From 680e1e763b8d899b3601b5ab0cf6f1fc2a114e1d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 3 Jun 2021 18:51:36 +0200
Subject: phases

---
 vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex | 27 +++++++++++++++-------
 1 file changed, 19 insertions(+), 8 deletions(-)

(limited to 'vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex')

diff --git a/vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex b/vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex
index e2c26f5..de9383f 100644
--- a/vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex
+++ b/vorlesungen/slides/2/hilbertraum/rieszbeispiel.tex
@@ -19,30 +19,33 @@ f({\color{blue}x})
 &= 
 \begin{pmatrix}f_1&f_2&\dots&f_n\end{pmatrix} {\color{blue}x}
 \\
+\uncover<2->{
 {\color{red}v}&=
 \rlap{$
 \begin{pmatrix}
 \overline{f}_1&\overline{f}_2&\dots&\overline{f}_n
 \end{pmatrix}^t
-\;\Rightarrow\;
-f({\color{blue}x})=\langle {\color{red}v},{\color{blue}x}\rangle
-$}
+\uncover<3->{\;\Rightarrow\;
+f({\color{blue}x})=\langle {\color{red}v},{\color{blue}x}\rangle}
+$}}
 \end{align*}
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<4->{%
 \begin{block}{Linearform auf $L^2([a,b])$}
 \begin{align*}
 {\color{red}x}&\in L^2([a,b])
 \\
+\uncover<5->{
 f&\colon L^2([a,b]) \to \mathbb{C}
-: {\color{red}x} \mapsto f({\color{red}x})
-\intertext{Riesz-Darstellungssatz: $\exists {\color{blue}v}\in L^2([a,b])$}
-f({\color{red}x})
+: {\color{red}x} \mapsto f({\color{red}x})}
+\intertext{\uncover<6->{Riesz-Darstellungssatz: $\exists {\color{blue}v}\in L^2([a,b])$}}
+\uncover<7->{f({\color{red}x})
 &=
-\int_a^b {\color{blue}\overline{v}(t)}{\color{red}x(t)}\,dt
+\int_a^b {\color{blue}\overline{v}(t)}{\color{red}x(t)}\,dt}
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 \begin{center}
@@ -50,10 +53,12 @@ f({\color{red}x})
 \begin{scope}[xshift=-3.5cm]
 \def\s{0.058}
 \foreach \n in {0,...,5}{
+\uncover<3->{
 	\draw[color=red,line width=3pt]
 		({\n+\s},{1/(\n+0.5)}) -- ({\n+\s},0);
 	\node[color=red] at ({\n},{-0.2+1/(\n+0.5)})
 		[above right] {$v_\n\mathstrut$};
+}
 	\draw[color=blue,line width=3pt]
 		({\n-\s},{0.4+0.55*sin(200*\n)+0.25*\n}) -- ({\n-\s},0);
 	\node[color=blue] at ({\n},{-0.2+0.4+0.55*sin(200*\n)+0.25*\n})
@@ -67,17 +72,22 @@ f({\color{red}x})
 }
 \node at (5.6,0) [below] {$\cdots$\strut};
 \end{scope}
+\uncover<4->{
 \begin{scope}[xshift=3.5cm]
+\uncover<7->{
 \fill[color=red!40,opacity=0.5] 
 	plot[domain=0:5,samples=100] (\x,{1/(\x+0.5)})
 	--
 	(5,0) -- (0,0) -- cycle;
+}
 \fill[color=blue!40,opacity=0.5]
 	plot[domain=0:5,samples=100] (\x,{0.4+0.55*sin(200*\x)+0.25*\x})
 	-- (5,0) -- (0,0) -- cycle;
+\uncover<7->{
 \draw[color=red,line width=1.4pt]
 	plot[domain=0:5,samples=100] (\x,{1/(\x+0.5)});
 \node[color=red] at (0,2) [right] {$x(t)$};
+}
 
 \draw[color=blue,line width=1.4pt]
 	plot[domain=0:5,samples=100] (\x,{0.4+0.55*sin(200*\x)+0.25*\x});
@@ -90,6 +100,7 @@ f({\color{red}x})
 \draw (5.0,-0.1) -- (5.0,0.1);
 \node at (5.0,0) [below] {$b$\strut};
 \end{scope}
+}
 \end{tikzpicture}
 \end{center}
 \end{frame}
-- 
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