Approximate methods in modern Physics
APPROXIMATION is a must because exact solutions are rare in physics and engineering. It can be analytical, numerical or both. This course teaches students how to find analytical approximations.
The main topics
- Qualitative and dimensional methods. How to solve a problem without actually solving it.
- Asymptotic expansions.First thing to try, if you have an equation with a small parameter.
- Qualitative and dimensional methods. How to solve a problem without actually solving it.
- Perturbation theory. How to to get new results by small perturbation of the old ones.
- The method of multiple scales. According to Nayfeh it is rediscovered every six months.
- The method of averaging. A special case of the previous method. However, it is so popular that it has its own name.
REMARKS. IAs a rule, we will take concrete problems and show how to solve them instead of developing a general theory. The course is addressed to students having passed das Vordiplom.
Three typical problems
- Can you solve
either for small
or large 
?
- Why
is a bad approximation of
even for 
- Why it is so difficult to calculate oscillating integrals, e.g.,
Literature:
A. H. Nayfeh, Perturbation methods, Wiley 1973.
Lectures will be given in Deutsch
