3 hours Theory of vector-valued functions on Euclidean space. Derivative as best linear-transformation approximation to a function. Divergence, gradient, curl. Vector fields, path integrals, surface integrals. Constrained extrema and Lagrange multipliers. Implicit function theorem. Jacobian matrices. Green’s, Stokes’, and Gauss’ (divergence) theorems in Euclidean space. Differential forms and an introduction to differential geometry.