Integral Transforms

An integral transform is an operator that takes a set, a function to be operated and another specific function (called the integral kernel), returning one more function that’s obtained through integration. It’s basically just integrating the product of a function by the integral kernel over a given set.

Laplace Transform

The Laplace transform is an integral transform whose integral kernel is and integration interval is .

We can obtain the Laplace transform of varios simple functions to facilitate other more complex transforms. Similarly, there are several fundamental theorems that we can also use to our convenience. We can use one of them to easily obtain the Laplace transform of a piecewise function after having it rewritten in terms of shifted unit step functions.

We can guarantee the existence of a Laplace transform by means of the consequences of two theorems.