The Laplace transform is a mathematical technique used to convert a function of time, often denoted as f(t) , into a function of a complex variable, typically represented as F(s) . This transformation simplifies the analysis of linear time-invariant systems, making it easier to solve differential equations by changing them into algebraic equations. In engineering and physics, the Laplace transform is particularly useful for analyzing systems such as electrical circuits and mechanical systems. It helps in understanding system behavior, stability, and response to inputs by providing a clearer view of the system's dynamics in the frequency domain.