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author | JODBaer <JODBaer@github.com> | 2021-04-20 12:38:29 +0200 |
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committer | JODBaer <JODBaer@github.com> | 2021-04-20 12:38:29 +0200 |
commit | f9154b1070929ac3063a9676e11723e5ec0c8deb (patch) | |
tree | 3b2da1b4ee8f80ebe5c05a6c74f48832b57ffc9e /vorlesungen/08_dgl | |
parent | Merge remote-tracking branch 'upstream/master' (diff) | |
parent | Merge branch 'master' of github.com:AndreasFMueller/SeminarMatrizen (diff) | |
download | SeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.tar.gz SeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.zip |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/08_dgl')
-rw-r--r-- | vorlesungen/08_dgl/Makefile | 46 | ||||
-rw-r--r-- | vorlesungen/08_dgl/MathSem-08-dgl.tex | 35 | ||||
-rw-r--r-- | vorlesungen/08_dgl/common.tex | 27 | ||||
-rw-r--r-- | vorlesungen/08_dgl/dgl-handout.tex | 11 | ||||
-rw-r--r-- | vorlesungen/08_dgl/slides.tex | 35 |
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 @@ -0,0 +1,46 @@ +# +# 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} |