Continuation of Phys 501. A working knowledge of tensor analysis, differential geometry, and topology as broadly applied to physics. Elements of elasticity theory. Smooth manifolds, tangent and co-tangent bundles. Lie-derivatives and flow. Foliations and Frobenius' theorem. Differential forms. Generalized Stokes theorem. Poincare's lemma. Hodge dual and Maxwell's equations in covariant form. Covariant derivatives. Connections and parallel transport. Frames. Curvature and Riemannian manifolds. Elements of general relativity. Spin textures, Brouwer degree, the Hopf map and Hopf index, Skyrmions, elements of homotopy. Prerequisite: Phys 501, or permission of instructor.