diff options
| author | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
|---|---|---|
| committer | Lukaszogg <82384106+Lukaszogg@users.noreply.github.com> | 2021-07-08 20:10:11 +0200 |
| commit | 14033ca595b5c933caea3b214d2246529e6845b8 (patch) | |
| tree | 0d6d2b2eb34e5ef5df3c517be5c1c9d803fa066c /vorlesungen/slides/7/exponentialreihe.tex | |
| parent | Update teil1.tex (diff) | |
| parent | Only include buch.ind if it exists. (diff) | |
| download | SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.tar.gz SeminarMatrizen-14033ca595b5c933caea3b214d2246529e6845b8.zip | |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/slides/7/exponentialreihe.tex')
| -rw-r--r-- | vorlesungen/slides/7/exponentialreihe.tex | 24 |
1 files changed, 24 insertions, 0 deletions
diff --git a/vorlesungen/slides/7/exponentialreihe.tex b/vorlesungen/slides/7/exponentialreihe.tex new file mode 100644 index 0000000..b1aeda6 --- /dev/null +++ b/vorlesungen/slides/7/exponentialreihe.tex @@ -0,0 +1,24 @@ +% +% exponentialreihe.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Exponentialreihe} +\begin{align*} +h(s) &= \exp(tA_0 + sB) = \sum_{k=0}^\infty \frac{1}{k!} (tA_0 + sB)^k +\\ +&= +I + (tA_0 + sB) + \frac{1}{2!}(t^2A_0^2 + ts(A_0B + BA_0) + s^2B^2) ++ \frac{1}{3!}(t^3A_0^3 + t^2s(A_0^2B + A_0BA_0 + BA_0^2) + \dots) ++ \dots +\\ +\frac{dg(s)}{ds} +&= +B + \frac1{2!}t(A_0B+BA_0) + \frac{1}{3!}t^2(A_0^2B+A_0BA_0+BA_0^2) + \dots +\end{align*} +\end{frame} +\egroup |