Course content

The course is given every second year, next time autumn 2026. The aim of the course is to give an introduction to, and training of, useful methods of finding approximate solutions to physics problems, in particular situations where regular perturbation expansions cannot be used. Even in cases where a given problem must be treated numerically, approximative solutions may give valuable information of qualitative behaviour for choice and implementation of numerical method. The course covers e.g. local analysis of differential equations, approximate evaluation of integrals, asymptotic expansions, singular perturbation expansions, the boundary layer method, the WKB method, multiple scale expansions.

Learning outcome

Knowledge

The candidate should have knowledge about the most useful methods for finding approximate analytical solutions of mathematical problems which often occur when modeling physical systems.

Skills

The candidate should be able to

• identify various classes of mathematical problems
• simplify or rewrite the problem to a form which enables use of an appropriate method
• apply the method to find an approximate analytical solution

General competence

The candidate should

• know about relevant mathematical reference works and software
• be able to use these to find/extract information efficiently

Learning methods and activities

Lectures and problem sessions. Some problems make use of mathematical software. When lectures and lecture material are in English, the exam may be given in English only.

Specific conditions

Recommended previous knowledge

Mathematical knowledge and maturity as obtained through a completed (theoretically oriented) master's degree in physics.

Course materials

Literature: C.M. Bender and S.A. Orszag: Advanced Mathematical Methods for Scientists and Engineeres, McGraw-Hill 1978.

Credit reductions