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Perturbation Methods: Course Outline (MAT 664)

A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbation" parts.

Course Contents

Parameter perturbations, Co-ordinate perturbations, Order symbols and gauge functions, Asymptotic series and expansions, Asymptotic expansion of integrals, Integration by parts, Laplace’s method and Watson’s lemma, Method of stationary phase and the method of steepest descent. Straightforward expansions and source of non-uniformity, the Duffing equation, small Reynolds number flow past a sphere, small parameter multiplying the highest derivative. The method of strained co-ordinates, Lindstedt-Poincare method, renormalization method. Variation of parameters and method of averaging, examples. Method of multiple scales with examples.

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