The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace, who used a similar transform in his work on probability theory. The transform has many applications in science and engineering because it is a tool for solving differential equations. The Laplace transform has a number of properties that make it useful for analyzing linear dynamical systems.

Laplace transformation provides a powerful means to solve linear ordinary differential equations in the time domain, by converting these differential equations into algebraic equations. These may then be solved and the results inverse transformed back into the time domain. Laplace transformation belongs to a general area of mathematics called operational calculus which focuses on the analysis of linear systems.

Laplace transformation converts differential and integral equations into rather simple algebraic equations. Laplace transform is nothing but a simple operational tool, used to solve linear differential equations with constant coefficients.

The transformation is only applied to general signals and not to sinusoidal signals. Also, it cannot handle steady state conditions. It enables us to study complicated control systems with integrators, differentiators and gains.

Laplace transform is a mathematical operation that is used to “transform” a variable (such as x, or y, or z in space, or at time t) to a parameter (s) – a “constant” under certain conditions. It transforms ONE variable at a time. Laplace transform is a valuable “tool” in solving: Differential equations for example: electronic circuit equations, and In “feedback control” for example, in stability and control of aircraft systems