The Laplace transforms

In this chapter, we introduce a linear transformation called the Laplace transform on a 'large' class of functions. In view of its very interesting properties, the Laplace transform is very useful in solving linear ODEs. In particular, Laplace transform methods are widely used to solve linear the initial value problems and boundary value problems. In fact, methods of dealing with different types of differential/difference equations using the Laplace transforms, Fourier transforms, Mellin transforms, Z-transforms etc. have many applications in various branches of engineering sciences. Here we focus only on Laplace transforms.