This unit is not longer offered. I am making my (concise, no pictures) lecture notes available from this page, for students wanting more background in these topics. They could be of particular interest to students taking Applied Partial Differential Equations 2 or Maths Methods 3.

Contents:

1. Introduction,

2. Dimensions and scaling of differential
equations,

3. Conservation laws and how to express them mathematically,

4. Quasilinear
first order PDEs including shocks and the Dirac delta,

5. The 1D
wave equation,
superposition and energy flow,

6. 3D vector calculus, including
how to derive the gradient and divergence in arbitrary orthogonal
coordinate systems,

7. The heat equation and similarity solutions.

Lecture notes (70 pages): ps,pdf

Carl Dettmann / carl.dettmann@bristol.ac.uk / Last edited March 19, 2009