Fourier series are of great importance in both theoretical and applied mathematics. This paper will focus on the Fourier series of the complex exponentials of the many possible methods of estimating complex valued functions, Fourier series are especially attractive because uniform convergence of the Fourier series (as more terms are added) is guaranteed for continuous, bounded functions.After studying this paper we will learn about how Fourier transforms is useful in many physical applications, such as partial differential equations and heat transfer equations. one can solve many important problems of physics with very simple way.