- Final Exam Review will
take place on Friday, December 5, 5-7pm in BA6183.
- The Final will take place on
Monday, December 8, 10-1 in
- It will cover everything we've covered
in class, lecture notes and on homework.
Specifically, it will cover the following material:
- Chapter 1: Generalized
manifolds (not in the book) + everything in this chapter
except for topological manifolds.
- Chapter 3: Everything except functors.
- Chapter 4: Everything except for covering maps.
- Chapter 5: Submanifolds, embeddings.
- Chapter 6: Sard's Theorem, Whitney embedding
theorem for compact manifolds.
- Chapter 8 : Vector fields, criteria of
smoothness, sufficient condition for the triviality of
the tangent bundle.
- Chapter 12: Everything except tensor products of
- Chapter 14: Alternating tensors, cotangent
bundle, tensor bundles on manifolds, differential forms,
- Chapter 15: Orientations on vector spaces,
orientations on manifolds.
- Chapter 16: Integration of forms, Stokes's
Formula, applications to De Rham cohomology
- Rules for the Final : No
calculators or notes!
- We will have a Review Session on Friday, December
5, 5-7pm. I will post a room number later.
- Here are some practice problems on
recent material (including Stokes's formula) to help you
prepare for the Final.