What is the Fourier transform & Laplace transform used for?
Almost everything the deals with waves is described using Fourier transforms: radio transmissions, sounds waves, optics, etc. Laplace transforms are used in circuit equations that have on/off switches. The switch is described as a step-function, and Laplace transforms can easily describe this behavior. These are just examples. Both transforms are extremely useful. They basically convert differential equations into algebraic equations and make life easier.