Utility of Laplace Transform in Mathematics

Abstract

The paper seeks to analyze the use of Laplace transform in mathematics. However it contributes in mathematics as well as in arena of physics and engineering also. Laplace transform is an important skill to solve linear ordinary and partial differential equations with constant coefficients under suitable initial and boundary conditions. It is a good technique to simplify complex differential equations to a simpler form having polynomials in the area of stability and control. The current far-reaching use of the transform (mainly in engineering) happened during and soon after 2nd World War ,With the ease of application of Laplace transforms in myriad of scientific applications, many research softwares have made it possible to activate the Laplace transformable equations directly supporting the researchers. The transformation is usually used in stochastic performance modelling and analysis of computer and communication systems. It gets significant applications in various areas of physics, electrical engineering, control engineering, optics, mathematics and signal processing.