Vector Analysis

More emphasis will be placed on Vector Fields and Tensors. Topics covered may include: basic geometry and topology of Euclidean space, curves, surfaces and manifolds in n-dimensinal vector spaces, arclength, curvature and torsion, surface area, linear and non-linear Transformations on Euclidean spaces, gradients and linearization, chain rules, inverse and implicit function theorems, geometric applications, optimization, vector fields, Leibnitz's rule, conservative and solenoidal vector fields, divergence and curl, surfaces and orientability, surface integrals, generalized Gauss-Green and Stokes's theorem, tensors and their applications.