phasen

2 files changed, 63 insertions, 41 deletions

diff --git a/vorlesungen/slides/7/algebraisch.tex b/vorlesungen/slides/7/algebraisch.tex
index 5b33566..31d209a 100644
--- a/vorlesungen/slides/7/algebraisch.tex
+++ b/vorlesungen/slides/7/algebraisch.tex
@@ -19,23 +19,25 @@ Längenmessung mit Skalarprodukt
 \langle \vec{v},\vec{v}\rangle
 =
 \vec{v}\cdot \vec{v}
-=
-\vec{v}^t\vec{v}
+\uncover<2->{=
+\vec{v}^t\vec{v}}
 \end{align*}
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<3->{%
 \begin{block}{Flächeninhalt/Volumen}
 $n$ Vektoren $V=(\vec{v}_1,\dots,\vec{v}_n)$
 \\
 Volumen des Parallelepipeds: $\det V$
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 %
 \vspace{-7pt}
 \begin{columns}[t,onlytextwidth]
 \begin{column}{0.48\textwidth}
+\uncover<4->{%
 \begin{block}{Längenerhaltende Transformationen}
 $A\in\operatorname{GL}_n(\mathbb{R})$
 \begin{align*}
@@ -44,38 +46,45 @@ $A\in\operatorname{GL}_n(\mathbb{R})$
 (A\vec{x})
 \cdot
 (A\vec{y})
-=
+\uncover<5->{=
 (A\vec{x})^t
-(A\vec{y})
+(A\vec{y})}
 \\
+\uncover<6->{
 \vec{x}^tI\vec{y}
 &=
-\vec{x}^tA^tA\vec{y}
-\Rightarrow I=A^tA
+\vec{x}^tA^tA\vec{y}}
+\uncover<7->{
+\Rightarrow I=A^tA}
 \end{align*}
-Begründung: $\vec{e}_i^t B \vec{e}_j = b_{ij}$
-\end{block}
+\uncover<8->{Begründung: $\vec{e}_i^t B \vec{e}_j = b_{ij}$}
+\end{block}}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<9->{%
 \begin{block}{Volumenerhaltende Transformationen}
 $A\in\operatorname{GL}_n(\mathbb{R})$
 \begin{align*}
 \det(V)
 &=
 \det(AV)
-=
-\det(A)\det(V)
+\uncover<10->{=
+\det(A)\det(V)}
 \\
-1&=\det(A)
+\uncover<11->{
+1&=\det(A)}
 \end{align*}
+\uncover<10->{
 (Produktsatz für Determinante)
-\end{block}
+}
+\end{block}}
 \end{column}
 \end{columns}
 %
 \vspace{-3pt}
 \begin{columns}[t,onlytextwidth]
 \begin{column}{0.48\textwidth}
+\uncover<12->{%
 \begin{block}{Orthogonale Matrizen}
 Längentreue Abbildungen = orthogonale Matrizen:
 \[
@@ -87,9 +96,10 @@ A \in \operatorname{GL}_n(\mathbb{R})
 A^tA=I
 \}
 \]
-\end{block}
+\end{block}}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<13->{%
 \begin{block}{``Spezielle'' Matrizen}
 Volumen-/Orientierungserhaltende Transformationen:
 \[
@@ -97,7 +107,7 @@ Volumen-/Orientierungserhaltende Transformationen:
 =
 \{ A \in \operatorname{GL}_n(\mathbb{R}) \;|\; \det A = 1\}
 \]
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 
diff --git a/vorlesungen/slides/7/symmetrien.tex b/vorlesungen/slides/7/symmetrien.tex
index 79f9ef7..35d62d8 100644
--- a/vorlesungen/slides/7/symmetrien.tex
+++ b/vorlesungen/slides/7/symmetrien.tex
@@ -14,7 +14,7 @@
 \begin{column}{0.48\textwidth}
 \begin{block}{Diskrete Symmetrien}
 \begin{itemize}
-\item
+\item<2->
 Ebenen-Spiegelung:
 \[
 {\tiny
@@ -22,12 +22,13 @@ Ebenen-Spiegelung:
 }
 \mapsto
 {\tiny
-\begin{pmatrix*}[r]-x_1\\x_2\\x_3 \end{pmatrix*},
+\begin{pmatrix*}[r]-x_1\\x_2\\x_3 \end{pmatrix*}
 }
-\;
+\uncover<4->{\!,\;
 \vec{x}
 \mapsto
 \vec{x} -2 (\vec{n}\cdot\vec{x}) \vec{n}
+}
 \]
 \vspace{-10pt}
 \begin{center}
@@ -41,34 +42,39 @@ Ebenen-Spiegelung:
 \coordinate (C) at ({90+\a}:{\r*cos(90+\a-\b)});
 \coordinate (N) at (\a:2);
 \coordinate (D) at (\a:{\r*cos(\b-\a)});
+\uncover<3->{
 \clip (-2.5,-0.45) rectangle (2.5,1.95);
 
