Day	Topic	Book pages	Homework
8/28	Topological manifolds	P. 2-10.
8/30	Smooth atlases	P. 10-13	Homework 1, due 9/6.
9/4	No class (Labor Day)
9/6	Smooth structures, examples	P. 14-20
9/11	Smooth functions, smooth maps	P. 31-38
9/13	Bump functions, locally finite covers, partitions of unity	P. 40-44	Homework 2, due 9/20.
9/18	Applications of partitions of unity; tangent vectors	P. 43-46
9/20	Tangent vectors and derivations	P. 51-55	Homework 3, due 9/27.
9/25	Tangent space, differential of a map	P. 56-61
9/27	The tangent budle	P. 65-68	Homework 4, due 10/4
10/2	Immersions, submersions, rank theorem	P. 77-86
10/4	The rank theorem and embedded submanifolds	P. 99-106	Homework 5, due 10/11.
10/9	Sard's Theorem	P. 127-131
10/11	Whitney embedding theorem, part 1	P. 131-133
10/16	Whitney theorem & applications	P. 133-135
10/18	Midterm exam
10/23	Transversality	P. 143-147	Homework 6, due 11/1.
10/25	Vector fields, pushforwards	P. 174-185
10/30	Integral curves and flows	P. 205-211
11/1	Local flows, complete vector fields	P. 211-216	Homework 7, due 11/8
11/6	Canonical form of vector field, Lie brackets	P. 185-188, P. 331-332 of 1st ed
11/8	Commuting vector fields	P. 227-235	Homework 8, due 11/15
11/13	Tangent covectors	P. 273-276, 280-284.
11/15	Pullbacks and line integrals	P. 284-291.	Homework 9, due 12/1
11/27	Multilinear algebra	P. 305-307, 349-356.
11/29	Differential forms, exterior derivatives	P. 359-367.	Homework 10, due 12/8
12/4	Closed and exact forms; orientation	P. 295-297, 377-386.
12/6	Integration on manifolds	P. 402-410.
12/11	Stokes' theorem	P. 411-415.