Course content

The course is taught every second year, next time fall 2014. 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 students should become familiar with a toolbox of standard approximation methods for analysis of mathematical problems which often occur when modeling physical systems, and know how this can be combined with numerical tools.
Skills and general competence:
The students should become able to approach any mathematically
formulated problem with confidence that it can be solved in at least some
limiting cases. The students should become skilled in simplifying complicated mathematical problems to analyzable form, and to perform the subsequent analysis.

Learning methods and activities

Lectures and problem sessions. Some problems may be formulated to be solved by use of computer algebra programs. When lectures and lecture material are in English, the exam may be given in English only.
The re-sit examination (in August) may be changed from written to oral.

Recommended previous knowledge

Mathematical knowledge and maturity as obtained through about 3-4 years of (theoretically oriented) studies in physics.

Course materials

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

Credit reductions