Content

The calculus of variations is a branch of optimization theory.
It seeks to find curves and surfaces that maximize or minimize integrals.

I will cover core topics in the calculus of variations.

These include the Euler-Lagrange equation, constraints, the second
variaion, the Legendre condition, the Jacobi equation, homogeneous
problems, transversality conditions, broken extremals, the
Weierstrass excess function, sufficient conditions, the royal road,
and Hamilton-Jacobi theory.

Examples will include such classic gems as the brachistochrone, minimum surfaces
of revolution (soap films), and geodesics. I will also include numerous examples
from classical mechanics, optics, and other applied areas.

Please see the class notes for further details regarding class content.

Course Catalog