SUNY at Stony Brook MAT 322: Analysis in Several Dimensions
Spring 2018

Welcome to MAT 322

This course develops in depth the calculus on smoothly curved subspaces of Euclidean space. By the end of the course, we will have covered both differentiation and integration on manifolds, realized as submanifolds of Euclidean space.

This requires building on the topics covered in multivariable calculus on domains in Euclidean space and so a solid grounding in MAT 203 (Multivariable Calculus) and MAT 211, MAT 310 (Linear Algebra) and MAT 320 (Analysis in 1 dimension) will be important. Without this backgrond, it will be hard to follow the pace of the class.

This is a rigorous class with an emphasis on new concepts and proofs.

Textbook: "Analysis on Manifolds" by James R. Munkres, Westview Press, 1991

For a good, brief discussion on submanifolds, see
Lectures 3 and 4 (as well as Lectures 13 and 14) of
Lectures on Differential Geometry by Ben Andrews at Australia National University here.

Please click on the links to the left for further information.