MAT 626E - Perturbation Methods

Course Objectives

1 To introduce parameter perturbations, asymptotic sequences, asymptotic expansions and asymptotic approximation concepts.
2 To introduce regular and singular parameter perturbation problems.
3 To introduce some basic singular perturbation methods and investigate certain problems in applied mathematics by these methods.

Course Description

Parameter perturbations. Order symbol, gauge functions, asymptotic sequences and asymptotic expansions.Asymptotic approximations of integrals.Regular and singular perturbation problems. Singular perturbation methods; matched asymptotic expansions, boundary layers, composite expansions, the method of strained coordinates, the method of multiple scales, the method of averaging, the WKBJ method. Aplications in initial and boundary value problems for ordinary and partial differential equations.