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authorJODBaer <JODBaer@github.com>2021-04-20 12:38:29 +0200
committerJODBaer <JODBaer@github.com>2021-04-20 12:38:29 +0200
commitf9154b1070929ac3063a9676e11723e5ec0c8deb (patch)
tree3b2da1b4ee8f80ebe5c05a6c74f48832b57ffc9e /vorlesungen/08_dgl
parentMerge remote-tracking branch 'upstream/master' (diff)
parentMerge branch 'master' of github.com:AndreasFMueller/SeminarMatrizen (diff)
downloadSeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.tar.gz
SeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.zip
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/08_dgl')
-rw-r--r--vorlesungen/08_dgl/Makefile46
-rw-r--r--vorlesungen/08_dgl/MathSem-08-dgl.tex35
-rw-r--r--vorlesungen/08_dgl/common.tex27
-rw-r--r--vorlesungen/08_dgl/dgl-handout.tex11
-rw-r--r--vorlesungen/08_dgl/slides.tex35
5 files changed, 154 insertions, 0 deletions
diff --git a/vorlesungen/08_dgl/Makefile b/vorlesungen/08_dgl/Makefile
new file mode 100644
index 0000000..7a3960a
--- /dev/null
+++ b/vorlesungen/08_dgl/Makefile
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+#
+# Makefile -- dgl
+#
+# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil
+#
+all: dgl-handout.pdf MathSem-08-dgl.pdf
+
+# SHELL = /bin/bash
+
+include ../slides/Makefile.inc
+
+SOURCES = common.tex slides.tex $(slides)
+IMAGES = vektorfelder-1.pdf
+
+
+MathSem-08-dgl.pdf: MathSem-08-dgl.tex $(SOURCES) $(IMAGES)
+ pdflatex --synctex=1 MathSem-08-dgl.tex > /dev/null
+
+dgl-handout.pdf: dgl-handout.tex $(SOURCES) $(IMAGES)
+ pdflatex dgl-handout.tex > /dev/null
+
+vektorfelder-1.pdf: ../slides/10/vektorfelder.mp
+ cd ../slides/10/; \
+ TEX=latex mpost vektorfelder.mp; \
+ for f in vektorfelder.[0-9]*; \
+ do \
+ mptopdf $${f} > /dev/null; \
+ done; \
+ rm -f vektorfelder.[0-9]* vektorfelder.log vektorfelder.mpx
+
+thumbnail: thumbnail.jpg # fix1.jpg
+
+thumbnail.pdf: MathSem-08-dgl.pdf
+ pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \
+ MathSem-08-dgl.pdf 1
+thumbnail.jpg: thumbnail.pdf
+ convert -density 300 thumbnail.pdf \
+ -resize 1920x1080 -units PixelsPerInch thumbnail.jpg
+
+fix1.pdf: MathSem-08-dgl.pdf
+ pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \
+ MathSem-08-dgl.pdf 1
+fix1.jpg: fix1.pdf
+ convert -density 300 fix1.pdf \
+ -resize 1920x1080 -units PixelsPerInch fix1.jpg
+
diff --git a/vorlesungen/08_dgl/MathSem-08-dgl.tex b/vorlesungen/08_dgl/MathSem-08-dgl.tex
new file mode 100644
index 0000000..e4ece1b
--- /dev/null
+++ b/vorlesungen/08_dgl/MathSem-08-dgl.tex
@@ -0,0 +1,35 @@
+%
+% MathSem-08-dgl.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
+ \vspace{-1.5cm}
+ \begin{columns}
+ \begin{column}{.48\textwidth}
+ \centering
+ \includegraphics[width=.7\linewidth]{../slides/10/vektorfelder-6.pdf}
+ \end{column}
+ \begin{column}{.48\textwidth}
+ \begin{align*}
+ x(t)
+ &=
+ \exp(At) x_0
+ \\
+ \exp(At)
+ &=
+ 1 + At + \frac{A^2t^2}{2} + \frac{A^3 t^3}{3!} + \ldots
+ \\
+ &=
+ \lim_{n\to \infty} \left(1 + \frac{At}{n}\right)^n
+ \end{align*}
+ \end{column}
+ \end{columns}
+\end{frame}
+\input{slides.tex}
+\end{document}
diff --git a/vorlesungen/08_dgl/common.tex b/vorlesungen/08_dgl/common.tex
new file mode 100644
index 0000000..fbf3ad9
--- /dev/null
+++ b/vorlesungen/08_dgl/common.tex
@@ -0,0 +1,27 @@
+%
+% 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[DGL]{Differential-Gleichungen}
+\author[R.~Seitz]{Roy Seitz}
+\date[]{}
+\newboolean{presentation}
+
+\newcommand{\gSL}[2]{\ensuremath{\text{SL}(#1, \mathbb{#2})}}
+\newcommand{\gSO}[1]{\ensuremath{\text{SO}(#1)}}
+\newcommand{\gGL}[2]{\ensuremath{\text{GL}(#1, \mathbb #2)}}
+
+\newcommand{\asl}[2]{\ensuremath{\mathfrak{sl}(#1, \mathbb{#2})}}
+\newcommand{\aso}[1]{\ensuremath{\mathfrak{so}(#1)}}
+\newcommand{\agl}[2]{\ensuremath{\mathfrak{gl}(#1, \mathbb #2)}}
+
+\DeclareMathOperator{\Spur}{Spur}
+
+
diff --git a/vorlesungen/08_dgl/dgl-handout.tex b/vorlesungen/08_dgl/dgl-handout.tex
new file mode 100644
index 0000000..2bd08a1
--- /dev/null
+++ b/vorlesungen/08_dgl/dgl-handout.tex
@@ -0,0 +1,11 @@
+%
+% dgl-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/08_dgl/slides.tex b/vorlesungen/08_dgl/slides.tex
new file mode 100644
index 0000000..029e1c7
--- /dev/null
+++ b/vorlesungen/08_dgl/slides.tex
@@ -0,0 +1,35 @@
+%
+% slides.tex -- XXX
+%
+% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil
+%
+
+% Wie findet man die Lösung von \dot x = Ax?
+% Fall \dot x = ax
+% Potenzreihenansatz -> exp(ax) x_0
+
+%% Plan:
+% 1. Tailor-Reihen p_n -> f
+% 2. x' = ax => x = exp(ax) x_0 via Potenzreihe finden
+% 3. n-Dim-skalar -> 1-Dim-Matrix
+% 4. Analogie zur Vektor-Matrix-Form
+% 5. exp(Ax) x_0 als Fluss
+% 6. Strömungslinien = Pfade für Lie-Theorie, A lokal, exp(Ax) global
+% 7. Beispiele so(2), Jordan-Block, vielleicht [0 1; 1 0]
+
+\section{Einführung}
+\folie{10/intro.tex}
+\section{Woher kommt $\exp(At)$?}
+\subsection{Taylor-Reihen}
+\folie{10/taylor.tex}
+\folie{10/potenzreihenmethode.tex}
+\subsection{Ableitung von $\exp(At)$}
+\folie{10/ableitung-exp.tex}
+\section{Lösen einer Matrix-DGL}
+\folie{10/n-zu-1.tex}
+\folie{10/matrix-dgl.tex}
+\section{Lie-Gruppen und -Algebren}
+\folie{10/repetition.tex}
+\folie{10/so2.tex}
+\section{Was bedeutet $\exp(At)$?}
+\folie{10/vektorfelder.tex}