21-356 Principles of Real Analysis II

9 units, Carnegie Mellon University

This course provides a rigorous and proof-based treatment of functions of several real variables. The course presumes some mathematical sophistication including the ability to recognize, read, and write proofs. Topics include: Metric spaces. Differential calculus in Euclidean spaces: continuity, differentiability, partial derivatives, gradients, differentiation rules, implicit and inverse function theorems. Multiple integrals. Integration on curves and hypersurfaces: arclength, and generalized area. The divergence theorem and the 3D Stokes theorem. Regarding prerequisites, 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)

Offered: Spring 2027, Fall 2026, Spring 2026, Fall 2025

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