Math 518: Differentiable Manifolds I
Basic Information
 Instructor: Eugene Lerman
 email: lerman at math uiuc edu
 Homepage:
https://math.uiuc.edu/~lerman
 Course page:
https://math.uiuc.edu/~lerman/518/f15/518f15.html
 Office: 336 Illini Hall
 Office Hours: see my calender and/or
by appointment
 Phone: 2449510
 Class meets: MWF 12 am in 345
Altgeld Hall
 Homework assignments and supplementary notes are posted at
https://math.uiuc.edu/~lerman/518/f15/518f15hw.html
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 email.
Course outline
 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.
 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

Introduction to Smooth Manifolds by John M. Lee,
Springer, ISBN: 9781441999818 (Print) 9781441999825 (Online)
[free online access from a campus computer]

Manifolds, Tensors, and Forms
An Introduction for Mathematicians and Physicists by
Paul Renteln, Cambridge, ISBN: 9781107042193
Grades
The
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