Mathematics 797CV - ST- Calculus of Variations

The calculus of variations is the study of the minimization of integrals with respect to a function, whose integrand depends on the function and its derivatives. It is a powerful tool for solving PDE with an associated energy functional and arises in the theory of minimal surfaces. This course will consider both the classical methods and the direct methods in the theory of the calculus of variations. Applications will be made to classical mechanics as well as to the development of numerical methods. We will also introduce the basic theory of gamma convergence and variational coarse-graining techniques.

Open to Graduate students only. Note: Prerequisites for this course: Math 623 or 731 or instructor permissions. Students should have knowledge of L^p spaces and familiarity with undergraduate level ODE and PDE.