add Fresnel presentation

1 files changed, 83 insertions, 0 deletions

diff --git a/vorlesungen/slides/fresnel/numerik.tex b/vorlesungen/slides/fresnel/numerik.tex
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+++ b/vorlesungen/slides/fresnel/numerik.tex
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+%
+% numerik.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Numerik}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Taylor-Reihe}
+\begin{align*}
+\sin t^2
+&=
+\sum_{k=0}^\infty
+(-1)^k \frac{t^{2k+1}}{(2k+1)!}
+\\
+%\int \sin t^2\,dt
+\uncover<2->{
+S(t)
+&=
+\sum_{k=0}^\infty
+(-1)^k \frac{t^{4k+3}}{(2k+1)!(4n+3)}
+}
+\\
+\cos t^2
+&=
+\sum_{k=0}^\infty
+(-1)^k \frac{t^{2k}}{(2k)!}
+\\
+%\int \sin t^2\,dt
+\uncover<3->{
+C(t)
+&=
+\sum_{k=0}^\infty
+(-1)^k \frac{t^{4k+1}}{(2k)!(4k+1)}
+}
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<4->{
+\begin{block}{Differentialgleichung}
+\[
+\dot{\gamma}(t)
+=
+\begin{pmatrix}
+\sin t^2\\ \cos t^2
+\end{pmatrix}
+\]
+\end{block}}
+\uncover<5->{%
+\begin{block}{Hypergeometrische Reihen}
+\begin{align*}
+\uncover<6->{%
+S(t)
+&=
+\frac{\pi z^3}{6}\,
+\mathstrut_1F_2\biggl(
+\begin{matrix}\frac34\\\frac32,\frac74\end{matrix}
+;
+-\frac{\pi^2z^4}{16}
+\biggr)
+}
+\\
+\uncover<7->{
+C(t)
+&=
+z\,
+\mathstrut_1F_2\biggl(
+\begin{matrix}\frac14\\\frac12,\frac54\end{matrix}
+;
+-\frac{\pi^2z^4}{16}
+\biggr)}
+\end{align*}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup