This course provides the student with an in-depth study of boundary value problems in partial differential equations, including the heat, wave, and potential equations. Techniques studied include characteristics, series solutions, Green's functions, and integral transforms. MATH 630 Optimization. Prerequisite is MATH 532 or instructor consent. This course provides a study of constrained and unconstrained optimization problems, including eigenvalue and generalized least-squares problems.
Techniques used include orthogonalization, conjugate gradient, and quasi-Newton algorithms.
MATH 631 Control Theory. Prerequisite is MATH 626 or instructor consent. This course provides a study of observability, controllability, and system stabilization, as well as Lyaponov methods, otpimal control, the calculus of variations, and vector space applications to system analysis.