Principles of Real Analysis II

9 units · Undergraduate

Fall and Spring: 9 units This course provides a rigorous and proof-based treatment of functions of several real variables. 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. The course presumes some mathematical sophistication including the ability to recognize, read, and write proofs. 21-268 or 21-269 are strongly recommended rather than 21-259 . (Three 50 minute lectures) Prerequisites: ( 21-259 or 21-269 or 21-268 ) and ( 21-241 or 21-242 ) and ( 21-455 or 21-355 ) Course Website: https://www.cmu.edu/math/undergrad/math-course-information.html