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diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex
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+%
+% integrale.tex -- Definition der Fresnel Integrale
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\input{../slides/fresnel/eulerpath.tex}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\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*}
+\color{red}S(t)
+&=
+\int_0^t \sin\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau
+\\
+\color{blue}C(t)
+&=
+\int_0^t \cos\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau
+\end{align*}
+\uncover<3->{%
+Können nicht in geschlossener Form ausgewertet werden.
+}
+\end{block}
+\uncover<4->{%
+\begin{block}{Euler-Spirale}
+\[
+\gamma_a(t)
+=
+\begin{pmatrix}
+C_a(t)\\S_a(t)
+\end{pmatrix}
+=
+\begin{pmatrix}
+\displaystyle
+\int_0^t \cos (a\tau^2)\,d\tau\\[8pt]
+\displaystyle
+\int_0^t \sin (a\tau^2)\,d\tau
+\end{pmatrix}
+\]
+\end{block}}
+\end{column}
+\begin{column}{0.48\textwidth}
+\ifthenelse{\boolean{presentation}}{
+\only<2-4>{%
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=1]
+\def\dx{0.6}
+\def\dy{1.5}
+
+\begin{scope}
+	\draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy});
+	\draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy});
+	\draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}];
+	\draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$S(t)$}];
+	\draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy});
+	\node at (-0.1,{0.5*\dy}) [left] {$\frac12$};
+	\draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy});
+	\node at (0.1,{-0.5*\dy}) [right] {$-\frac12$};
+	\draw[color=red,line width=1.4pt] \Splotright;
+	\draw[color=red,line width=1.4pt] \Splotleft;
+\end{scope}
+
+\begin{scope}[yshift=-3.4cm]
+	\draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy});
+	\draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy});
+	\draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}];
+	\draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$C(t)$}];
+	\draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy});
+	\node at (-0.1,{0.5*\dy}) [left] {$\frac12$};
+	\draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy});
+	\node at (0.1,{-0.5*\dy}) [right] {$-\frac12$};
+	\draw[color=blue,line width=1.4pt] \Cplotright;
+	\draw[color=blue,line width=1.4pt] \Cplotleft;
+\end{scope}
+
+\end{tikzpicture}
+\end{center}
+}}{}
+\uncover<5->{%
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=3.5]
+
+\draw[color=gray!50] (-0.5,-0.5) rectangle (0.5,0.5);
+
+\draw[->] (-0.8,0) -- (0.9,0) coordinate[label={$\color{blue}C(t)$}];
+\draw[->] (0,-0.8) -- (0,0.9) coordinate[label={right:$\color{red}S(t)$}];
+
+\draw[color=darkgreen,line width=1.0pt] \fresnela;
+\draw[color=darkgreen,line width=1.0pt] \fresnelb;
+
+\fill[color=orange] (0.5,0.5) circle[radius=0.02];
+\fill[color=orange] (-0.5,-0.5) circle[radius=0.02];
+
+\draw (0.5,-0.02) -- (0.5,0.02);
+\node at (0.5,-0.02) [below right] {$\frac12$};
+
+\draw (-0.5,-0.02) -- (-0.5,0.02);
+\node at (-0.5,0.02) [above left] {$-\frac12$};
+
+\draw (-0.01,0.5) -- (0.02,0.5);
+\node at (-0.02,0.5) [above left] {$\frac12$};
+
+\draw (-0.02,-0.5) -- (0.02,-0.5);
+\node at (0.02,-0.5) [below right] {$-\frac12$};
+
+\end{tikzpicture}
+\end{center}
+}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup