Fourier Analysis

Abstract

The Fourier analysis contains two components: Fourier series and Fourier transform. The Fourier series is named in the honor of Joseph Fourier, who made an important contribution in mathematics. Fourier introduced the series for the purpose of solving the heat equation in a metal plate, publishing his initial results in his 1807 memoir to the Institute de France. Although the original motivation was to solve the heat equation, it later became obvious that the same techniques could be applied to a wide variety of mathematical and physical problems. The Fourier series has many applications in different branches of science and engineering. Fourier series is more universal than Taylor series because many discontinuous periodic functions of practical interest can be developed in the form of Fourier series.