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authorAndreas Müller <andreas.mueller@ost.ch>2021-05-06 11:33:00 +0200
committerAndreas Müller <andreas.mueller@ost.ch>2021-05-06 11:33:00 +0200
commitb6114e0a8c7f800d36c199c0ee6af64d337e5320 (patch)
tree36f16fb2bf368cddb0c520ebd069ff95e5d08f58 /vorlesungen/slides/7
parenttypo (diff)
downloadSeminarMatrizen-b6114e0a8c7f800d36c199c0ee6af64d337e5320.tar.gz
SeminarMatrizen-b6114e0a8c7f800d36c199c0ee6af64d337e5320.zip
add slide
Diffstat (limited to 'vorlesungen/slides/7')
-rw-r--r--vorlesungen/slides/7/Makefile.inc1
-rw-r--r--vorlesungen/slides/7/chapter.tex1
-rw-r--r--vorlesungen/slides/7/integration.tex66
3 files changed, 68 insertions, 0 deletions
diff --git a/vorlesungen/slides/7/Makefile.inc b/vorlesungen/slides/7/Makefile.inc
index 8b2b9e0..52c37d8 100644
--- a/vorlesungen/slides/7/Makefile.inc
+++ b/vorlesungen/slides/7/Makefile.inc
@@ -27,5 +27,6 @@ chapter5 = \
../slides/7/ueberlagerung.tex \
../slides/7/hopf.tex \
../slides/7/haar.tex \
+ ../slides/7/integration.tex \
../slides/7/chapter.tex
diff --git a/vorlesungen/slides/7/chapter.tex b/vorlesungen/slides/7/chapter.tex
index 0068cf4..172b78a 100644
--- a/vorlesungen/slides/7/chapter.tex
+++ b/vorlesungen/slides/7/chapter.tex
@@ -26,3 +26,4 @@
\folie{7/ueberlagerung.tex}
\folie{7/hopf.tex}
\folie{7/haar.tex}
+\folie{7/integration.tex}
diff --git a/vorlesungen/slides/7/integration.tex b/vorlesungen/slides/7/integration.tex
new file mode 100644
index 0000000..525e6de
--- /dev/null
+++ b/vorlesungen/slides/7/integration.tex
@@ -0,0 +1,66 @@
+%
+% integration.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Invariante Integration}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Koordinatenwechsel}
+Die Koordinatentransformation
+$f\colon\mathbb{R}^n\to\mathbb{R}^n:x\to y$
+hat die Ableitungsmatrix
+\[
+t_{ij}
+=
+\frac{\partial y_i}{\partial x_j}
+\]
+\uncover<2->{%
+$n$-faches Integral
+\begin{gather*}
+\int\dots\int
+h(f(x))
+\det
+\biggl(
+\frac{\partial y_i}{\partial x_j}
+\biggr)
+\,dx_1\,\dots dx_n
+\\
+=
+\int\dots\int
+h(y)
+\,dy_1\,\dots dy_n
+\end{gather*}}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<3->{%
+\begin{block}{auf einer Lie-Gruppe}
+Koordinatenwechsel sind Multiplikationen mit einer
+Matrix $g\in G$
+\end{block}}
+\uncover<4->{%
+\begin{block}{Volumenelement in $I$}
+Man muss nur das Volumenelement in $I$ in einem beliebigen
+Koordinatensystem definieren:
+\[
+dV = dy_1\,\dots\,dy_n
+\]
+\end{block}}
+\uncover<5->{%
+\begin{block}{Volumenelement in $g$}
+\[
+\text{``\strut}g\cdot dV\text{\strut''}
+=
+\det(g) \, dy_1\,\dots\,dy_n
+\]
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup