Difference between revisions of "CDS 202, Winter 2009"

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'''Instructor:'''
: Richard Murray, 109 Steele
: murray@cds.caltech.edu
|
'''Teaching Assistant:'''
: Paul Skerritt
|-
|'''Lectures:'''
: TuTh 9-10:30a
|
'''Office Hours:'''
: TBD
|} __NOTOC__
=== 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 ===
=== Course Schedule ===
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{{cds202-wi08 week|10|10 Mar|12 Mar|Integration on manifolds|mra|8|text|None}}
{{cds202-wi08 week|10|10 Mar|12 Mar|Integration on manifolds|mra|8|text|None}}
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=== 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.
=== Grading ===


[[Category:Courses]]
[[Category:Courses]]

Revision as of 18:57, 6 December 2008

Instructor:

Richard Murray, 109 Steele
murray@cds.caltech.edu

Teaching Assistant:

Paul Skerritt
Lectures:
TuTh 9-10:30a

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.

Grading