Méthodes asymptotiques en physique

-Dimensional analysis-Asymptotic approximations-Regular vs singular pertubations-Evaluation of integrals: Laplace, Stationnary phase and Saddle point methods-WKB-Matched Asymptotic Expansions-Method of Multiple Scales

To acquire resolution techniques of differential problems that arise frequently in research.

By nature, the course contains an exposition of methods with great emphasis on their applications. Half of the course consists in resolutions of exercices.

Contribution to the teaching profile

Mathematical problems encountered in basic science or engineering are rarely analytically soluble. However, one can often consider limiting cases which considerably ease the analysis while keeping the basic physical content that one wishes to understand.Asymptotic methods are a collection of approaches to systematically and consistently deal with limiting cases. When successfully applied, they may provide useful approximation of solution or new mathematical models that are simpler to study numerically.Asymptotics is also useful in that it brings scaling laws and trends and allow one to build intuition on complex phenomena.A large number of examples drawn from quantum mechanics, laser physics, fluid mechanics and optic will illustrate the course.

References, bibliography, and recommended reading

C.M. Bender & S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag 1999E. J. Hinch, Perturbation Methods, Cambridge University Press 1991

Contacts

Gregory Kozyreff, room 2o6.103, gkozyref@ulb.ac.be

Method(s) of evaluation

• written examination

written examination

Written examination

Mark calculation method (including weighting of intermediary marks)

The mark is entirely built from the written examination