace*{-12pt} +\uncover<5->{% +\begin{block}{Definition} +Änderungsgeschwindigkeit des Polarwinkels der Tangente +\[ +\kappa += +\frac{1}{r} +\uncover<6->{= +\frac{\Delta\varphi}{s}} +\uncover<7->{= +\frac{d\varphi}{dt}} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\begin{scope} +\clip (-1,-1) rectangle (4,4); + +\def\r{3} +\def\winkel{30} + +\fill[color=blue!20] (0,0) -- (0:\r) arc (0:\winkel:\r) -- cycle; +\node[color=blue] at ({0.5*\winkel}:{0.5*\r}) {$\Delta\varphi$}; + +\draw[line width=0.3pt] (0,0) circle[radius=\r]; + +\draw[->] (0,0) -- (0:\r); +\draw[->] (0,0) -- (\winkel:\r); + +\uncover<4->{ +\draw[->] (0:\r) -- ($(0:\r)+(90:0.7*\r)$); +\draw[->] (\winkel:\r) -- ($(\winkel:\r)+({90+\winkel}:0.7*\r)$); +} + +\draw[color=red,line width=1.4pt] (0:\r) arc (0:\winkel:\r); +\node[color=red] at ({0.5*\winkel}:\r) [left] {$s$}; +\fill[color=red] (0:\r) circle[radius=0.05]; +\fill[color=red] (\winkel:\r) circle[radius=0.05]; + +\node at (\winkel:{0.5*\r}) [above] {$r$}; +\node at (0:{0.5*\r}) [below] {$r$}; +\end{scope} + +\end{tikzpicture} +\end{center} +\uncover<4->{% +Für $\varphi$ kann man auch den Polarwinkel des Tangentialvektors nehmen +} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/numerik.tex b/vorlesungen/slides/fresnel/numerik.tex new file mode 100644 index 0000000..0bd4d5a --- /dev/null +++ b/vorlesungen/slides/fresnel/numerik.tex @@ -0,0 +1,124 @@ +% +% numerik.tex -- numerische Berechnung der Fresnel Integrale +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Numerik} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Taylor-Reihe} +\begin{align*} +\sin t^{\uncover<2->{\color<2>{red}2}} +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{ +\ifthenelse{\boolean{presentation}}{\only<1>{2k+1}}{} +\only<2->{\color<2>{red}4k+2} +} +}{ +(2k+1)! +} +\\ +%\int \sin t^2\,dt +\uncover<4->{ +S_1(t) +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{4k+3}}{(2k+1)!(4n+3)} +} +\\ +\cos t^{\uncover<3->{\color<3>{red}2}} +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{ +\ifthenelse{\boolean{presentation}}{\only<-2>{2k}}{} +\only<3->{\color<3>{red}4k}} +}{ +(2k)! +} +\\ +%\int \sin t^2\,dt +\uncover<5->{ +C_1(t) +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{4k+1}}{(2k)!(4k+1)} +} +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<6->{ +\begin{block}{Differentialgleichung} +\[ +\dot{\gamma}_1(t) += +\begin{pmatrix} +\cos t^2\\ \sin t^2 +\end{pmatrix} +\uncover<7->{ +\; +\to +\; +\gamma_1(t) += +\begin{pmatrix} +C_1(t)\\S_1(t) +\end{pmatrix} +} +\] +\end{block}} +\uncover<8->{% +\begin{block}{Hypergeometrische Reihen} +\begin{align*} +\uncover<9->{% +S(t) +&= +\frac{\pi z^3}{6} +\cdot +\mathstrut_1F_2\biggl( +\begin{matrix}\frac34\\\frac32,\frac74\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr) +} +\\ +\uncover<10->{ +C(t) +&= +z +\cdot +\mathstrut_1F_2\biggl( +\begin{matrix}\frac14\\\frac12,\frac54\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr)} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\uncover<11->{% +\begin{block}{Komplexe Fehlerfunktion} +\[ +\left. +\begin{matrix} +S(z)\\ +C(z) +\end{matrix} +\right\} += +\frac{1\pm i}{4} +\left( +\operatorname{erf}\biggl({\frac{1+i}2}\sqrt{\pi}z\biggr) +\mp i +\operatorname{erf}\biggl({\frac{1-i}2}\sqrt{\pi}z\biggr) +\right) +\] +\end{block}} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/Makefile.inc b/vorlesungen/slides/hermite/Makefile.inc new file mode 100644 index 