Math — Laplace Transforms
Definition and standard Laplace transforms.
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\mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st}\,dt
\mathcal{L}\{1\} = \frac{1}{s}
\mathcal{L}\{e^{at}\} = \frac{1}{s-a}
\mathcal{L}\{f'(t)\} = sF(s) - f(0)