From 1fb743df08b0734932d510c6b11405d0a2dbbe47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 19:57:13 +0200
Subject: new slides

---
 vorlesungen/slides/7/kurven.tex | 85 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 vorlesungen/slides/7/kurven.tex

(limited to 'vorlesungen/slides/7/kurven.tex')

diff --git a/vorlesungen/slides/7/kurven.tex b/vorlesungen/slides/7/kurven.tex
new file mode 100644
index 0000000..196fa2a
--- /dev/null
+++ b/vorlesungen/slides/7/kurven.tex
@@ -0,0 +1,85 @@
+%
+% kurven.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Kurven und Tangenten}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Kurven}
+Kurve in $\mathbb{R}^n$:
+\vspace{-12pt}
+\[
+\gamma
+\colon
+I=[a,b] \to \mathbb{R}^n
+:
+t\mapsto \gamma(t)
+=
+\begin{pmatrix}
+x_1(t)\\
+x_2(t)\\
+\vdots\\
+x_n(t)
+\end{pmatrix}
+\]
+\vspace{-15pt}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+\coordinate (A) at (1,0.5);
+\coordinate (B) at (4,0.5);
+\coordinate (C) at (2,2.2);
+\coordinate (D) at (5,2);
+\coordinate (E) at ($(C)+(80:2)$);
+
+\draw[color=red,line width=1.4pt]
+	(A) to[in=-160] (B) to[out=20,in=-100] (C) to[out=80] (D);
+\fill[color=red] (C) circle[radius=0.06];
+\node[color=red] at (C) [left] {$\gamma(t)$};
+
+\draw[->,color=blue,line width=1.4pt,shorten <= 0.06cm] (C) -- (E);
+\node[color=blue] at (E) [right] {$\dot{\gamma}(t)$};
+
+\draw[->] (-0.1,0) -- (5.9,0) coordinate[label={$x_1$}];
+\draw[->] (0,-0.1) -- (0,4.3) coordinate[label={right:$x_2$}];
+\end{tikzpicture}
+\end{center}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Tangenten}
+Ableitung
+\[
+\frac{d}{dt}\gamma(t)
+=
+\dot{\gamma}(t)
+=
+\begin{pmatrix}
+\dot{x}_1(t)\\
+\dot{x}_2(t)\\
+\vdots\\
+\dot{x}_n(t)
+\end{pmatrix}
+\]
+Lineare Approximation:
+\[
+\gamma(t+h)
+=
+\gamma(t)
++
+\dot{\gamma}(t) \cdot h
++
+o(h)
+\]
+Sinnvoll, weil sowohl $\gamma(t)$ und $\dot{\gamma}(t)$
+in $\mathbb{R}^n$ liegen
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From 15881729aa3f1293d546a1692a02094ed3f24e2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 11 Apr 2021 10:30:05 +0200
Subject: phases

---
 vorlesungen/slides/7/kurven.tex | 31 +++++++++++++++++++++++++------
 1 file changed, 25 insertions(+), 6 deletions(-)

(limited to 'vorlesungen/slides/7/kurven.tex')

diff --git a/vorlesungen/slides/7/kurven.tex b/vorlesungen/slides/7/kurven.tex
index 196fa2a..e0690eb 100644
--- a/vorlesungen/slides/7/kurven.tex
+++ b/vorlesungen/slides/7/kurven.tex
@@ -20,6 +20,7 @@ Kurve in $\mathbb{R}^n$:
 I=[a,b] \to \mathbb{R}^n
 :
 t\mapsto \gamma(t)
+\uncover<2->{
 =
 \begin{pmatrix}
 x_1(t)\\
@@ -27,6 +28,7 @@ x_2(t)\\
 \vdots\\
 x_n(t)
 \end{pmatrix}
+}
 \]
 \vspace{-15pt}
 \begin{center}
@@ -42,16 +44,21 @@ x_n(t)
 \fill[color=red] (C) circle[radius=0.06];
 \node[color=red] at (C) [left] {$\gamma(t)$};
 
-\draw[->,color=blue,line width=1.4pt,shorten <= 0.06cm] (C) -- (E);
-\node[color=blue] at (E) [right] {$\dot{\gamma}(t)$};
+\uncover<4->{
+	\draw[->,color=blue,line width=1.4pt,shorten <= 0.06cm] (C) -- (E);
+	\node[color=blue] at (E) [right] {$\dot{\gamma}(t)$};
+}
 
-\draw[->] (-0.1,0) -- (5.9,0) coordinate[label={$x_1$}];
-\draw[->] (0,-0.1) -- (0,4.3) coordinate[label={right:$x_2$}];
+\uncover<2->{
+	\draw[->] (-0.1,0) -- (5.9,0) coordinate[label={$x_1$}];
+	\draw[->] (0,-0.1) -- (0,4.3) coordinate[label={right:$x_2$}];
+}
 \end{tikzpicture}
 \end{center}
 \end{block}
 \end{column}
 \begin{column}{0.48\textwidth}
+\uncover<4->{%
 \begin{block}{Tangenten}
 Ableitung
 \[
@@ -66,6 +73,7 @@ Ableitung
 \dot{x}_n(t)
 \end{pmatrix}
 \]
+\uncover<5->{%
 Lineare Approximation:
 \[
 \gamma(t+h)
@@ -75,10 +83,21 @@ Lineare Approximation:
 \dot{\gamma}(t) \cdot h
 +
 o(h)
-\]
+\]}%
+\vspace{-10pt}
+\begin{itemize}
+\item<6->
 Sinnvoll, weil sowohl $\gamma(t)$ und $\dot{\gamma}(t)$
 in $\mathbb{R}^n$ liegen
-\end{block}
+\item<7->
+Gilt auch für
+\[
+\operatorname{GL}_n(\mathbb{R})
+\uncover<8->{\subset M_n(\mathbb{R})}
+\uncover<9->{ = \mathbb{R}^{n\times n}}
+\]
+\end{itemize}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}
-- 
cgit v1.2.1

