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 s . This transformation simplifies the process of solving differential equations by turning them into algebraic equations, making it easier to analyze systems, especially in engineering and physics. The formula for the Laplace Transform is given by L\f(t)\ = \int_0^\infty e^-st f(t) dt . This integral transforms the time-domain function into the frequency domain, allowing for easier manipulation and solution of problems related to control systems, signal processing, and other fields in applied mathematics.