ABSTRACT

Most real life problems are represented mathematically by ordinary differential equations. Many such representations are complicated, hence difficult to solve. The Fourier transforms which is a class of the Fourier integral provides an easier, less-burdensome approach to the solutions of such differential equations. In fact, in this thesis, I have run from the Fourier series, which is a representation of a sum sinusoids of a given periodic function through Fourier integrals to the Fourier transform, a representation defined over an infinite interval of one of the independent variables. The functions have no particular periodicity. One of the many applications of the Fourier Transforms method is the solution of boundary value problems of mathematical physics. The Fourier transforms is worth learning.