MTH322: Calculus on Manifolds

Details of the course

Lecture Hall: LHC-304

Timings:

Mondays: 4 -- 4:55

Thursday and Fridays: 11 -- 11:55

Here is a rough plan for the course.

Piazza:
Resources Enrol Home

Exam dates

To be announced.

Resources and summary of lectures:

  1. January 2: A quick review of differentiation.
  2. January 3: Chain rule.
  3. January 6: Some lemmas needed to prove inverse function theorem.
  4. January 9: Inverse function theorem.
  5. January 10: Examples and comments on the use of inverse function theorem. Problem set.
  6. January 13: Implicit function theorem, level sets, examples.
  7. January 16: Inverse function theorem
  8. January 17: Integration of a bounded function on a rectangle
  9. January 20: Measure zero sets and a criterion for existence of integrals
  10. January 23: Fubini's theorem
  11. January 24: Basic properties of integrals. Integrating continuous functions
  12. January 27: Rectifiable sets: volume.
  13. January 30: Quiz 1
  14. January 31: Improper (extended) integrals
  15. February 3: Comparison theorem: comparing ordinary and extended integrals
  16. February 6: Partitions of unity. Criterion of existence of (extended) integral in terms of partition of unity.
  17. February 7: Change of variable formula
  18. February 10: Continuation of the proof.
  19. February 13: Quiz 2
  20. February 14: Integration of a parametrized manifold.
  21. February 17: (No class).
  22. Mid-Sem (February 26: 10AM-12noon)
  23. February 27: (Midsem extended)

Online classes

  1. April 13: Review of forms
  2. April 20: Tangent spaces