%
% 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}