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MSc in Mathematical Modelling & Scientific Computing MSc in Applied and Computational Mathematics |
Course A2 |
16 lectures & 8 classes HT 2004 Dr P Howell |
Scalar first order partial differential equations; characteristics, weak solutions, Charpit's method.
Quasi-linear systems of partial differential equations (in two independent variables); well-posedness, Cauchy-Kowalewski Theorem, hyperbolicity, Riemann invariants; weak solutions of conservation systems.
Classification of linear second-order partial differential equations, Green-Riemann functions, for hyperbolic elliptic and parabolic equations, conformal transformations.
The wave equation in higher dimensions, Huygens principle.
G F Carrier and C E Pearson, Partial Differential Equations, Academic Press, 1988
J Ockendon, S Howison, A Lacey and A Movchan, Applied Partial Differential Equations OUP, 1999 (main text).