Laplace Transform

Abstract

The comprehensive use of information contained in signals requires performing on them various mathematical operations, transforms, or conversions. One of the most useful transforms, commonly used in various fields of technical sciences and mathematics, is the Laplace transform . It has several practical applications, of which some of the most noteworthy are the solution of ordinary linear differential equations having constant coefficients, the examination of dynamic properties of systems, the synthesis of mathematical models, the simplification of their order , or the determination of the $\exp ({\mathbf{A}}t)$ matrix, which is indispensable for solving the state equation presented in the matrix form.