MAT 626E - Perturbation Methods

Course Objectives

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

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