Laplace Transform
Summary
We introduce the Laplace transform $$ F(s)=\mathcal{L}[f(t)]=\int_{0}^{\infty} \mathrm{e}^{-s t} f(t) \mathrm{d} t $$ of a function $f(t)$ defined for $t\geq 0$. We cover the existence theory and properties of this transform.