MAT 467E - Boundary Value Problems

Course Objectives

1. To develop a basic understanding of occurrence of two point boundary value problems,
their classification and related problems; such as, initial value, boundary value and initialboundary
value problems in the real world.
2. To develop a basic understanding of the theory and methods of solutions for these
problems.

Course Description

Two-point boundary-value problems; definition, examples, existence and uniqueness of
solutions. Linear homogeneous boundary-value problems; eigenvalues and eigenvectors. SturmLiouville
boundary-value problems; Lagrange identity, orthogonality of eigenfunctions, selfadjoint
problems. Nonhomogeneous boundary-value problems; non-homogeneous SturmLiouville
problems, non-homogeneous heat conduction problems. Singular Sturm-Liouville
problems; definition, continuous spectrum, vibration of a circular elastic membrane, Series of
orthogonal functions; convergence and completeness. Techniques of Green`s function;
generalised functions, Green`s function, modified Green`s function.