Inverse Laplace Transform

Reverse of Laplace transform. Denoted as $\mathcal{L}^{-1} \{ F(s) \}$ .

\mathcal{L}\{ f(t) \} = F(s) \implies \mathcal{L}^{-1} \{ F(s) \} = f(t)

Properties

L^{-1}\{F(s+a)\} = e^{-at}f(t)

\mathcal{L}^{-1} \{ cF(s) + G(s) \} = c\mathcal{L}^{-1}\{ F(s) \} + \mathcal{L}^{-1} \{ G(s) \}

L^{-1}\{e^{-as}F(s)\}=u(t-a)f(t-a)

For $\alpha \gt 0$ .

L^{-1}\{F(\alpha s)\} = \frac{1}{\alpha} f\left(\frac{t}{\alpha}\right)

Written by

September 29, 2026 1 min read

Was this helpful?