Difference between revisions of "CDS 202, Winter 2009"

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{| width=100% border=1
{{cds202-wi08 week|Week|Lec 1|Lec 2|Topic|text|Reading|text|Homework}}
{{cds202-wi08 week|Week|Lec 1|Lec 2|Topic|text|Reading|text|Homework}}
{{cds202-wi08 week| 1| 6 Jan| 8 Jan|Course introduction + point set topology|mra|1|homework|1}}
{{cds202-wi08 week| 1| 6 Jan| N/A|Course introduction and scheduling|text|None|text|None}}
{{cds202-wi08 week| 2|13 Jan|15 Jan|Differential calculus, inverse function theorem|mra|2|homework|2}}
{{cds202-wi08 week| 2| 8 Jan|13 Jan|Point set topology|mra|1|homework|1}}
{{cds202-wi08 week| 3|20 Jan|22 Jan|Manifolds|mra|3|homework|3}}
{{cds202-wi08 week| 3|15 Jan|20 Jan|Differential calculus, inverse function theorem|mra|2|homework|2}}
{{cds202-wi08 week| 4|27 Jan|29 Jan|Tangent bundle|mra|3|homework|4}}
{{cds202-wi08 week| 4|22 Jan|27 Jan|Manifolds, tangent bundle|mra|3|homework|3}}
{{cds202-wi08 week| 5|3 Feb|5 Feb|Vector fields and flows|mra|4|homework|5}}
{{cds202-wi08 week| 5|29 Jan|3 Feb|Vector fields and flows|mra|4|homework|4}}
{{cds202-wi08 week| 6|10 Feb|12 Feb|Distributions, Frobenius theorem|mra|4|homework|6}}
{{cds202-wi08 week| 6|5 Feb|10 Feb|Distributions, Frobenius theorem|mra|4|homework|5}}
{{cds202-wi08 week| 7|17 Feb|19 Feb|Lie groups and Lie algebras|mra|5|homework|7}}
{{cds202-wi08 week| 7|12 Feb|17 Feb|Lie groups and Lie algebras|mra|5|homework|6}}
{{cds202-wi08 week| 8|24 Feb|26 Feb|Tensor fields|mra|6|homework|8}}
{{cds202-wi08 week| 8|19 Feb|24 Feb|Tensor fields|mra|6|homework|7}}
{{cds202-wi08 week| 9|3 Mar|5 Mar|Differential forms|mra|7|homework|9}}
{{cds202-wi08 week| 9|26 Feb|3 Mar|Differential forms|mra|7|homework|8}}
{{cds202-wi08 week|10|10 Mar|N/A|Integration on manifolds|mra|8|text|None}}
{{cds202-wi08 week|10|5 Mar|10 Mar|Integration on manifolds|mra|8|text|None}}
|}
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Revision as of 06:50, 31 December 2008

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

Instructor:

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

Lectures:

  • 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 6 Jan N/A Course introduction and scheduling None None
2 8 Jan 13 Jan Point set topology MTA Ch 1 HW #1 (solns)
3 15 Jan 20 Jan Differential calculus, inverse function theorem MTA Ch 2 HW #2 (solns)
4 22 Jan 27 Jan Manifolds, tangent bundle MTA Ch 3 HW #3 (solns)
5 29 Jan 3 Feb Vector fields and flows MTA Ch 4 HW #4 (solns)
6 5 Feb 10 Feb Distributions, Frobenius theorem MTA Ch 4 HW #5 (solns)
7 12 Feb 17 Feb Lie groups and Lie algebras MTA Ch 5 HW #6 (solns)
8 19 Feb 24 Feb Tensor fields MTA Ch 6 HW #7 (solns)
9 26 Feb 3 Mar Differential forms MTA Ch 7 HW #8 (solns)
10 5 Mar 10 Mar Integration on manifolds MTA Ch 8 None

Course Text

The primary course text is the third edition of Manifolds, Tensor Analysis, and Applications:

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 8 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.

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.