From 9e7524c25a0ba5a643fbb7555d01311f69aa603e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 3 Jun 2021 17:18:58 +0200
Subject: add slides

---
 vorlesungen/slides/2/hilbertraum/sturm.tex | 56 ++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 vorlesungen/slides/2/hilbertraum/sturm.tex

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

diff --git a/vorlesungen/slides/2/hilbertraum/sturm.tex b/vorlesungen/slides/2/hilbertraum/sturm.tex
new file mode 100644
index 0000000..1d772d6
--- /dev/null
+++ b/vorlesungen/slides/2/hilbertraum/sturm.tex
@@ -0,0 +1,56 @@
+%
+% sturm.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Sturm-Liouville-Problem}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Wellengleichung}
+Saite mit variabler Massedichte führt auf die DGL
+\[
+-y''(t) + q(t) y(t) = \lambda y(t),
+\quad
+q(t) > 0
+\]
+mit Randbedingungen $y(0)=y(1)=0$
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Sturm-Liouville-Operator}
+\[
+A=-\frac{d^2}{dt^2} + q(t) = -D^2 + p
+\]
+auf differenzierbaren Funktionen $\Omega=[0,1]\to\mathbb{C}$ mit Randwerten
+\[
+f(0)=f(1)=0
+\]
+\end{block}
+\end{column}
+\end{columns}
+\begin{block}{Selbstadjungiert}
+\begin{align*}
+\langle f,Ag \rangle
+&=
+\langle f,-D^2 g\rangle + \langle f,qg\rangle
+=
+-
+\int_0^1 \overline{f}(t) \frac{d^2}{dt^2}g(t)\,dt
++\langle f,qg\rangle
+\\
+&=-\underbrace{[\overline{f}(t)g'(t)]_0^1}_{\displaystyle=0}
++\int_0^1 \overline{f}'(t)g'(t)\,dt
++\langle f,qg\rangle
+=-\int_0^1 \overline{f}''(t)g(t)\,dt
++\langle qf,g\rangle
+\\
+&=\langle Af,g\rangle
+\end{align*}
+\end{block}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


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/sturm.tex | 20 +++++++++++---------
 1 file changed, 11 insertions(+), 9 deletions(-)

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

diff --git a/vorlesungen/slides/2/hilbertraum/sturm.tex b/vorlesungen/slides/2/hilbertraum/sturm.tex
index 1d772d6..a6865ab 100644
--- a/vorlesungen/slides/2/hilbertraum/sturm.tex
+++ b/vorlesungen/slides/2/hilbertraum/sturm.tex
@@ -22,6 +22,7 @@ mit Randbedingungen $y(0)=y(1)=0$
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<2->{%
 \begin{block}{Sturm-Liouville-Operator}
 \[
 A=-\frac{d^2}{dt^2} + q(t) = -D^2 + p
@@ -30,27 +31,28 @@ auf differenzierbaren Funktionen $\Omega=[0,1]\to\mathbb{C}$ mit Randwerten
 \[
 f(0)=f(1)=0
 \]
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
+\uncover<3->{%
 \begin{block}{Selbstadjungiert}
 \begin{align*}
 \langle f,Ag \rangle
-&=
+&\uncover<4->{=
 \langle f,-D^2 g\rangle + \langle f,qg\rangle
 =
 -
 \int_0^1 \overline{f}(t) \frac{d^2}{dt^2}g(t)\,dt
-+\langle f,qg\rangle
++\langle f,qg\rangle}
 \\
-&=-\underbrace{[\overline{f}(t)g'(t)]_0^1}_{\displaystyle=0}
+&\uncover<5->{=-\underbrace{[\overline{f}(t)g'(t)]_0^1}_{\displaystyle=0}
 +\int_0^1 \overline{f}'(t)g'(t)\,dt
-+\langle f,qg\rangle
-=-\int_0^1 \overline{f}''(t)g(t)\,dt
-+\langle qf,g\rangle
++\langle f,qg\rangle}
+\uncover<6->{=-\int_0^1 \overline{f}''(t)g(t)\,dt
++\langle qf,g\rangle}
 \\
-&=\langle Af,g\rangle
+&\uncover<7->{=\langle Af,g\rangle}
 \end{align*}
-\end{block}
+\end{block}}
 \end{frame}
 \egroup
-- 
cgit v1.2.1

