Introduction to Differential Geometry

(suitable for scientists and engineers)



Course News

Our FINAL EXAM is scheduled for Wednesday May 13.

Our second in-class exam is scheduled for Tuesday April 28.

  • Solutions to Test 2

    Our first in-class exam is scheduled for Thursday March 5.

  • Solutions to Test 1


    Course Details

    Lectures: Tuesday and Thursday from 10:30 - 11:50PM in 343 Altgeld Hall

    Instructor: Ely Kerman, ekerman@math.uiuc.edu

    Office & Telephone: 326 Illini Hall, 265-6710

    Office Hours: Thursday 1:00-3:00, or by appointment.

    Textbook (required): Theodore Frankel, The Geometry of Physics, Cambridge U.P. (paperback).

    Course Material:
    1. Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.
    2. Calculus on manifolds: Vector fields, flows, tensor fields.
    3. Differential forms and exterior calculus.
    4. Integration theory: Generalized Stokes theorem, de Rham cohomology.
    5. Riemannian geometry: Riemannian metrics, geodesics.

    Grading Scheme:
  • Weekly Homework Assignment, 20%
  • Two In-class Exams 2x20% =40% (Test 1: Thur. March 5, Test 2: TBA)
  • Comprehensive Final Exam, 1:30–4:30 PM, Wednesday, May 13, 40%


    Homework Assignments

  • Assignment 1 due Tuesday Feb.3. Solutions

  • Assignment 2 due Tuesday Feb.10. Solutions

  • Assignment 3 due Tuesday Feb.17. Solutions

  • Assignment 4 due Tuesday Feb.23. Solutions

  • Assignment 5 due Thursday March 19. Solutions

  • Assignment 6 due Tuesday April 7.
    (Question 5 has been corrected in this version.) Solutions

  • Assignment 7 due Thursday April 9. Solutions

  • Assignment 8 due Thursday April 16.Solutions

  • Assignment 9 due Thursday April 23.Solutions