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MSc in Mathematical Modelling & Scientific Computing MSc in Applied and Computational Mathematics | Special Topic |
16 lectures MT Prof J Chapman |
Synopsis
Asymptotic expansions. Regular perturbation methods: Poincare-Lindstedt method. Application to ordinary differential equations.
Singular perturbation theory: boundary layers, transition layers; application to partial differential equations; method of multiple scales; WKB method.
Asymptotic evaluation of integrals: Laplace s method, method of steepest descent; Stokes phenomenon.
Reading List
E J Hinch, Perturbation methods, CUP, Cambridge, 1991, Chs. 1-3, 5-7
C M Bender and S A Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978, Chs. 6,7,9-11
Kevorkian and J D Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, Berlin, 1981 Chs. 1,2,1-2.5,3.1,3.6,4.1,5.2