ABSTRACT
There are two good reasons for considering the differentiation and integration of Fourier series. One is that derivatives and integrals of Fourier series often arise in applications. In the next chapter, for example, we will use Fourier series to solve differential equations describing flow of heat in a rod and vibrations in a string. The other reason is that I have already quoted some results from this chapter concerning the convergence of the Fourier series of a smooth function (see page 162). So we had better develop those results.
