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MSc in Mathematical Modelling & Scientific Computing MSc in Applied and Computational Mathematics |
Course A1 |
16 lectures & 8 classes MT Dr J Norbury |
Synopsis
Linear algebraic and integral equations. Fredholm alternative, linear differential equations, initial and boundary value problems, Green's functions, generalized functions, complex Fourier transform.
Nonlinearity. Picard's theorem, phase-plane, phase-space, nonlinear oscillations.
Asymptotic methods; Singular perturbations, matched asymptotic expansions, WKB and multi-scale methods.
Hamiltonian systems, introduction to variational problems and optimal control.
Reading List
J Kevorkian and J D Cole, Perturbation Methods in Applied Mathematics, Springer, 1981
J Kevorkian and J D Cole, Multiple Scale and Singular Perturbation Methods, Springer, 1996
*C M Bender and J A Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw Hill, 1978 (Reprinted in 1999)
I Stakgold, Green's Functions and Boundary Value Problems, Wiley, 2nd edition, 1998
*D W Jordan and P Smith, Nonlinear Ordinary Differential Equations, OUP, 3rd edition, 1999
E J Hinch, Perturbation Methods, CUP, 1991