Difference between revisions of "CDS 202, Winter 2009"

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This is the homepage for CDS 202 (Geometry of Nonlinear Systems) for Winter 2009.
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{| width=100%
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: Richard Murray, 109 Steele
* Richard Murray (murray@cds.caltech.edu), 109 Steele
: murray@cds.caltech.edu
* TuTh 9-10:30a, 214 Steele
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'''Teaching Assistant:'''
'''Teaching Assistant:'''
: Paul Skerritt
* Paul Skerritt
: TuTh 9-10:30a, 214 Steele
'''Office Hours:'''
'''Office Hours:'''
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|} __NOTOC__

Revision as of 19:03, 6 December 2008

This is the homepage for CDS 202 (Geometry of Nonlinear Systems) for Winter 2009.


  • Richard Murray (murray@cds.caltech.edu), 109 Steele


  • TuTh 9-10:30a, 214 Steele

Teaching Assistant:

  • Paul Skerritt

Office Hours:

  • TBD

Course Description

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 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

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 [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.


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

  • Homework: 75%
There will be 8 one-week problem sets, due in class. 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.

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.