digital-brain/content/zettels/laplace_transform.md

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title = "Laplace Transform"
author = ["Dehaeze Thomas"]
draft = false
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Tags
: [Continuous Transfer Functions]({{< relref "continuous_transfer_functions.md" >}})
## Definition {#definition}
Laplace transform:
\begin{equation}
\boxed{F(s) = \mathcal{L}{f(t)} = \int\_0^\infty e^{-st} f(t) dt}
\end{equation}
## Laplace transform of signals {#laplace-transform-of-signals}
<https://en.wikipedia.org/wiki/List_of_Laplace_transforms>
## Laplace transform of functions {#laplace-transform-of-functions}
<https://en.wikibooks.org/wiki/Signals_and_Systems/Table_of_Laplace_Transforms>
## Solving Linear Differential equations {#solving-linear-differential-equations}
### Mechanical System {#mechanical-system}
### Electrical System {#electrical-system}