Day	Topic	Book pages	Homework
8/24	Review of topological notions	Appendix A.
8/26	Topological manifolds	P. 2-10.	Homework 1, due 9/2.
8/31	Smooth atlases	P. 10-13
9/2	Smooth structures, examples	P. 14-20	Homework 2, due 9/9
9/7	Smooth functions, smooth maps	P. 31-36
9/9	Diffeomorphisms, bump functions	P. 38-42
9/14	Partitions of unity	P. 40-46
9/16	No class (Yom Kippur)
9/17	Immersions, submersions, embeddings	P. 77-81	Homework 3, due 9/23
9/21	The rank theorem	P. 81-86
9/23	Embedded submanifolds	P. 99-106	Homework 4, due 9/30.
9/28	Tangent vectors and derivations	P. 51-55
9/30	Tangent space, differential of a map	P. 56-61, 68-70	Homework 5, due 10/7.
10/5	The tangent budle	P. 65-68
10/7	Sard's Theorem	P. 127-131	Homework sheet, not due
10/12	Whitney embedding theorem	P. 131-135
10/14	Transversality	P. 143-147	Homework 6, due 10/21.
10/19	Vector fields, pushforwards	P. 174-185
10/21	Integral curves and flows	P. 205-212
10/26	Lie derivatives, Lie Brackets	P. 185-188, 227-231
10/28	Commuting vector fields	P. 231-235	Homework 7, due 11/4
11/2	Tangent covectors	P. 273-276, 280-284.
11/4	Pullbacks and line integrals	P. 284-291.	Homework 8, due 11/11
11/9	Multilinear algebra	P. 349-356.
11/11	Differential forms	P. 359-362.	Homework 9, due 11/18
11/16	Exterior derivatives; closed and exact forms	P. 362-367.
11/18	Orientation forms	P. 377-386.	Homework 10, extra credit
11/30	Integration on manifolds	P. 402-410.
12/2	Stokes' theorem	P. 411-415.