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more laplace transforms
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Signed-off-by: Thomas Gassmann <tgassmann@student.ethz.ch>
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thomasgassmann committed Aug 3, 2024
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Expand Up @@ -1930,6 +1930,8 @@ \subsubsection{Laplace-Transformationen}
$\int_0^t f(\tau)d\tau$&$\frac{1}{s}\cdot \mathcal{L}[f](s)$\\
$\cosh(at)$ & $\frac{s}{s^2 - a^2}, \; \Re(s) > a$\\
$\sinh(at)$ & $\frac{a}{s^2 - a^2}, \; \Re(s) > a$\\
$t \cosh(at)$ & $\frac{s^2 + a^2}{(s^2 - a^2)^2}, \; \Re(s) > a$\\
$t \sinh(at)$ & $\frac{2as}{(s^2 - a^2)^2}, \; \Re(s) > a$\\
$\delta(t - a)$ & $e^{-as}$\\
\bottomrule
\end{tabularx}
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