The governing equations of physical, biological and economic models often involve features which make it impossible to obtain their exact solution. In MATH3365 (15 credits) and MATH5366M (20 credits) we shall analyse such model equations using precise approximations, by which is meant that the errors incurred in the approximating process are both understood and controllable.

This course develops analytical methods for finding approximate answers to problems in terms of exact mathematical expressions, as opposed to computationally calculated data. In particular, perturbation methods draw their name from the fact that they provide a means of solving realistically motivated problems which contain a "small" parameter in the governing equation, whose exact answer is known in the zero-parameter limit. In this sense, the equations which have to be solved are perturbations of idealised cases. As such, perturbation methods enjoy wide application in diverse Applied Mathematics research areas.

• Course content:
  • syllabus overview;
  • lecture-by-lecture summary.
• Downloadable course material in PostScript or PDF:
  • supplementary course notes ;
  • example sheets ;
  • Maple 9 worksheets;
  • past examination papers.
• Background material:
  • Internet links;
  • reading list.