-\fill[color=darkgreen!20] (O) -- ({\a-90}:0.2) arc ({\a-90}:\a:0.2) -- cycle;
-\draw[->,color=darkgreen] (O) -- (N);
-\node[color=darkgreen] at (N) [above] {$\vec{n}$};
+	\fill[color=darkgreen!20] (O) -- ({\a-90}:0.2) arc ({\a-90}:\a:0.2)
+		-- cycle;
+	\draw[->,color=darkgreen] (O) -- (N);
+	\node[color=darkgreen] at (N) [above] {$\vec{n}$};
 
 
-\fill[color=blue!20] (C) -- ($(C)+(\a:0.2)$) arc (\a:{90+\a}:0.2) -- cycle;
-\fill[color=red] (O) circle[radius=0.06];
-\draw[color=red] ({\a-90}:2) -- ({\a+90}:2);
-\fill[color=blue] (C) circle[radius=0.06];
-\draw[color=blue,line width=0.1pt] (A) -- (D);
-\node[color=darkgreen] at (D) [below,rotate=\a] {$(\vec{n}\cdot\vec{x})\vec{n}$};
-\draw[color=blue,line width=0.5pt] (A)--(B);
+	\fill[color=blue!20] (C) -- ($(C)+(\a:0.2)$) arc (\a:{90+\a}:0.2)
+		-- cycle;
+	\fill[color=red] (O) circle[radius=0.06];
+	\draw[color=red] ({\a-90}:2) -- ({\a+90}:2);
+	\fill[color=blue] (C) circle[radius=0.06];
+	\draw[color=blue,line width=0.1pt] (A) -- (D);
+	\node[color=darkgreen] at (D) [below,rotate=\a]
+		{$(\vec{n}\cdot\vec{x})\vec{n}$};
+	\draw[color=blue,line width=0.5pt] (A)--(B);
 
-\node[color=blue] at (A) [above right] {$\vec{x}$};
-\node[color=blue] at (B) [above left] {$\vec{x}'$};
+	\node[color=blue] at (A) [above right] {$\vec{x}$};
+	\node[color=blue] at (B) [above left] {$\vec{x}'$};
 
-\node[color=red] at (O) [below left] {$O$};
+	\node[color=red] at (O) [below left] {$O$};
 
-\draw[->,color=blue,shorten <= 0.06cm] (O) -- (A);
-\draw[->,color=blue,shorten <= 0.06cm] (O) -- (B);
+	\draw[->,color=blue,shorten <= 0.06cm,line width=1.4pt] (O) -- (A);
+	\draw[->,color=blue,shorten <= 0.06cm,line width=1.4pt] (O) -- (B);
+}
 
 \end{tikzpicture}
 \end{center}
 \vspace{-5pt}
 $\vec{n}$ ein Einheitsnormalenvektor auf der Ebene, $|\vec{n}|=1$
-\item
+\item<5->
 Punkt-Spiegelung:
 \[
 {\tiny
@@ -84,13 +90,15 @@ Punkt-Spiegelung:
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<6->{%
 \begin{block}{Kontinuierliche Symmetrien}
 \begin{itemize}
-\item Translation:
+\item<7-> Translation:
 \(
 \vec{x} \mapsto \vec{x} + \vec{t}
 \)
-\item Drehung:
+\item<8-> Drehung:
+\vspace{-3pt}
 \begin{center}
 \begin{tikzpicture}[>=latex,thick]
 \def\a{25}
@@ -103,14 +111,15 @@ Punkt-Spiegelung:
 \fill[color=blue!20] (O) -- (90:\r) arc (90:{90+\a}:\r) -- cycle;
 \node at ({0.5*\a}:1) {$\alpha$};
 \node at ({90+0.5*\a}:1) {$\alpha$};
-\draw[->,color=blue] (O) -- (\a:2);
-\draw[->,color=darkgreen] (O) -- ({90+\a}:2);
+\draw[->,color=blue,line width=1.4pt] (O) -- (\a:2);
+\draw[->,color=darkgreen,line width=1.4pt] (O) -- ({90+\a}:2);
 \end{scope}
 \draw[->] (-1.1,0) -- (2.3,0) coordinate[label={$x$}];
 \draw[->] (0,-0.1) -- (0,2.3) coordinate[label={right:$y$}];
 \end{tikzpicture}
 \end{center}
 \[
+\uncover<9->{%
 \begin{pmatrix}x\\y\end{pmatrix}
 \mapsto
 \begin{pmatrix}
@@ -118,15 +127,18 @@ Punkt-Spiegelung:
 {\color{blue}\sin\alpha}&{\color{darkgreen}\phantom{-}\cos\alpha}
 \end{pmatrix}
 \begin{pmatrix}x\\y\end{pmatrix}
+}
 \]
 \end{itemize}
-\end{block}
+\end{block}}
 \vspace{-10pt}
+\uncover<10->{%
 \begin{block}{Definition}
 Längen/Winkel bleiben erhalten
 \\
-$\Rightarrow$ $\exists$ Erhaltungsgrösse
-\end{block}
+\uncover<11->{%
+$\Rightarrow$ $\exists$ Erhaltungsgrösse}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}