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author | JODBaer <JODBaer@github.com> | 2021-04-20 12:38:29 +0200 |
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committer | JODBaer <JODBaer@github.com> | 2021-04-20 12:38:29 +0200 |
commit | f9154b1070929ac3063a9676e11723e5ec0c8deb (patch) | |
tree | 3b2da1b4ee8f80ebe5c05a6c74f48832b57ffc9e /vorlesungen/slides/10/ableitung-exp.tex | |
parent | Merge remote-tracking branch 'upstream/master' (diff) | |
parent | Merge branch 'master' of github.com:AndreasFMueller/SeminarMatrizen (diff) | |
download | SeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.tar.gz SeminarMatrizen-f9154b1070929ac3063a9676e11723e5ec0c8deb.zip |
Merge remote-tracking branch 'upstream/master'
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-rw-r--r-- | vorlesungen/slides/10/ableitung-exp.tex | 60 |
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diff --git a/vorlesungen/slides/10/ableitung-exp.tex b/vorlesungen/slides/10/ableitung-exp.tex new file mode 100644 index 0000000..10ce191 --- /dev/null +++ b/vorlesungen/slides/10/ableitung-exp.tex @@ -0,0 +1,60 @@ +% +% ableitung-exp.tex -- Ableitung von exp(x) +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% Erstellt durch Roy Seitz +% +% !TeX spellcheck = de_CH +\bgroup +\begin{frame}[t] + \setlength{\abovedisplayskip}{5pt} + \setlength{\belowdisplayskip}{5pt} + %\frametitle{Ableitung von $\exp(x)$} + %\vspace{-20pt} + \begin{columns}[t,onlytextwidth] + \begin{column}{0.48\textwidth} + \begin{block}{Ableitung von $\exp(at)$} + \begin{align*} + \frac{d}{dt} \exp(at) + &= + \frac{d}{dt} \sum_{k=0}^{\infty} a^k \frac{t^k}{k!} + \\ + &\uncover<2->{ + = \sum_{k=0}^{\infty} a^k\frac{kt^{k-1}}{k(k-1)!} + } + \\ + &\uncover<3->{ + = a \sum_{k=1}^{\infty} + a^{k-1}\frac{t^{k-1}}{(k-1)!} + } + \\ + &\uncover<4->{ + = a \exp(at) + } + \end{align*} + \end{block} + \end{column} + \begin{column}{0.48\textwidth} + \uncover<5->{ + \begin{block}{Ableitung von $\exp(At)$} + \begin{align*} + \frac{d}{dt} \exp(At) + &= + \frac{d}{dt} \sum_{k=0}^{\infty} A^k \frac{t^k}{k!} + \\ + &= + \sum_{k=0}^{\infty} A^k\frac{kt^{k-1}}{k(k-1)!} + \\ + &= + A \sum_{k=1}^{\infty} A^{k-1}\frac{t^{k-1}}{(k-1)!} + \\ + &= + A \exp(At) + \end{align*} + \end{block} + } + \end{column} + \end{columns} +\end{frame} + +\egroup |