ABSTRACT
A very important technique used to solve many differential and integral equations is to transform a given equation into a more manageable one, to find the solution to the transformed equation, and by an inverse procedure, use the solution of the transformed equation to determine a solution to the original equation. This chapter discusses some detail the Fourier transform, one of the most commonly used transforms that can be employed in this context. The Fourier transform may be derived easily from the Fourier integral formula by expressing this formula in complex form. One of the most important aspects of the Laplace transform and the inverse Laplace transform is that they are linear operators, as the reader is asked to establish in the next exercise. The Laplace transform is especially useful in solving many initial value problems.
