diff options
Diffstat (limited to 'vorlesungen/slides/7/kurven.tex')
| -rw-r--r-- | vorlesungen/slides/7/kurven.tex | 31 |
1 files changed, 25 insertions, 6 deletions
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} |