Academic year 2006-2007

Section de mathématiques, Master

Teaching

Teacher: Prof. J.H. Maddocks
Assistant: Jessika Walter

Timetable

Course: Thursday 13:15 - 15:00, in MA31
Exercises: Thursday 15:15 - 17:00, in MA30

Bibliography

C.C. Lin, L.A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences, Classics in Applied Mathematics, Siam.

Credits

4+2

Description of the course

Mathematical models describing natural systems invariably contain parameters, in other words there is not just one set of governing equations, but a family of governing equations as one or more parameters vary. Typically it is of interest to understand solutions to the model equations as a function of the parameters --this leads to ideas of parameter continuation, which is a useful technique both for analysis and for numerics. Often there is, or it can be arranged that there is, a particular set of values of the parameters where the solution set is particularly simple. Perturbation theory and asymptotics concerns methods to understand how such simple solutions change as the parameters in the problem are changed by small amounts.

This course will introduce basic methods of both regular (where the perturbed and original system are of essentially the same character) and singular perturbation theory via a case-study approach involving mathematical models based on ordinary differential equations.