Geometry of Nonlinear Systems

WeekLec 1Lec 2TopicReadingHomework 1 5 Jan (M) N/ACourse introduction Boothby, Ch1 Syllabus 2 7 Jan (W) 16 Jan (F)Point set topology AMR, Ch 1 HW 1 [solns] 3 21 Jan (W) 23 Jan (F)Manifolds, mappings, tangent space Boothby 3.1-3.3 HW 2 [solns] 4 26 Jan (M) 28 Jan (W)Inverse fcn thm, immersions, submersions Boothby 2.6-2.7, 3.4-3.5 HW 3 [solns] 5 2 Feb (M) 4 Feb (W)Tangent bundle, vector fields Boothby 4.1-4.4 HW 4 [solns] 6 9 Feb (M) 11 Feb (W)Distributions, Frobenius theorem Boothby 4.7-4.8 HW 5 [solns] 7 18 Feb (W) 20 Feb (F)Lie groups and Lie algebras Boothby 3.6-3.6, 4.6-4.7, AMR Ch 4 HW 6 [solns] 8 23 Feb (M) 25 Feb (W)Tensor fields and exterior forms Boothby 5.1-5.3, 5.6-5.8 HW 7 [solns] 9 1 Mar (M) 3 Mar (W)Integration on manifolds Boothby 6.1-6.2, 6-4-6.5 HW 8 [solns] 10 8 Mar (M) 10 Mar (W)Applications and review none Final

- Bootby, An Introduction to Differential Manifolds and Riemannian Geometry, Revised second edition, 2002.
- Abraham, Marsden, Ratiu, Manifolds, Tensor Analysis, and Applications (if you are registered for the course, send e-mail to Richard Murray [murray@cds] for the password).