Day	Topic	Book pages	Homework
8/27	Review of topological notions	Appendix, p. 541-544.
8/29	Topological manifolds	P. 1-8.	Homework 1, due 9/5.
9/5	Smooth structures	P. 11-14, 17-18	Homework 2, due 9/12
9/10	More about smooth atlases	P. 14, 19-24
9/12	Partitions of unity	P. 49-54	Homework 3, due 9/19
9/17	Smooth functions, smooth maps	P. 31-36, 55-57
9/19	The rank theorem	P. 156-158, 163-168
9/24	Immersions and embeddings	P. 174-176, 180-183	Homework 4, due 10/3.
10/1	Embedding manifolds in R^n
10/3	Sard's Theorem	Handout
10/8	Tangent vectors	P. 61-65
10/10	Pushforwards, tangent bundle	P. 66-71, 81-82	Homework 5, due 10/22.
10/15	Vector fields	P. 82-89
10/17	Integral curves and flows	P. 435-442
10/22	Regular points of a vector field	P. 447-450
10/24	Lie derivatives, Lie Brackets	P. 89-91, 465-468	Homework 6, due 11/5
10/31	Commuting vector fields	P. 468-472
11/5	Frobenius integrability theorem	P. 495-496, 500-505
11/7	Tangent covectors	P. 125-134.	Homework 7, due 11/14
11/12	Pullbacks and line integrals	P. 136-142.
11/14	Multilinear algebra	P. 294-302.
11/19	Differential forms	P. 302-310.	Homework 8, due 11/28
11/26	Closed and exact forms	P. 143-148; 310.
11/28	Orientation forms	P. 327-329; 334-340.
12/3	Integration on manifolds	P. 350-356.	Homework 9, due 12/12
12/5	Stokes' theorem	P. 359-362.