Applied Partial Differential Equations:  2008-2009

Overview

The course consists of the 16 lectures of the undergraduate course B5b Applied Partial Differential Equations.

There are a further 8 supplementary lectures on more advanced material.

Examination questions will be set on the whole course.

Learning outcomes

Students will know a range of techniques to solve PDEs including non-linear first order and second order and their classification. They will be able to demonstrate various principles for solving PDEs including Green’s function, maximum principle and eigenfunctions.

Synopsis

Course B5b: 

Charpit’s equations; eikonal equation.

Systems of partial differential equations, characteristics. Weak solutions. Riemann’s function.

Maximum principles, comparison methods, well-posed problems, and Green’s functions for the heat equation and for Laplace’s equation.

Delta functions. Eigenfunction expansions.

Supplementary Lectures:

Fredholm alternative and Green's functions for non-self-adjoint problems; application of delta functions. Review of classification of second-order linear equations [3 lectures, 1 class]

Further development of hyperbolic equations: Cauchy-Kovalevskaya theorem, Riemann invariants, shocks and weak solutions, causality. [3 lectures, 1 class]

More details of the course are available from Dr Porter's website.

Reading list

1. Dr Norbury’s web notes.
2. Institute lecture notes are now available (JN).
3. M. Renardy and R.C. Rogers An introduction to partial differential equations, 2004, Springer–Verlag, New York.
4. J.P. Keener 2000 Principles of Applied Mathematics: Transformation and Approximation, revised edition. Perseus Books, Cambridge, Mass.
5. J.R. Ockendon, S. D. Howison, A.A. Lacey and A.B. Movchan 2003 Applied Partial Differential Equations, revised edition. OUP, Oxford.

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.