Basic Information

• Instructor: Eugene Lerman
• e-mail: 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 calendar and/or by appointment
• Phone: 244-9510
• Class meets: MWF 10 am    in 343 Altgeld Hall
• Homework assignments and supplementary notes are posted at here
  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 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

• 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]

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 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