6: Sturm Liouville

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In the last chapters we have explored the solution of boundary value problems that led to trigonometric eigenfunctions. Such functions can be used to represent functions in Fourier series expansions. We would like to generalize some of those techniques in order to solve other boundary value problems. A class of problems to which our previous examples belong and which have eigenfunctions with similar properties are the Sturm-Liouville Eigenvalue Problems. These problems involve self-adjoint (differential) operators which play an important role in the spectral theory of linear operators and the existence of the eigenfunctions described previousl. These ideas will be introduced in this chapter.

6.1: Introduction
6.2: Properties of Sturm-Liouville Eigenvalue Problems
There are several properties that can be proven for the (regular) SturmLiouville eigenvalue problem. However, we will not prove them all here. We will merely list some of the important facts and focus on a few of the properties.
6.3: The Eigenfunction Expansion Method
In this section we will apply the eigenfunction expansion method to solve a particular nonhomogenous boundary value problem.
6.4: The Fredholm Alternative Theorem
6.5: Problems