Laplace Transform

The Laplace Transform is a powerful mathematical tool used to convert a function of time (usually denoted by t) into a function of a complex variable (usually denoted by s). It is particularly useful in solving linear ordinary differential equations and partial differential equations, as well as in analyzing complex systems in engineering and physics, such as control systems and signal processing.

The Laplace Transform simplifies the analysis of a system by converting differential equations into algebraic equations, which are often easier to solve. Once the algebraic equation is solved, the inverse Laplace Transform can be applied to convert the solution back into the original time-domain function.