U ovom radu ćemo proučiti pojam Fourierovog reda i Fourierovih koeficijenata. Potom ćemo analizirati vrste konvergencija Fourierovog reda ( Konvergencija po točkama, uniformna konvergencija, konvergencija u smislu \(L^{2}\) -norme) te definirati kompleksni oblik Fourierovog reda i Fourierovih koeficijenata. Takoder ćemo definirati i Fourierovu transformaciju koja se koristi za procesiranje signala te je pružila veliki doprinos u tehničkim znanostima i medicini. U zadnjem poglavlju ćemo navesti dva primjera primjene Fourierovog reda, provodenje topline i valna jednadžba.

In this paper we will study the terms Fourier series and Fourier coefficients. Then we will analyze the types of convergence of Fourier series (pointwise convergence, uniform convergence, convergence in \(L^{2}\) -norm) and define the complex form of Fouriers series. We will also define Fourier transform which is used to process the signal and has contributed greatly to technical sciences and medicine. In the last section, there are two examples of the application of the Fourier series, heat conduction and wave equation.