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Mathematical Methods (10/24.539)
IX. The Sturm-Liouville Problem
Introduction
The special functions discussed in the previous section are mostly special cases of a particular class of problems called
Sturm-Liouville Problems or simply Eigenvalue Problems. Most homogeneous 2-point Boundary Value Problems (BVPs) with homogeneous boundary conditions (BCs) fall into this classification. The Sturm-Liouville problem is important because the solutions to a homogeneous BVP with homogeneous BCs represent a set of orthogonal functions - and we have seen that these are important for applications via Generalized Fourier Series. Thus, this section of notes is designed to generalize some of the material from Section VIII on Special Functions and to give the student a good introduction to the base terminology and solution techniques associated with classical eigenvalue problems (continuous 2nd order homogeneous BVPs with homogeneous boundary conditions).The topics covered in this section are itemized below:
Example 9.1 - A Simple Eigenvalue/Eigenfunction Problem
Example 9.2 - Neutron Diffusion in a Nuclear Reactor (Bare Cylindrical Core)
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10/24.539 Lecture Notes by Dr. J. R. White, UMass-Lowell (updated November 1998).
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