Fourier series and boundary value problems

In this thesis, Fourier series and some definitions and theorems related to Sturm Liouville boundary value problem, are emphasized, and the Fourier method and d'Alembert method which are used in the solution of one-dimensional wave equation are described. The thesis study aims to create a resource for the solution of many physics problems. The thesis is organized as follows. In the introductory part of the thesis, the branches and fields in which the Fourier series and the Sturm-Liouville boundary value problem are used are included and their importance is emphasized. In the second chapter, definitions, theorems and examples about Fourier series are given. In the third chapter, Boundary Value Problems are discussed and Sturm-Liouville methods are emphasized, eigenvalues and eigenfunctions are examined on problems. In the last chapter, the solution of the one-dimensional wave equation used in Physics and Engineering and the solution of the heat conduction equation in flux discontinuity are emphasized.