Readings

Readings listed in the table below are from the following textbooks and notes:

(M) Munkres, J. Analysis on Manifolds. Cambridge, MA: Perseus Publishing, 1991. ISBN: 0201510359, ISBN: 0201315963 (paperback).

(S) Spivak, M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus. Cambridge, MA: Perseus Publishing, 1965. ISBN: 0805390219.

(MLA) Notes on Multi-linear Algebra (PDF)

(SN) Supplementary Notes (PDF)

Course readings.
LEC #	TOPICS	READINGS
2	Compactness, Connectedness	M, sections 1 and 2
3	Differentiation in n Dimensions	M, end of section 4 on connectedness
8	Reimann Integrals of Several Variables, Conditions for Integrability	M, section 10
10	Fubini Theorem, Properties of Reimann Integrals Graded	M, section 11
13	Exhaustions	M, theorem 15.3 and following paragraph
15	Partitions of Unity (cont.), Exhaustions (cont.)	M, sections 1 and 2 MLA
22	The d Operator (cont.), Pullback Operator on Exterior Forms	M, section 29
24	Poincare Theorem	SN, section 1
34	Orientations of Manifolds	MLA, section 7
35	Integration on Manifolds, Degree on Manifolds	M, section 34, pp. 281-286 only

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