Through the study of Sturm-Liouville problems, this chapter connects several ideas of applied math-ematics. After establishing the orthogonality of eigenfunctions of a Sturm-Liouville problem, we examine the same property among some of the special functions that appeared in the previous chapter. Further, we proceed into the topic of eigenfunction expansions, which leads to several useful and fertile techniques and opens the doors to some of the following chapters of this book.
In our study of ordinary differential equations through several chapters, there has been a lot of discussion on initial value problems. Mentions of boundary value problems have been comparatively few and far between. We make up, ...