Math 518: Differentiable Manifolds I
- Instructor: Eugene Lerman
- e-mail: lerman at illinois edu
- Course page:
- Office: 336 Illini Hall
- Office Hours: see my calender and/or
- Phone: 244-9510
- Class meets: MWF 10 am in 343
- Homework assignments and supplementary notes are posted at
I will post my hand-written lecture notes on this page
Prerequisites Point set topology and linear algebra.
If you have any questions or concerns, please talk to me or contact me
- 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;
- 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.
Introduction to Smooth Manifolds by John M. Lee,
Springer, ISBN: 978-1-4419-9981-8 (Print) 978-1-4419-9982-5 (Online)
[free online access from a campus computer]
course grade will be based on weekly homework (35%),
a midterm (25%) and a final (40%).
The midterm will take place on
October 30 7-10 pm note time (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: Fri Aug 23 14:45:08 CDT 2019