MTH3011 Partial differential equations

When you finish this unit, you should be able to:

1. 1

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

2. 2

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

3. 3

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

4. 4

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

5. 5

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

6. 6

   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;

7. 7

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