Math 518: Differentiable Manifolds I
- Instructor: Eugene Lerman
- e-mail: lerman at math uiuc edu
- Course page:
- Office: 336 Illini Hall
- Office Hours: see my calender and/or
- Phone: 244-9510
- Class meets: MWF 12 am in 345
- Homework assignments and supplementary notes are posted at
I may also occasionally post my lecture notes on this page
Prerequisites Point set topology and linear algebra.
If you have any questions or concerns, please contact me by e-mail.
- 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]
Manifolds, Tensors, and Forms
An Introduction for Mathematicians and Physicists by
Paul Renteln, Cambridge, ISBN: 9781107042193
course grade will be based on weekly homework (35%),
a midterm (25%) and a final (40%).
Last modified: Fri March 20 15:06:06 CST 2015