0000000..58c21f2 --- /dev/null +++ b/vorlesungen/slides/hermite/Makefile.inc @@ -0,0 +1,12 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterhermite = \ + ../slides/hermite/normalintegrale.tex \ + ../slides/hermite/normalhermite.tex \ + ../slides/hermite/hermiteentwicklung.tex \ + ../slides/hermite/loesung.tex \ + ../slides/hermite/skalarprodukt.tex \ + ../slides/hermite/test.tex diff --git a/vorlesungen/slides/hermite/chapter.tex b/vorlesungen/slides/hermite/chapter.tex new file mode 100644 index 0000000..b7dd260 --- /dev/null +++ b/vorlesungen/slides/hermite/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter hermite +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{hermite/test.tex} diff --git a/vorlesungen/slides/hermite/hermiteentwicklung.tex b/vorlesungen/slides/hermite/hermiteentwicklung.tex new file mode 100644 index 0000000..e1ced30 --- /dev/null +++ b/vorlesungen/slides/hermite/hermiteentwicklung.tex @@ -0,0 +1,69 @@ +% +% hermiteentwicklung.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Beliebige Polynome} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Polynom} +\[ +P(x) += +p_0 + p_1x + p_2x^2 + \dots + p_nx^n +\] +als Linearkombination von Hermite-Polynome schreiben: +\begin{align*} +P(x) +&= +a_0H_0(x)% + a_1H_1(x) ++ \dots + a_nH_n(x) +\\ +&= +a_0\cdot 1 +\\ +&\quad + a_1\cdot 2x +\\ +&\quad + a_2\cdot(4x^2-2) +\\ +&\quad + a_3\cdot(8x^3-12x) +\\ +&\quad + a_4\cdot(16x^4-48x^2+12) +\\ +&\quad\;\;\vdots +\\ +&\quad + a_n(2^nx^n + \dots) +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Koeffizientenvergleich} +führt auf ein Gleichungssystem +\begin{center} +\begin{tabular}{|>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}c<{$}|>{$}c<{$}|} +\hline +a_0&a_1&a_2&a_3&a_4&\dots&\\ +\hline + 1& 0& 0& 0& 0&\dots&p_0\\ + 0& 2& 0& 0& 0&\dots&p_1\\ +-2& 0& 4& 0& 0&\dots&p_2\\ + 0&-12& 0& 8& 0&\dots&p_3\\ +12& 0&-48& 0& 16&\dots&p_4\\ +\vdots&\vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ +\hline +\end{tabular} +\end{center} +Dreiecksmatrix, Diagonalelement +$\ne 0$ +$\Rightarrow$ +$\exists$ eindeutige Lösung +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/loesung.tex b/vorlesungen/slides/hermite/loesung.tex new file mode 100644 index 0000000..7d4741f --- /dev/null +++ b/vorlesungen/slides/hermite/loesung.tex @@ -0,0 +1,56 @@ +% +% loesung.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Lösung} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Frage} +Für welche Polynome $P(t)$ kann man eine Stammfunktion +\[ +\int +P(t)e^{-\frac{t^2}2} +\,dt +\] +in geschlossener Form angeben? +\end{block} +\begin{block}{``Hermite-Antwort''} +\[ +\int H_n(x)e^{-x^2}\,dx +\] +kann genau für $n>0$ in geschlossener Form angegeben werden. +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Allgemein} +\begin{align*} +\int P(x)e^{-x^2}\,dx +&= +\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx +\\ +&= +\sum_{k=0}^n +a_k +\int +H_k(x)e^{-x^2}\,dx +\\ +&= +a_0\operatorname{erf}(x) + C +\\ +&\hspace*{2mm} + \sum_{k=1}^n a_k\int H_k(x)e^{-x^2}\,dx +\end{align*} +\end{block} +\begin{theorem} +Das Integral von $P(x)e^{-x^2}$ ist genau dann elementar darstellbar, wenn +$a_0=0$ +\end{theorem} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/normalhermite.tex b/vorlesungen/slides/hermite/normalhermite.tex new file mode 100644 index 0000000..16a314c --- /dev/null +++ b/vorlesungen/slides/hermite/normalhermite.tex @@ -0,0 +1,88 @@ +% +% normalhermite.tex -- integrability of hermite polynomials +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Hermite-Polynome} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Definition (Rodrigues-Formel)} +\[ +H_n(x) += +(-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} +\] +\end{block} +\vspace{-10pt} +\begin{block}{Orthogonalität} +$H_n(x)$ sind orthogonale Polynome bezüglich $w(x)=e^{-x^2}$, d.