# 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:

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### Exam dates

To be announced.
### Resources and summary of lectures:

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

### Online classes

- April 13: Review of forms
- April 20: Tangent spaces