MATLAB® and Its Applications in Engineering: [Based on MATLAB 7.5 (R2007b)]

11.2. Laplace Transform

Laplace Transform helps in converting differential equations describing the behaviour of dynamic systems into algebraic equations of a complex variable ‘s’. The operations such as differentiation and integration can be replaced by algebraic operations in the complex plane. The solution of a differential equation may thus be easily found by use of Laplace Transform. Another advantage of the Laplace Transform is that both the transient component and steady-state component of the solution can be obtained simultaneously.

Definition:

Laplace Transform can be defined as follows:

Let f(t) be a function of time t such that f(t) = 0 for t < 0, and s be a complex variable. If L stands for an operation symbol indicating the Laplace ...