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PHYS-F427

Asymptotic Methods in Physics

academic year
2025-2026
2026-2027

Course teacher(s)

Gregory KOZYREFF (Coordinator) and Fabian BRAU

ECTS credits

5

Language(s) of instruction

english

Course content

-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

Objectives (and/or specific learning outcomes)

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

Teaching methods and learning activities

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

References, bibliography, and recommended reading

  • G. Kozyreff, Practical Asymptotics, Cambridge University Press 2026
  • C.M. Bender & S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag 1999E.
  • J. Hinch, Perturbation Methods, Cambridge University Press 1991

Course notes

  • Syllabus

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.

Other information

Contacts

gregory.kozyreff@ulb.be

Campus

Plaine

Evaluation

Method(s) of evaluation

  • Other

Other

Continuous evaluation: 5 short tests evenly spread during the semester.

Examination schedule/ calendrier des interrogations: 2/10/2026, 23/10/2026, 6/11/2026, 1/12/2026, 11/12/2026

Mark calculation method (including weighting of intermediary marks)

Each test allows the student to get 6 points. The final mark is min(20,P), where P is the sum of points obtained over the 5 tests.

Language(s) of evaluation

  • english
  • (if applicable french )

Programmes