One of the most widely used applications of Fourier Transforms, like Laplace Transforms, is to convert difficult equations (like solving Differential Equations) into easier-to-solve ALGEBRAIC equations. Most of the time you will just be looking up known Fourier Transforms from your tables, so it is IMPERATIVE that your algebraic skills are good enough to:

1. Be able to get your problem into forms where you can read off the Fourier Transform, and

2. Be able to solve the algebraic equation that it gets transformed into.