The continuation of a two-semester review of some of the mathematical methods that are essential for the study of Physics. Theory of functions of complex variables, including analyticity, Cauchy's integral formula, residue theory; review of ordinary differential equations, introduction to partial differential equations, Fourier series, Sturm-Liouville theory, integral transforms. Introduction to function spaces; self-adjoint and unitary operators; eigenvalue problems. Partial differential equations of hyperbolic, elliptic, and parabolic type; special functions. Perturbation theory; integral equations; introduction to tensors and group theory. Prerequisite: Phys 501, or permission of instructor.