I will discuss the Euler-Lagrange equation, homogeneous problems,
transversality conditions, corner conditions, constraints, the second
variation, the Legendre condition, the Jacobi equation, the Weierstrass
excess function, and the relationship between the calculus of
variations, dynamic programming, and optimal control theory.

We will look at numerous examples from mechanics, optics, and other disciplines.
Examples will include such classic gems as the brachistochrone, minimum surfaces
of revolution (soap films), geodesics, the loaded cantilever, navigation problems,
and rolling pennies.

Course Catalog