Qualitative and quantitative analysis of systems of differential equations. Gradient systems, Sturm-Liouville problems. Elementary techniques for boundary value problems of partial differential equations. 627 Advanced Differential Equations II . Solution techniques for boundary value problems.
Problems involve heat, wave, and potential equations.
Topics include the method of characteristics, series solutions, integral transforms, and Green's functions. 630 Optimization . Constrained and unconstrained optimization problems, including the generalized least squares problem and Eigenvalue problems. Methods include orthogonalization, conjugate gradient, and quasi-Newton algorithms. 631 Control Theory .