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)
| 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 |