Undergraduate Courses 21-356
Principles of Real Analysis II
Spring: 9 units

Topology in metric spaces, specialization to finite dimensional normed linear spaces. Vector differential calculus: continuity and the total derivative, partial derivatives, directional derivatives, gradients, Jacobians, the chain rule, implicit function theorem. Vector integral calculus: double and triple integrals, arclength and surface area, line integrals, Green's Theorem, surface integrals, Divergence and Stokes Theorems. If time permits: trigonometric series, Fourier series for orthonormal bases, minimization of square error. 3 hours lecture. Prerequisite: 21-355.

For curricula requiring 21-356, that requirement can also be fulfilled by taking 21-357 which is offered in the Fall semester.