Term	Michaelmas Term 2008  (10 lectures)

Synopsis

Introduction to partial derivatives. Chain rule, change of variable; examples to include plane polar coordinates. Examples of solving some simple partial differential equations (e.g. ). Jacobians for two variable systems, calculations of areas including basic examples of double integrals. Gradient vector; normal to surface, directional derivative. Critical points and classification using directional derivatives (non-degenerate case only). Laplace's and Poisson's equation, including change of variable to plane polar coordinates and circularly symmetric solutions. The wave equation in two variables, including derivation of general solution.

(Jordan & Smith, Chapters 27-29, 31. Kreyszig appendix 3.2, Sections 8.8, 8.9, 9.3, 9.5, 9.6, 11.1, 11.2. Bourne & Kendall, Sections 4.1-4.5.)

Reading list

1. D. W. Jordan & P. Smith, Mathematical Techniques (OUP, 3rd Edition, 2003).
2. Erwin Kreyszig, Advanced Engineering Mathematics (Wiley, 8th Edition, 1999).
3. D. E. Bourne & P. C. Kendall, Vector Analysis and Cartesian Tensors (Stanley Thornes, 1992).
4. David Acheson, From Calculus to Chaos: An Introduction to Dynamics (OUP, 1997).
5. G. F. Carrier & C. E. Pearson, Partial Differential Equations � Theory and Technique (Academic Press, 1988). [Advanced � leads on to 2nd year PDEs]

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