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Analysis II >> Content Detail



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Readings

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

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

(S) Amazon logo 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 #TOPICSREADINGS
2Compactness, ConnectednessM, sections 1 and 2
3Differentiation in n DimensionsM, end of section 4 on connectedness
8Reimann Integrals of Several Variables, Conditions for IntegrabilityM, section 10
10Fubini Theorem, Properties of Reimann Integrals GradedM, section 11
13ExhaustionsM, theorem 15.3 and following paragraph
15Partitions of Unity (cont.), Exhaustions (cont.)M, sections 1 and 2

MLA
22The d Operator (cont.), Pullback Operator on Exterior FormsM, section 29
24Poincare TheoremSN, section 1
34Orientations of ManifoldsMLA, section 7
35Integration on Manifolds, Degree on ManifoldsM, section 34, pp. 281-286 only

 








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