ABSTRACT
A Fourier series is an infinite series of sines and cosines, capable of representing almost any periodic function whether continuous or not. Periodic functions that occur in scientific problems are often very complicated and it is desirable to represent them in terms of simple periodic functions. Unnecessary work in determining Fourier coefficients of a function can be avoided if the function is ‘odd’ or ‘even’. The Fourier sine or cosine series in this case is often called a half-range Fourier series. The Fourier series of a function f(x) may always be integrated term-by-term to give a new series which converges to the integral of f(x). A Fourier expansion of a function of two or three variables is often very useful in many applications. The properties of Fourier series allow the expansion of any periodic function that satisfies the Dirichlet conditions.
