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CDS 202 -- Winter 2005 Second Term Geometry of Nonlinear Systems Prerequisites: CDS 201 or AM 125 a Recommended Reading from Course Text

Manifolds, Tensors, Analysis, and Applications R. Abraham, J. E. Marsden, and T. Ratiu (Draft Third Edition, February 10, 2004) Chapter 2 : Section 2.1 : omitting the proof of 2.1.10, supplement 2.1A, 2.1B Section 2.2 : omitting Supplement 2.2A, Theorem 2.2.6, integration of Banach space valued functions, supplement 2.2B, 2.2C Section 2.3 : read all of it Section 2.4 : omitting all the supplements Section 2.5 : omitting all the supplements and proofs of some of the trickier theorems, such as the rank Theorem 2.5.14. Chapter 3 : Section 3.1 : Skip the proofs in Example 3.1.8G Section 3.2 : All Section 3.3 : All Section 3.4 : Skip Supplements 3.4A and B, proofs in Propositions 3.4.17--20, Prop 3.4.26, 3.4.28, 3.4.30 Section 3.5 : Skip proof of Theorem 3.5.25, Supplement 3.5A Section 3.6 : Skip whole section Chapter 4 : Section 4.1 : All but skip Supplement 4.1A, 4.1B, 4.1C Section 4.2 : All, but skip the proof of 4.2.16, Supplement 4.2A, 4.2B, 4.2C, 4.2D Section 4.3 : This overlaps quite a bit with CDS 140a,b and so we will just cover it lightly; skip the proof of 4.3.4 (including 4.3.5-4.3.9), proof of 4.3.21 Section 4.4 : All Chapter 5 : Section 5.1 : all Section 5.2 : pages 305-311 in detail, the rest of the section only lightly Section 5.3 : pages 324-331 in detail; omit 332-336. Chapter 6 : Section 6.1 : all Section 6.2 : skip "Alternative Approach to Tensor Fields" on page 355 Section 6.3 : all Section 6.4 : skip Lemmas 6.4.8 and 6.4.9 Section 6:5 : skip for now (will be needed later for integration) Chapter 7 : Section 7.1 : all Section 7.2 : all Section 7.3 : all Section 7.4 : skip Supplement 7.4A ; skip Cohomology up to the end of page 424 ; skip Supplement 7.4B ; skip Maurer-Cartan Equations Section 7:5 : all Chapter 8 : Section 8.1 : omit measures and from 8.1.14 to the end of the section Section 8.2 : omit Supplements 8.2A, 8.2B, 8.2C Section 8.3 : all Section 8.4 : whole section is optional Section 8:5 : whole section is optional