The Fourier Series For Discontinuous Intervals

The Fourier series, which is named after Joseph Fourier, has become an indispensable tool in many fields. In particular, it is widely used in mathematics, physics and engineering to describe functions or signals that are periodic with respect to time or space. A Fourier series decomposes periodic functions or periodic function,s into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines. The study of Fourier series is a branch of Fourier analysis. The Fourier series representations are important in many areas: in applied mathematics for solving physical problems involving differential equations with sinusoidal coefficients; in pure mathematics as an example of an infinite product; as part-sum representation for analytic functions.