You know that it's all the time a little scary while we devote an entire section just to the definition of something. Laplace transforms or just transforms can appear scary while we first start searching at them. Though, as we will notice, they aren't as bad as they may seem at first.

Before we begin with the definition of the Laplace transform we require getting another definition out of the manner.

A function is termed as piecewise continuous on an interval if the interval can be broken in a finite number of subintervals on that the function is continuous on all open subintervals that is the subinterval without its endpoints and has a finite restrict at the endpoints of all subintervals.

There is a sketch of a piecewise continuous function is given below:

Conversely, a piecewise continuous function is a function which has a finite number of breaks in this and doesn't blow up to infinity anywhere.

Here, let's take a see the definition of the Laplace transform.