CDS 202, Spring 2013

This is the homepage for ACM/CDS 202 (Geometry of Nonlinear Systems) for Spring 2013.

Instructor: Richard Murray (murray@cds.caltech.edu), 109 Steele Lectures and course mailing list: TuTh 9-10:30a, 214 Steele Course mailing list

Teaching Assistant: Katie Broersma Office hours/recitations: Office hours: TBD

Course Description

ACM/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.

Course Schedule

Week	Lec 1	Lec 2	Topic	Template:Cds202-sp13 text	Template:Cds202-sp13 text
1	6 Jan	N/A	Course introduction and scheduling	None}}	{{{8}}}}}
2	8 Jan	13 Jan	Point set topology	Template:Cds202-sp13 MTA 1	Template:Cds202-sp13 1
3	15 Jan	20 Jan	Manifolds, maps, tangent spaces	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
4	22 Jan	27 Jan	Immersions, submersions, inverse function theorem	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
5	29 Jan	3 Feb	Tangent bundle, vector fields, flows	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
6	5 Feb	10 Feb	Distributions, Frobenius theorem	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
7	12 Feb	17 Feb	Lie groups and Lie algebras	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
8	19 Feb	24 Feb	Applications of Lie groups	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
9	26 Feb	3 Mar	Differential forms	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework
10	5 Mar	10 Mar	Integration on manifolds, exterior derivative	Template:Cds202-sp13 mra	Template:Cds202-sp13 homework

Course Text

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 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.

Grading

The final grade will be based on homework and a final exam:

• Homework (75%) - There will be 9 one-week problem sets, due in class one week after they are assigned. Late homework will not be accepted without prior permission from the instructor.
• Final exam (25%) - The final will be handed out the last day of class and is due back at the end of finals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the final is higher than the weighted average of your homework and final, your final will be used to determine your course grade.

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course is not allowed. All solutions that are handed should reflect your understanding of the subject matter at the time of writing.

No collaboration is allowed on the final exam.