Variational Calculus

Outline: (copied from here) 

The calculus of variations is concerned with finding extrema and can therefore be seen as a branch of optimization. The techniques and problems, however, differ in an important aspect, the space over which one optimizes is usually infinite dimensional, e.g. a space of curves lying in a vector space fulfilling certain boundary and smoothness conditions. The techniques and ideas from finite dimensional calculus therefore have to be generalized appropriately. Nevertheless, it is often possible to apply certain rules to derive the so-called Euler-Lagrange equations in a straightforward way. To find solutions for them can be a real challenge, even numerically.

Other useful resources:

There are lecture notes available (which is copied down from the write board during the lecture).  If you want to have a look, send me an email and cc to Dr. Dr  Knut Hüper.  Ref my notes here.