new slides chapter 3

4 files changed, 132 insertions, 0 deletions

diff --git a/vorlesungen/slides/3/Makefile.inc b/vorlesungen/slides/3/Makefile.inc
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+
+#
+# Makefile.inc -- additional depencencies
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+chapter3 =								\
+	../slides/3/motivation.tex					\
+	../slides/3/chapter.tex
+
diff --git a/vorlesungen/slides/3/chapter.tex b/vorlesungen/slides/3/chapter.tex
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index 0000000..f8d422e
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+++ b/vorlesungen/slides/3/chapter.tex
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+%
+% chapter.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, Hochschule Rapperswi
+%
+\folie{3/polynome.tex}
+\folie{3/motivation.tex}
diff --git a/vorlesungen/slides/3/motivation.tex b/vorlesungen/slides/3/motivation.tex
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index 0000000..cf28d46
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+++ b/vorlesungen/slides/3/motivation.tex
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+%
+% motivation.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Motivation}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.24\textwidth}
+\begin{block}{Imaginäre Einheit}
+\vspace{-15pt}
+\begin{align*}
+J &= \begin{pmatrix} 0&-1\\1&0\end{pmatrix}
+\\
+p(X) &= X^2 + 1
+\\
+p(J) &= J^2 + I = 0
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.25\textwidth}
+\uncover<2->{%
+\begin{block}{Wurzel $\sqrt{2}$}
+\vspace{-15pt}
+\begin{align*}
+W&=\begin{pmatrix}0&2\\1&0\end{pmatrix}
+\\
+p(X) &= X^2-2
+\\
+p(W) &= W^2-2I=0
+\end{align*}
+\end{block}}
+\end{column}
+\begin{column}{0.41\textwidth}
+\uncover<3->{%
+\begin{block}{Drehmatrix}
+\vspace{-15pt}
+\begin{align*}
+D&=\begin{pmatrix}
+\cos \frac{\pi}{1291} & -\sin\frac{\pi}{1291}\\
+\sin \frac{\pi}{1291} &  \cos\frac{\pi}{1291}
+\end{pmatrix}
+\\
+p(X)&= \only<-3>{X^{1291}+1\phantom{+\frac{\mathstrut}{\mathstrut}}}
+\only<4->{X^2-2X\cos\frac{\pi\mathstrut}{1291\mathstrut}+I}
+\\
+p(D) &= \only<-3>{D^{1291}+I\phantom{+\frac{\mathstrut}{\mathstrut}}}
+\only<4->{D^2-2D\cos\frac{\pi\mathstrut}{1291\mathstrut}+I}
+\end{align*}
+\end{block}}
+\end{column}
+\end{columns}
+\vspace{-20pt}
+\uncover<5->{
+\begin{block}{3D-Beispiel}
+$p(x) = -x^3-5x^2+5x+1$
+\[
+\only<5-8>{
+A=
+\begin{pmatrix*}[r]
+-5&-1&1\\
+-5&-2&3\\
+-1&-1&2
+\end{pmatrix*}}
+\only<6-8>{
+\quad\Rightarrow\quad}
+\uncover<6->{
+-
+\only<-9>{A^3}\only<10->{
+\begin{pmatrix*}[r]
+-169&-35&35\\
+-185&-39&40\\
+ -45&-10&11
+\end{pmatrix*}}
+-5
+\only<-8>{A^2}\only<9->{
+\begin{pmatrix*}[r]
+29&6&-6\\
+32&6&-5\\
+ 8&1& 0
+\end{pmatrix*}}
++5
+\only<-7>{A}\only<8->{
+\begin{pmatrix*}[r]
+-5&-1&1\\
+-5&-2&3\\
+-1&-1&2
+\end{pmatrix*}}
++
+\only<-6>{I}\only<7->{
+\begin{pmatrix*}[r]
+1&0&0\\
+0&1&0\\
+0&0&1
+\end{pmatrix*}}
+}
+\uncover<11->{=0}
+\]
+\end{block}}
+\vspace{-10pt}
+\uncover<12->{%
+{\usebeamercolor[fg]{title}$\Rightarrow$
+Rechenregeln von Matrizen können durch Polynome ausgedrückt werden}
+}
+\end{frame}
diff --git a/vorlesungen/slides/3/polynome.tex b/vorlesungen/slides/3/polynome.tex
new file mode 100644
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+++ b/vorlesungen/slides/3/polynome.tex
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+%
+% polynome.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}
+\frametitle{Polynome}
+
+\end{frame}