~h. +\begin{align*} +\langle H_n,H_m\rangle_w +&= +\int H_n(x)H_m(x)e^{-x^2}\,dx +\\ +&= +\biggl\{ +\renewcommand{\arraycolsep}{1pt} +\begin{array}{l@{\quad}l} +1&\text{falls $n=m$}\\ +0&\text{sonst} +\end{array} +\biggr\} += +\delta_{mn} +\end{align*} +\end{block} +\vspace{-10pt} +\begin{block}{Rekursion: Auf-/Absteigeoperatoren} +Rekursionsformel: +\[ +H_n(x) += +2x\cdot H_{n-1}(x) - H_{n-1}'(x) +\] +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Stammfunktion} +\begin{align*} +\int H_n(x) e^{-x^2}\,dx +&= +\int \bigl({\color{red}2x}H_{n-1}(x) +\\ +&\qquad -H_{n-1}'(x)\bigr) e^{-x^2}\,dx +\\ +{\color{gray}((e^{-x^2})'=-2x)} +&= +{\color{red}-}\int {\color{red}(e^{-x^2})'} H_{n-1}(x)\,dx +\\ +&\qquad +- +\int H_{n-1}'(x) e^{-x^2}\,dx +\\ +\text{\color{gray}(Produktregel)} +&= +\int (e^{-x^2}H_{n-1}(x))'\,dx +\\ +\text{\color{gray}(Ableitung)} +&= +e^{-x^2}H_{n-1}(x) +\end{align*} +ausser für $n=0$: +\[ +\int +H_0(x)e^{-x^2}\,dx += +\int +e^{-x^2}\,dx +\] +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/normalintegrale.tex b/vorlesungen/slides/hermite/normalintegrale.tex new file mode 100644 index 0000000..88abbe8 --- /dev/null +++ b/vorlesungen/slides/hermite/normalintegrale.tex @@ -0,0 +1,54 @@ +% +% normalintegrale.tex -- +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Integranden $P(t)e^{-t^2}$} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Frage} +Für welche Polynome $P(t)$ kann man eine Stammfunktion +\[ +\int +P(t)e^{-t^2} +\,dt +\] +in geschlossener Form angeben? +\end{block} +\begin{block}{Allgemeine Antwort} +Satz von Liouville und +Risch- Algorithmus können entscheiden, ob es eine elementare Stammfunktion gibt +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Negativbeispiel} +$P(t) = 1$, das Normalverteilungsintegral +\[ +F(x) += +\frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-t^2}\,dt +\] +ist nicht elementar darstellbar. +\end{block} +\begin{block}{Positivbeispiel} +$P(t)=t$. Wegen +\begin{align*} +\frac{d}{dx}e^{-x^2} +&= +-xe^{-x^2} +\intertext{ist} +\int te^{-t^2}\,dt +&= +-e^{-x^2}+C +\end{align*} +elementar darstellbar. +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/skalarprodukt.tex b/vorlesungen/slides/hermite/skalarprodukt.tex new file mode 100644 index 0000000..32b933f --- /dev/null +++ b/vorlesungen/slides/hermite/skalarprodukt.tex @@ -0,0 +1,72 @@ +% +% skalarprodukt.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Skalarprodukt} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Orthogonale Zerlegung} +Orthogonale $H_k$ normalisieren: +\[ +\tilde{H}_k(x) = \frac{1}{\|H_k\|_w} H_k(x) +\] +mit Gewichtsfunktion $w(x)=e^{-x^2}$ +\end{block} +\begin{block}{``Hermite''-Analyse} +\begin{align*} +P(x) +&= +\sum_{k=1}^\infty a_k H_k(x) += +\sum_{k=1}^\infty \tilde{a}_k \tilde{H}_k(x) +\\ +\tilde{a}_k +&= +\| H_k\|_w\, a_k +\\ +a_k +&= +\frac{1}{\|H_k\|} +\langle \tilde{H}_k, P\rangle_w += +\frac{1}{\|H_k\|^2} +\langle H_k, P\rangle_w +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Integrationsproblem} +Bedingung: +\begin{align*} +a_0=0 +\qquad\Leftrightarrow\qquad +\langle H_0,P\rangle_w +&= +0 +\\ +\int_{-\infty}^\infty +P(t) w(t) \,dt += +\int_{-\infty}^\infty +P(t) e^{-t^2} \,dt +&= +0 +\end{align*} +\end{block} +\begin{theorem} +Das Integral von $P(t)e^{-t^2}$ ist in geschlossener Form darstellbar +genau dann, wenn +\[ +\int_{-\infty}^\infty P(t)e^{-t^2}\,dt = 0 +\] +\end{theorem} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/test.tex b/vorlesungen/slides/hermite/test.tex new file mode 100644 index 0000000..c169024 --- /dev/null +++ b/vorlesungen/slides/hermite/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Auf- und Absteigeoperatoren} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/kra/Makefile.inc b/vorlesungen/slides/kra/Makefile.inc new file mode 100644 index 0000000..585adb3 --- /dev/null +++ b/vorlesungen/slides/kra/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterkra = \ + ../slides/kra/test.tex diff --git a/vorlesungen/slides/kra/chapter.tex b/vorlesungen/slides/kra/chapter.tex new file mode 100644 index 0000000..5c17331 --- /dev/null +++ b/vorlesungen/slides/kra/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter kra +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{kra/test.tex} diff --git a/vorlesungen/slides/kra/test.tex b/vorlesungen/slides/kra/test.tex new file mode 100644 index 0000000..8a1452a --- /dev/null +++ b/vorlesungen/slides/kra/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Kalman, Riccati, Abel} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/kreismembran/Makefile.inc b/vorlesungen/slides/kreismembran/Makefile.inc new file mode 100644 index 0000000..3a4ba8a --- /dev/null +++ b/vorlesungen/slides/kreismembran/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterkreismembran = \ + ../slides/kreismembran/test.tex diff --git a/vorlesungen/slides/kreismembran/chapter.tex b/vorlesungen/slides/kreismembran/chapter.tex new file mode 100644 index 0000000..640c225 --- /dev/null +++ b/vorlesungen/slides/kreismembran/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter kreismembran +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{kreismembran/test.tex} diff --git a/vorlesungen/slides/kreismembran/test.tex b/vorlesungen/slides/kreismembran/test.tex new file mode 100644 index 0000000..dd3605e --- /dev/null +++ b/vorlesungen/slides/kreismembran/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Schwingungen einer kreisförmigen Membran} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/kugel/Makefile.inc b/vorlesungen/slides/kugel/Makefile.inc new file mode 100644 index 0000000..55f0c25 --- /dev/null +++ b/vorlesungen/slides/kugel/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterkugel = \ + ../slides/kugel/test.tex diff --git a/vorlesungen/slides/kugel/chapter.tex b/vorlesungen/slides/kugel/chapter.tex new file mode 100644 index 0000000..1b629f6 --- /dev/null +++ b/vorlesungen/slides/kugel/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter kugel +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{kugel/test.tex} diff --git a/vorlesungen/slides/kugel/test.tex b/vorlesungen/slides/kugel/test.tex new file mode 100644 index 0000000..799e24a --- /dev/null +++ b/vorlesungen/slides/kugel/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Auf- und Absteigeoperatoren für Kugelfunktionen} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/laguerre/Makefile.inc b/vorlesungen/slides/laguerre/Makefile.inc