Prerequisites: Sobolev spaces, Elliptic boundary value problems, Heat and wave equations, Variational formulation and semigroup theory.

Optimal Control of PDE: Optimal control problems governed by elliptic equations and linear parabolic and hyperbolic equations with distributed and boundary controls, Computational methods.

Homogenization: Examples of periodic composites and layered materials. Various methods of homogenization.

Applications and Extensions: Control in coefficients of elliptic equations, Controllability and Stabilization of Infinite Dimensional Systems, Hamilton-Jacobi-Bellman equations and Riccati equations, Optimal control and stabilization of flow related models.