Math 518: Differentiable Manifolds I

Basic Information


Point set topology and linear algebra.
If you have any questions or concerns, please talk to me or contact me by e-mail.

Course outline

  1. Manifolds: Definitions and examples including projective spaces and Lie groups; smooth functions and mappings; submanifolds; Inverse Function Theorem and its applications including transversality; (co)tangent vectors and bundles; vector bundles; manifolds with boundary; orientations.

  2. Calculus on Manifolds: Vector fields, flows, and Lie derivative/bracket; differential forms and the exterior algebra of forms; orientations again; exterior derivative, contraction, and Lie derivative of forms; integration and Stokes Theorem, DeRham cohomology.

Recommended Texts


The course grade will be based on weekly homework (35%), a midterm (25%) and a final (40%).


The midterm will take place on October 30 7-9 pm in 241 Altgeld note time and place (the date is not likely to change).

The final, according to the non-combined final examination schedule is to take place on 7:00 - 10:00 PM, Friday, December 13

Requests for a make-up exam require a serious documentation and are almost never granted.

Last modified: Wed Oct 23 08:23:04 CDT 2019