ABSTRACT
This chapter looks at a specific type of series of functions: the Fourier Series. It reviews the vector space notions, a finite number of linearly independent objects, span of a set of vectors, and basis for a vector space. Since each object is continuous, each object is Riemann integrable. The chapter describes the Holder's inequality and Minkowski's inequality along with the finite dimensional approximation theorem. It also reviews orthogonal functions including the sine sequence and the cosine sequence. Fourier coefficients and the convergence of Fourier series are described along with Fourier sine series and Fourier cosine series. The chapter illustrates approximating of a pulse with a Fourier sine series approximation.
