Solving Partial Differential Equations Using Fourier Series

This research paper aims to study the methods of solving partial differential equations using Fourier series. Partial differential equations are a powerful and practical tool in mathematics and physics to describe many phenomena and processes that involve continuous change at the level of equations and functions. The basic concepts related to the Fourier series and how to represent functions using it in the field of mathematics will be reviewed. Application examples of partial differential equations, such as waves, heat and diffusion, and how to use the Fourier series to solve them will also be presented. The steps of solving the partial differential equation using the Fourier series will be explained. The importance of Fourier series in the theory of partial differential equations is that periodic functions f(x) defined on (-∞,∞) or functions defined on a finite interval can be represented by an infinite interval of sines and cosines. In this research, the solution of the partial differential equation using the Fourier series was studied with the solution of an example.