new file mode 100644 index 0000000..afea6ae --- /dev/null +++ b/vorlesungen/slides/laguerre/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterlaguerre = \ + ../slides/laguerre/test.tex diff --git a/vorlesungen/slides/laguerre/chapter.tex b/vorlesungen/slides/laguerre/chapter.tex new file mode 100644 index 0000000..9df7c5e --- /dev/null +++ b/vorlesungen/slides/laguerre/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter laguerre +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{laguerre/test.tex} diff --git a/vorlesungen/slides/laguerre/test.tex b/vorlesungen/slides/laguerre/test.tex new file mode 100644 index 0000000..25878e4 --- /dev/null +++ b/vorlesungen/slides/laguerre/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Laguerre-Polynome} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/lambertw/Makefile.inc b/vorlesungen/slides/lambertw/Makefile.inc new file mode 100644 index 0000000..9947597 --- /dev/null +++ b/vorlesungen/slides/lambertw/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterlambertw = \ + ../slides/lambertw/test.tex diff --git a/vorlesungen/slides/lambertw/chapter.tex b/vorlesungen/slides/lambertw/chapter.tex new file mode 100644 index 0000000..73beae3 --- /dev/null +++ b/vorlesungen/slides/lambertw/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter lambertw +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{lambertw/test.tex} diff --git a/vorlesungen/slides/lambertw/test.tex b/vorlesungen/slides/lambertw/test.tex new file mode 100644 index 0000000..85f30ea --- /dev/null +++ b/vorlesungen/slides/lambertw/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Verfolgungskurven und Lambert $W$-Funktion} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/nav/Makefile.inc b/vorlesungen/slides/nav/Makefile.inc new file mode 100644 index 0000000..2f70842 --- /dev/null +++ b/vorlesungen/slides/nav/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapternav = \ + ../slides/nav/test.tex diff --git a/vorlesungen/slides/nav/chapter.tex b/vorlesungen/slides/nav/chapter.tex new file mode 100644 index 0000000..4ddd1c0 --- /dev/null +++ b/vorlesungen/slides/nav/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter nav +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{nav/test.tex} diff --git a/vorlesungen/slides/nav/test.tex b/vorlesungen/slides/nav/test.tex new file mode 100644 index 0000000..1cd4f86 --- /dev/null +++ b/vorlesungen/slides/nav/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Sphärische Navigation} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/parzyl/Makefile.inc b/vorlesungen/slides/parzyl/Makefile.inc new file mode 100644 index 0000000..2567029 --- /dev/null +++ b/vorlesungen/slides/parzyl/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterparzyl = \ + ../slides/parzyl/test.tex diff --git a/vorlesungen/slides/parzyl/chapter.tex b/vorlesungen/slides/parzyl/chapter.tex new file mode 100644 index 0000000..456008b --- /dev/null +++ b/vorlesungen/slides/parzyl/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter parzyl +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{parzyl/test.tex} diff --git a/vorlesungen/slides/parzyl/test.tex b/vorlesungen/slides/parzyl/test.tex new file mode 100644 index 0000000..bb760b5 --- /dev/null +++ b/vorlesungen/slides/parzyl/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Parabolische Zylinderfunktionen} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/slides.tex