Every physical scientist knows the name Fourier; the Series, Integral, and Transform that bear his name are essential mathematical tools. Joseph Fourier's great achievement was to state the equation for the diffusion of heat. The Fourier Series is a series of origonometric terms which converges to a periodic function over one period. The Fourier Integral is the limiting form of a Fourier Series when the period of the periodic function tends to infinity. The Fourier Transform is an analytic tool derived from the coefficients of the integral expansion of a Fourier Series. He pioneered the use of Fourier Series and Integrals because he needed them to solve a range of problems related to the flow of heat. Fourier was not the first person to realize that certain trigonometric expressions could be used to represent certain functions but he did develop...