View source for CDS 202, Winter 2009

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

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'''Instructor:'''
* Richard Murray (murray@cds.caltech.edu), 109 Steele
'''Lectures and course mailing list:'''
* TuTh 9-10:30a, 214 Steele
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds202 Course mailing list]
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'''Teaching Assistant:'''
* Paul Skerritt
'''Office hours/recitations:'''
* Office hours: Tue 4-5pm, Wed 4-5pm, 110 Steele
* Problem solving sessions: Wed, 6-7pm, 214 Steele
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=== 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 ===
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{{cds202-wi08 week|Week|Lec 1|Lec 2|Topic|text|Reading|text|Homework}}
{{cds202-wi08 week| 1| 6 Jan| N/A|Course introduction and scheduling|text|[http://www.cds.caltech.edu/~murray/papers/1994f_mur94-nas.html Murray (1994)]|text|None}}
{{cds202-wi08 week| 2| 8 Jan|13 Jan|Point set topology|mra|1|homework|1}}
{{cds202-wi08 week| 3|15 Jan|20 Jan|Manifolds, maps, tangent spaces|mra|2.3-2.4, 3.1-3.3| homework |2}}
{{cds202-wi08 week| 4|22 Jan|27 Jan|Immersions, submersions, inverse function theorem|mra|2.5, 3.5| homework |3}}
{{cds202-wi08 week| 5|29 Jan|3 Feb|Tangent bundle, vector fields, flows|mra|3.3, 4.1-4.2| homework |4}}
{{cds202-wi08 week| 6|5 Feb|10 Feb|Distributions, Frobenius theorem|mra|4.2, 4.4| homework |5}}
{{cds202-wi08 week| 7|12 Feb|17 Feb|Lie groups and Lie algebras|mra|5.1-5.2| homework |6}}
{{cds202-wi08 week| 8|19 Feb|24 Feb|Applications of Lie groups|mra|5.3 + [[http:www.cds.caltech.edu/~murray/papers/1994h_km94-cds.html|KM94]]| homework |7}}
{{cds202-wi08 week| 9|26 Feb|3 Mar|Differential forms|mra|6.1-6.2, 7.1-7.3| homework |8}}
{{cds202-wi08 week|10|5 Mar|10 Mar|Integration on manifolds, exterior derivative|mra|7.4-7.5,8.1-8.3| homework |9}}
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=== Course Text ===
The primary course text is the third edition of ''Manifolds, Tensor Analysis, and Applications'':
* Marsden, Ratiu and Abraham, [http://www.cds.caltech.edu/~marsden/cds202-08/mta 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. 

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