Math 518: Differentiable Manifolds I
Basic Information
 Instructor: Eugene Lerman
 email: lerman at illinois edu
 Homepage:
http://faculty.math.illinois.edu/~lerman
 Course page:
http://faculty.math.illinois.edu/~lerman/518/f19/518f19.html
 Office: 336 Illini Hall
 Office Hours: see my calender and/or
by appointment
 Phone: 2449510
 Class meets: MWF 10 am in 343
Altgeld Hall
 Homework assignments and supplementary notes are posted at
http://faculty.math.illinois.edu/~lerman/518/f19/518f19hw.html
I will post my handwritten 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
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]
Grades
The
course grade will be based on weekly homework (35%),
a midterm (25%) and a final (40%).
Exams
The midterm will take place on
October 30 710 pm note time (the date is
not likely to change).
The final, according to the noncombined final
examination schedule is to take place on
7:00  10:00 PM, Friday, December 13
Requests for a makeup exam require a serious documentation and are
almost never granted.
Last modified: Fri Aug 23 14:45:08 CDT 2019