Gwybodaeth am y Modiwl

General structure of the module

As with most mathematics modules, the course will be delivered via 22 lectures (two per week).

There will be three assignments throughout the course. While these do not count towards the final module mark, there is always a very strong correlation between final module mark and number of assignments handed in. I therefore encourage you very strongly to hand in your attempts at assignments in order to get feedback. Also, make sure you read my red squiggles on your work carefully and ask if there's any feedback you don't understand!

The module is assessed through a two-hour exam in the May exam period, which is worth 100% of the module mark.

Learning outcomes

On successful completion of this module students should be able to:

  1. Demonstrate an understanding of the meaning of asymptotic solutions in the appropriate context and how to interpret these;

  2. Solve simple linear and nonlinear ordinary and partial differential equations by asymptotic methods;

  3. Illustrate with suitable examples the occurrence of asymptotic phenomena in mechanics.

Overview of content

The following is an outline of the topics to be covered in this module:

  1. Fundamentals: main ideas and techniques, definitions of Landau symbols, asymptotic sequences and series.

  2. Regular perturbation methods: polynomials, ordinary differential equations.

  3. Singular perturbation methods: dominant balance, Kruskal-Newton graphs.

  4. Asymptotic approximation of integrals: Taylor series, Laplace's method.

  5. Non-linear oscillations: physical motivation, Duffing equation, secular terms, Linstedt-Poincare method.

  6. Damped oscillations: physical motivation, two-scale method.

  7. Method of matched asymptotics: techniques and application.

Further information

Definitive module information is available on the Aberystwyth University module pages.