Handbook

Understand the role of partial differential equations in the mathematical modelling of physical processes;

Solve a range of first-order partial differential equations including using the 'method of characteristics';

Appreciate the properties of the three basic types of linear second-order partial differential equations, including suitable initial and/or boundary conditions;

Understand the mathematical properties of the diffusion equation, wave equation and Laplace's equation and solve them exactly under some simple conditions;

Analyse and interpret simple applications modelled by the advection equation, diffusion equation and Laplace's equation;

Understand the principles of finite-difference approximation of ordinary and partial differential equations and appreciate the advantages and disadvantages of a range of useful numerical techniques, including their stability;

Evaluate numerical solutions of some partial differential equations using computers, and display those results graphically.