CDS 202, Winter 2009
CDS 202. Geometry of Nonlinear Systems. 9 units (3-0-6); second term. Prerequisites: CDS 201 or AM 125 a. Basic diﬀerential geometry, oriented toward applications in control and dynamical systems. Topics include smooth manifolds and mappings, tangent and normal bundles. Vector ﬁelds and ﬂows. Distributions and Frobeniuss theorem. Matrix Lie groups and Lie algebras. Exterior diﬀerential forms, Stokes theorem.
|Week||Lec 1||Lec 2||Topic||Reading||Homework|
|1||N/A||8 Jan||Course introduction||None||None|
|2||13 Jan||15 Jan||Point set topology||MTA Ch 1||HW #1 (solns)|
|3||20 Jan||22 Jan||Inverse fcn thm, immersions, submersions||MTA Ch 2||HW #2 (solns)|
|4||27 Jan||29 Jan||Manifolds, mappings, tangent space||MTA Ch 3||HW #3 (solns)|
|5||3 Feb||5 Feb||Tangent bundle, vector fields||MTA Ch 4||HW #4 (solns)|
|6||10 Feb||12 Feb||Distributions, Frobenius theorem||MTA Ch 4||HW #5 (solns)|
|7||17 Feb||19 Feb||Lie groups and Lie algebras||MTA Ch 5||HW #6 (solns)|
|8||24 Feb||26 Feb||Tensor fields||MTA Ch 6||HW #7 (solns)|
|9||3 Mar||5 Mar||Differential forms||MTA Ch 7||HW #8 (solns)|
|10||10 Mar||12 Mar||Integration on manifolds||MTA Ch 8||None|
The primary course text is the third edition of Manifolds, Tensor Analysis, and Applications:
- Marsden, Ratiu and Abraham, Manifolds, Tensor Analysis, and Applications (if you are registered for the course, send e-mail to Richard Murray [murray@cds] for the password).
In addition, students may find the following textbooks useful:
- Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, Revised second edition, 2002.