Applied Partial Differential Equations

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.

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.

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.

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.