CDS 202, Winter 2009
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Course Description
CDS 202. Geometry of Nonlinear Systems. 9 units (306); 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 email 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
The ﬁnal grade will be based on homework and a ﬁnal exam.
 Homework: 75%
 There will be 8 oneweek 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.