Inverse Laplace transform

The inverse operation to the Laplace transform

In mathematics, the inverse Laplace transform of a function F {\displaystyle F} is a real function f {\displaystyle f} that is piecewise-continuous, exponentially-restricted (that is, | f ( t ) | ≤ M e α t {\displaystyle |f(t)|\leq Me^{\alpha t}} ∀ t ≥ 0 {\displaystyle \forall t\geq 0} for some constants M > 0 {\displaystyle M>0} and ⁠ α ∈ R {\displaystyle \alpha \in \mathbb {R} } ⁠) and has the property: L { f } ( s ) = F ( s ) , {\displaystyle {\mathcal {L}}\{f\}(s)=F(s),} where L {\displaystyle {\mathcal {L}}} denotes the Laplace transform....