From 8a32e72ace1b6442b2601b821e4d7ed24047939e Mon Sep 17 00:00:00 2001
From: Roy Seitz <roy.seitz@ost.ch>
Date: Mon, 19 Apr 2021 11:10:24 +0200
Subject: Titleseite und Handout.

---
 vorlesungen/08_dgl/MathSem-08-dgl.tex | 25 +++++++++++++++++++++++--
 1 file changed, 23 insertions(+), 2 deletions(-)

(limited to 'vorlesungen/08_dgl/MathSem-08-dgl.tex')

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}
-- 
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