Introduction  
The Laplace transform is a powerful tool formulated to solve a wide variety of initialvalue problems. The strategy is to transform the difficult differential equations into simple algebra problems where solutions can be easily obtained. One then applies the Inverse Laplace transform to retrieve the solutions of the original problems. This can be illustrated as follows:

Definition of the Laplace Transform  
For a function defined on , its Laplace transform is denoted as obtained by the following integral:
where is real and is called the Laplace Transform Operator.

Definition of the Inverse Laplace Transform  
If the Laplace transform of is , then the we say that the Inverse Laplace Transform of is . Or,
where is called the Inverse Laplace Transform Operator.
