In this chapter, Fourier series is introduced for functions which are
Riemann integrable and are of bounded exponential growth. Orthogonal relations;
least square error, completeness relation and Riemann- Lebesgue theorem are also
considered. The Fourier series is applied to obtain a series solution to some periodic
boundary value problems. Also provided are Maple examples for applications of
Fourier series to ordinary differential equations.
Keywords: Bounded exponential growth, Boundary value problems, Completeness relation, Differential equations, Fourier series, Least square error, Periodic solutions, Riemann- Lebesgue theorem
