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authorAndreas Müller <andreas.mueller@ost.ch>2021-04-19 20:49:14 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-04-19 20:49:14 +0200
commit962f46e09482dffceaba74d522c723d490c3344b (patch)
treec57598c0128ebcc0a6edbeda87de561446ead1e6 /vorlesungen/08_dgl/MathSem-08-dgl.tex
parentadd new slides (diff)
parentTitleseite und Handout. (diff)
downloadSeminarMatrizen-962f46e09482dffceaba74d522c723d490c3344b.tar.gz
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Merge branch 'master' of github.com:AndreasFMueller/SeminarMatrizen
Diffstat (limited to 'vorlesungen/08_dgl/MathSem-08-dgl.tex')
-rw-r--r--vorlesungen/08_dgl/MathSem-08-dgl.tex25
1 files changed, 23 insertions, 2 deletions
diff --git a/vorlesungen/08_dgl/MathSem-08-dgl.tex b/vorlesungen/08_dgl/MathSem-08-dgl.tex
index 1bcb946..e4ece1b 100644
--- a/vorlesungen/08_dgl/MathSem-08-dgl.tex
+++ b/vorlesungen/08_dgl/MathSem-08-dgl.tex
@@ -7,8 +7,29 @@
\input{common.tex}
\setboolean{presentation}{true}
\begin{document}
-\begin{frame}
-\titlepage
+ \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}