Laplace transform converts a time domain function to s-domain function by integration from zero to infinity of the time domain function, multiplied by $e^{-st}$. The Laplace transform is used to quickly find solutions for differential equations and integrals. Derivation in the time domain is transformed to multiplication by s in the s-domain. Integration in the time domain is transformed to division by s in the s-domain.

Laplace transform function : The Laplace transform is defined with the L{} operator: