diff options
author | Andreas Müller <andreas.mueller@ost.ch> | 2022-05-08 22:37:45 +0200 |
---|---|---|
committer | Andreas Müller <andreas.mueller@ost.ch> | 2022-05-08 22:37:45 +0200 |
commit | a866d7cd6672474e9376617aadc91424b9ba3506 (patch) | |
tree | 68e4969e2f70cc3e4386ed351e6328aca3ec3851 /vorlesungen/slides/fresnel/integrale.tex | |
parent | remove template paper (diff) | |
download | SeminarSpezielleFunktionen-a866d7cd6672474e9376617aadc91424b9ba3506.tar.gz SeminarSpezielleFunktionen-a866d7cd6672474e9376617aadc91424b9ba3506.zip |
add Fresnel presentation
Diffstat (limited to 'vorlesungen/slides/fresnel/integrale.tex')
-rw-r--r-- | vorlesungen/slides/fresnel/integrale.tex | 72 |
1 files changed, 72 insertions, 0 deletions
diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex new file mode 100644 index 0000000..7798932 --- /dev/null +++ b/vorlesungen/slides/fresnel/integrale.tex @@ -0,0 +1,72 @@ +% +% fresnel.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\input{../slides/fresnel/eulerpath.tex} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Fresnel-Integrale} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Definition} +Fresnel-Integrale: +\begin{align*} +S(t) +&= +\int_0^t \sin(\tau^2)\,d\tau +\\ +C(t) +&= +\int_0^t \cos(\tau^2)\,d\tau +\end{align*} +\uncover<2->{% +Können nicht in geschlossener Form ausgewertet werden. +} +\end{block} +\uncover<3->{% +\begin{block}{Kurve} +\[ +\gamma(t) += +\begin{pmatrix} +S(t)\\C(t) +\end{pmatrix} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<4->{% +\begin{block}{Euler-Spirale} +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=2.7] + +\draw[->] (-1.05,0) -- (1.05,0) coordinate[label={$C(t)$}]; +\draw[->] (0,-1.05) -- (0,1.05) coordinate[label={right:$S(t)$}]; + +\draw[color=red,line width=1.4pt] \fresnela; +\draw[color=red,line width=1.4pt] \fresnelb; + +\fill[color=blue] ({sqrt(3.14159/8)},{sqrt(3.14159/8)}) circle[radius=0.02]; +\fill[color=blue] ({-sqrt(3.14159/8)},{-sqrt(3.14159/8)}) circle[radius=0.02]; + +\draw (1,-0.03) -- (1,0.03); +\node at (1,-0.03) [below] {$1$}; +\draw (-1,-0.03) -- (-1,0.03); +\node at (-1,0.03) [above] {$-1$}; +\draw (-0.03,1) -- (0.03,1); +\node at (-0.03,1) [left] {$1$}; +\draw (-0.03,-1) -- (0.03,-1); +\node at (0.03,-1) [right] {$-1$}; +\node at (0,0) [below right] {$0$}; + +\end{tikzpicture} +\end{center} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |