Section 1.1 introduces Fourier series in descriptive mode, with an example of the existence of a convergent Fourier series using the power series you studied in Analysis I. The new concept of Fourier series is presented thereby within the familiar context of power series.




Section 1.2 reviews background material on ODEs from Introductory Calculus by collecting together the definitions you used to characterize ODEs and reminding you of the methods you used to solve ODE BVPs and IVPs.



Section 1.3 introduces PDEs in descriptive mode (hence the ODE review in section 1.2 to put them in context) and gives a concrete example of a PDE problem to illustrate the practical need to find the Fourier series representation of the widest possible class of functions.



Section 2.1 gives a refresher of periodic, even and odd functions through which we can characterize the building blocks of Fourier series — cosines and sines. This material has usually been studied at A-level or equivalent. Our focus is on geometric interpretation and the most useful properties for latter on in the course.