Ten reasons
why one should take
In
Math 701 one will learn, among others:
1. The mathematics of finding functions that
extremize/optimize a given functional (variational derivative)
2. The mathematics of
extremizing a functional subject to given constraints (isoperimetric
problem)
3. The mathematics of
extremizing a given functional at a boundary (end point problem)
4. The mathematics of finding
the shortest (or longest) path (geodesic problem)
5. The mathematics of setting
up the equations of mechanics from a single scalar (Hamilton's
principle)
6. The mathematics of phase
fronts and their interference (Hamilton-Jacobi theory)
7. The mathematics of tensors
(multi-linear algebra)
8. The mathematics of parallel
transport (covariant differentiation)
9. The mathematical
classification of of parallel transport (torsion and curvature)
10.The mathematics of a strained
elastic medium (metric-induced geometry)