diff options
Diffstat (limited to 'vorlesungen/slides/5/exponentialfunktion.tex')
| -rw-r--r-- | vorlesungen/slides/5/exponentialfunktion.tex | 14 |
1 files changed, 10 insertions, 4 deletions
diff --git a/vorlesungen/slides/5/exponentialfunktion.tex b/vorlesungen/slides/5/exponentialfunktion.tex index 698d8a5..caae16b 100644 --- a/vorlesungen/slides/5/exponentialfunktion.tex +++ b/vorlesungen/slides/5/exponentialfunktion.tex @@ -10,6 +10,7 @@ \vspace{-15pt} \begin{columns}[t,onlytextwidth] \only<1-6>{% +\ifthenelse{\boolean{presentation}}{ \begin{column}{0.48\textwidth} \begin{block}{$x(t) \in\mathbb{R}$} \vspace{-10pt} @@ -21,7 +22,7 @@ x(0) &= c&&\in\mathbb{R} \uncover<2->{x(t) &= ce^{at}} \end{align*} \end{block} -\end{column}} +\end{column}}{}} \begin{column}{0.48\textwidth} \uncover<3->{% \begin{block}{$X(t) \in M_n(\mathbb{R})$} @@ -45,6 +46,7 @@ vier Funktionen $x_{ij}(t)$}} \end{block}} \end{column} \only<7-9>{% +\ifthenelse{\boolean{presentation}}{ \begin{column}{0.48\textwidth} \begin{block}{Beispiel: Diagonalmatrix} %$D=\operatorname{diag}(\lambda_1,\dots,\lambda_n)$ @@ -60,7 +62,7 @@ Lösung: x_{ij}(t) =c_{ij}e^{\lambda_i t} \]} \end{block} -\end{column}} +\end{column}}{}} \uncover<10->{% \begin{column}{0.48\textwidth} \begin{block}{Beispiel: Jordan-Block} @@ -70,10 +72,11 @@ A&=\begin{pmatrix}\lambda&1\\0&\lambda\end{pmatrix} \rlap{$\displaystyle,\; X(t) = +\ifthenelse{\boolean{presentation}}{ \only<22>{ e^{\lambda t} \begin{pmatrix} 1&t/\lambda\\ 0&1 \end{pmatrix} -} +}}{} \only<23>{ \frac{e^{\lambda t}}{\lambda} \begin{pmatrix} \lambda&t\\ 0&\lambda \end{pmatrix} @@ -100,13 +103,16 @@ x_{2i}(t)&=c_{2i}e^{\lambda t} \dot{x}_{1i}(t)&=\lambda x_{1i}(t) + c_{2i}e^{\lambda t} } \\ -\only<16-17>{x_{1i\only<16>{,h}}(t)} +\ifthenelse{\boolean{presentation}}{ +\only<16-17>{x_{1i\only<16>{,h}}(t)}}{} \only<18->{\dot{x}_{1i}(t)} & +\ifthenelse{\boolean{presentation}}{ \only<16-17>{=c\only<17>{(t)}\lambda e^{\lambda t}} \only<18>{=\dot{c}(t)\lambda e^{\lambda t} + c(t)\lambda^2 e^{\lambda t}} +}{} \only<19->{=\lambda x_{1i}(t) + \dot{c}(t)\lambda e^{\lambda t}} \\ \uncover<20->{\Rightarrow |