b/vorlesungen/slides/slides.tex index 7529e2e..7234b8b 100644 --- a/vorlesungen/slides/slides.tex +++ b/vorlesungen/slides/slides.tex @@ -32,61 +32,100 @@ \input{0/chapter.tex} -%\title[Kombinatorik]{Kapitel 1: Kombinatorik} -%\section{Kombinatorik} -% -%\titel -% -%\input{1/chapter.tex} -% -%\title[Ereignisse und Wahrscheinlichkeit]{Kapitel 2: Ereignisse und Wahrscheinlichkeit} -%\section{Ereignisse und Wahrscheinlichkeit} -% -%\titel -% -%\input{2/chapter.tex} -% -%\title[Erwartungswert]{Kapitel 3: Erwartungswert und Varianz} -%\section{Erwartungswert} -% -%\titel -% -%\input{3/chapter.tex} -% -%\title[Wahrscheinlichkeitsverteilung]{Kapitel 4: Wahrscheinlichkeitsverteilung} -%\section{Wahrscheinlichkeitsverteilung} -% -%\titel -% -%\input{4/chapter.tex} -% -%\title[Katalog]{Kapitel 5: Katalog von Wahrscheinlichkeitsverteilungen} -%\section{Katalog von Wahrscheinlichkeitsverteilungen} -% -%\titel -% -%\input{5/chapter.tex} -% -%\title[Schätzen]{Kapitel 6: Schätzen} -%\section{Schätzen} -% -%\titel -% -%\input{6/chapter.tex} -% -%\title[Hypothesen]{Kapitel 7: Hypothesen testen} -%\section{Hypothesen testen} -% -%\titel -% -%\input{7/chapter.tex} -% -%\title[Filtern]{Kapitel 8: Filtern} -%\section{Filtern} -% -%\titel -% -%\input{8/chapter8.tex} -% +% 0f1 +\title[0F1]{Thema: $\mathstrut_0F_1$} +\section{$\mathstrut_0F_1$} +\titel +\input{0f1/chapter.tex} + +% parzyl +\title[ParZyl]{Thema: Parabolische Zylinderfunktionen} +\section{Par Zyl} +\titel +\input{parzyl/chapter.tex} + +% lambertw +\title[lambertw]{Thema: Verfolgungskurven und Lambert $W$-Funktion} +\section{lambertw} +\titel +\input{lambertw/chapter.tex} + +% fresnel +\title[fresnel]{Thema: Klothoide} +\section{fresnel} +\titel +\input{fresnel/chapter.tex} + +% nav +\title[nav]{Thema: Sphärische Navigation} +\section{nav} +\titel +\input{nav/chapter.tex} + +% fm +\title[fm]{Thema: Frequenzspektrum eines frequenzmodulierten Signals} +\section{fm} +\titel +\input{fm/chapter.tex} + +% kreismembran +\title[kreismembran]{Thema: Schwingungen einer kreisförmigen Membran} +\section{kreismembran} +\titel +\input{kreismembran/chapter.tex} + +% sturmliouville +\title[sturmliouville]{Thema: Sturm-Liouville-Problem} +\section{sturmliouville} +\titel +\input{sturmliouville/chapter.tex} + +% hermite +\title[hermite]{Thema: Auf- und Absteigeoperatoren für den harmonischen Oszillator} +\section{hermite} +\titel +\input{hermite/chapter.tex} + +% kugel +\title[kugel]{Thema: Auf- und Absteigeoperatoren und Kugelfunktionen} +\section{kugel} +\titel +\input{kugel/chapter.tex} + +% dreieck +\title[dreieck]{Thema: Dreieckstest und Beta-Funktion} +\section{dreieck} +\titel +\input{dreieck/chapter.tex} + +% ellfilter +\title[ellfilter]{Thema: Elliptische Filter} +\section{ellfilter} +\titel +\input{ellfilter/chapter.tex} + +% kra +\title[kra]{Thema: Kalman, Riccati, Abel} +\section{kra} +\titel +\input{kra/chapter.tex} + +% laguerre +\title[laguerre]{Thema: Laguerre-Polynome} +\section{laguerre} +\titel +\input{laguerre/chapter.tex} + +% transfer +\title[transfer]{Thema: Transferfunktionen} +\section{transfer} +\titel +\input{transfer/chapter.tex} + +% zeta +\title[zeta]{Thema: Riemann $\zeta$-Funktion} +\section{zeta} +\titel +\input{zeta/chapter.tex} diff --git a/vorlesungen/slides/sturmliouville/Makefile.inc b/vorlesungen/slides/sturmliouville/Makefile.inc new file mode 100644 index 0000000..7c7818c --- /dev/null +++ b/vorlesungen/slides/sturmliouville/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chaptersturmliouville = \ + ../slides/sturmliouville/test.tex diff --git a/vorlesungen/slides/sturmliouville/chapter.tex b/vorlesungen/slides/sturmliouville/chapter.tex new file mode 100644 index 0000000..eb029bb --- /dev/null +++ b/vorlesungen/slides/sturmliouville/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter sturmliouville +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{sturmliouville/test.tex} diff --git a/vorlesungen/slides/sturmliouville/test.tex b/vorlesungen/slides/sturmliouville/test.tex new file mode 100644 index 0000000..a8983fc --- /dev/null +++ b/vorlesungen/slides/sturmliouville/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Sturm-Liouville-Problem} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex index 6aa09f8..ca4ccc9 100644 --- a/vorlesungen/slides/test.tex +++ b/vorlesungen/slides/test.tex @@ -3,4 +3,8 @@ % % (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil % -\folie{0/intro.tex} +\folie{hermite/normalintegrale.tex} +\folie{hermite/normalhermite.tex} +\folie{hermite/hermiteentwicklung.tex} +\folie{hermite/loesung.tex} +\folie{hermite/skalarprodukt.tex} diff --git a/vorlesungen/slides/transfer/Makefile.inc b/vorlesungen/slides/transfer/Makefile.inc new file mode 100644 index 0000000..e42c7c5 --- /dev/null +++ b/vorlesungen/slides/transfer/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chaptertransfer = \ + ../slides/transfer/test.tex diff --git a/vorlesungen/slides/transfer/chapter.tex b/vorlesungen/slides/transfer/chapter.tex new file mode 100644 index 0000000..8f784ea --- /dev/null +++ b/vorlesungen/slides/transfer/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter transfer +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{transfer/test.tex} diff --git a/vorlesungen/slides/transfer/test.tex b/vorlesungen/slides/transfer/test.tex new file mode 100644 index 0000000..c8a5050 --- /dev/null +++ b/vorlesungen/slides/transfer/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Transferfunktionen} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/zeta/Makefile.inc b/vorlesungen/slides/zeta/Makefile.inc new file mode 100644 index 0000000..64e30d1 --- /dev/null +++ b/vorlesungen/slides/zeta/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterzeta = \ + ../slides/zeta/test.tex diff --git a/vorlesungen/slides/zeta/chapter.tex b/vorlesungen/slides/zeta/chapter.tex new file mode 100644 index 0000000..2b5f676 --- /dev/null +++ b/vorlesungen/slides/zeta/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter zeta +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{zeta/test.tex} diff --git a/vorlesungen/slides/zeta/test.tex b/vorlesungen/slides/zeta/test.tex new file mode 100644 index 0000000..f0ba7a8 --- /dev/null +++ b/vorlesungen/slides/zeta/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für Riemann $\zeta$-Funktion} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/stream/countdown.html b/vorlesungen/stream/countdown.html index d8ec82e..e9d7d6e 100644 --- a/vorlesungen/stream/countdown.html +++ b/vorlesungen/stream/countdown.html @@ -25,7 +25,7 @@ function checkfor(d) { console.log("time string: " + ds); let start = new Date(ds).getTime(); console.log("now: " + now); - if ((start > now) && ((start-now) < 3600*1000)) { + if ((start > now) && ((start-now) < 3300*1000)) { deadline = start; console.log("set deadline to: " + ds); } else { |
