ABSTRACT
The Laplace Transform is an integral transform named after its founder Pierre-Simon Laplace. The Laplace transform is a very important tool in engineering disciplines as it enables the following: It helps to solve linear differential equations with given initial conditions. The method is also particularly useful if the inputs to the differential equations, that is, the E term are discontinuous inputs like the unit step function. Incorporates the initial conditions are at the start of the solution to the problem. In systems engineering, the system is broken down into components as blocks. Each block can be represented in the s-domain and then manipulated. Most of the Laplace transforms and subsequently the inverse Laplace transforms are generally taken from a standard table of results. Therefore, it is useful to first show some of the more common Laplace transforms of functions in a table format and then to see how they are derived from first principles using the formula definition.
