ABSTRACT
A vibration string can be pinned down at the two endpoints. These are typical boundary conditions coming from a physical problem. This chapter shows how eigenfunctions and eigenvalues arise naturally in a physical problem. The situation with boundary conditions is quite different from that for initial conditions. The latter is a sophisticated variation of the fundamental theorem of calculus. The former is rather more subtle. It presents a formal procedure with series for solving a Dirichlet problem. It is also possible to produce a closed formula (i.e., an integral formula) for this solution.
