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)


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

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