Week #1

Sept 24-28

 Topology:
  • Open, closed, compact sets;
  • Derivative.
    		• September 24th: classes begin
    Week #2

    Oct 1-5

  • Continuously differentaible functions.
  • Implicit function; integral over a rectangle. Regular surfaces.
    • Week #3

    Oct 8-12

  • Evaluation of integral; existence of integral.
  • integral over a bounded set; rectifilable sets.

    • Oct 12th: Last day to add or drop a class.
    Week #4

    Oct 15-19

  • Integral over a bounded set; rectifilable sets.
  • Proof of change of variables; applications.
    • Week #5

    Oct 22-26

  • Volume of parallelopiped; volume of parametrized manifold.
    		• Oct 25: Midterm.
    Week #6

    Oct 29 - Nov 2

  • Manifolds in Rn; boundary of a manifold.
  • Integrating a function over a manifold.
    • Week #7

    Nov 5-9

  • Alternating tensors; wedge product.
  • Tangent vectors and differential forms; differential operators.
    • Week #8

    Nov 12-16
  • Appliactions of scalar and vector fields; action of differential map.
  • Integrating differential forms over a parametrized manifold.
    		• Nov 16th: Term withdrawal deadline.
    Change of grading basis deadline.
    Week #9

    Nov 26-30
  • Integrating differential forms; geometric interpretation.
  • Generalized Stokes and applications.
    • Week #10

    Dec 2-7

  • Poincare lemma; DeRham Groups.
  • Manifolds outside Rn.
    		• End-Quarter Period.
    Final Exam Monday, December 10th 12:15- 3:15 PM