MAT 365 - Variational Calculus

Course Objectives

To teach the basic theory and applications of the calculus of variations.

Course Description

Functionals; continuous, lower and upper semicontinuous functionals. Differentiable functionals.
Frechet and Gateax differential of a functional. Single variable and multivariable optimization, conjugate functions. Weak and strong extremum. A necessary condition for an extremum. Integral types functionals; A necessary condition of extremum for single variable functionals, Euler- Lagrange equation. Pontryagin’s maximum principle and Variation calculus. A necessary condition for multivariable functionals, geodesics of surface. Variational problems in parametric form. The canonical form of the Euler equation. Isoperimetric problems. Variable endpoint problem. Broken extremals. Transversality conditions. Sufficient conditions for an extremum. Jacobi’s condition,
Weierstrass function.