CDS 202, Spring 2013: Difference between revisions

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* Richard Murray (murray@cds.caltech.edu), 109 Steele
* Richard Murray (murray@cds.caltech.edu), 109 Steele
'''Lectures and course mailing list:'''
'''Lectures and course mailing list:'''
* TuTh 9-10:30a, 214 Steele
* MWF, 10-11; 213 Annenberg
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds202 Course mailing list]
* [https://courses.caltech.edu/course/view.php?id=1313 Moodle site]
| width=50% |
| width=50% |
'''Teaching Assistant:'''
'''Teaching Assistant:'''
* Katie Broersma
* Katie Broersma
'''Office hours/recitations:'''
'''Office hours/recitations:'''
* Office hours: TBD
* Recitations: TBD
|} __NOTOC__
|} __NOTOC__


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=== Course Schedule ===
=== Course Schedule ===
{| width=100% border=1
{| width=100% border=1
{{cds202-sp13 week|Week|Lec 1|Lec 2|Topic|text|Reading|text|Homework}}
|-  
{{cds202-sp13 week| 1| 6 Jan| N/A|Course introduction and scheduling|[http://www.cds.caltech.edu/~murray/papers/1994f_mur94-nas.html Murray (1994)]|None}}
! Week
{{cds202-sp13 week| 2| 8 Jan|13 Jan|Point set topology|MTA 1|homework|1}}
! Date
{{cds202-sp13 week| 3|15 Jan|20 Jan|Manifolds, maps, tangent spaces|mra|2.3-2.4, 3.1-3.3| homework |2}}
! Topic
{{cds202-sp13 week| 4|22 Jan|27 Jan|Immersions, submersions, inverse function theorem|mra|2.5, 3.5| homework |3}}
! Reading
{{cds202-sp13 week| 5|29 Jan|3 Feb|Tangent bundle, vector fields, flows|mra|3.3, 4.1-4.2| homework |4}}
! Homework
{{cds202-sp13 week| 6|5 Feb|10 Feb|Distributions, Frobenius theorem|mra|4.2, 4.4| homework |5}}
|-
{{cds202-sp13 week| 7|12 Feb|17 Feb|Lie groups and Lie algebras|mra|5.1-5.2| homework |6}}
| 1 || 3 Apr (W) || Course introduction, scheduling || [[http:www.cds.caltech.edu/~murray/preprints/mur94-nas.pdf|Mur94-NAS]] || None
{{cds202-sp13 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}}
|- valign=top
{{cds202-sp13 week| 9|26 Feb|3 Mar|Differential forms|mra|6.1-6.2, 7.1-7.3| homework |8}}
| &nbsp;<br>2 || 5 Apr (F) <br> 10 Apr (W)
{{cds202-sp13 week|10|5 Mar|10 Mar|Integration on manifolds, exterior derivative|mra|7.4-7.5,8.1-8.3| homework |9}}
| Point set topology || {{cds202-sp13 pdf|caltech/MTA-ch1.pdf|MTA, 1.1-1.5}} || {{cds202-sp13 pdf|hw1.pdf|HW 1}}
|- valign=top
| &nbsp;<br>3 || 12 Apr (F) <br> 15 Apr (M)
| Manifolds, maps, tangent spaces || {{cds202-sp13 pdf|caltech/MTA-ch2.pdf|MTA 2.3-2.4}}, {{cds202-sp13 pdf|caltech/MTA-ch3.pdf | 3.1-3.3}},<br>Boothby II.1-II.3, III.1-III.3
| {{cds202-sp13 pdf|hw2.pdf|HW 2}}
|- valign=top
| 4 || 24 Apr (W) <br> 26 Apr (F)
| Immersions, submersions, inverse function theorem || {{cds202-sp13 pdf|caltech/MTA-ch2.pdf|MTA 2.5}}, {{cds202-sp13 pdf|caltech/MTA-ch3.pdf|3.5}}  
| {{cds202-sp13 pdf|hw3.pdf|HW 3}}
|- valign=top
| 5 || 29 Apr (M) <br> 1 May (W)
| Tangent bundle, vector fields, flows || {{cds202-sp13 pdf|caltech/MTA-ch3.pdf|MTA 3.5}}, {{cds202-sp13 pdf|caltech/MTA-ch4.pdf|4.1-4.2}}
|  {{cds202-sp13 pdf|hw4.pdf|HW 4}}
|- valign=top
| 6 || 6 May (M) <br> <s>10 May (F)</s> <br> <font color=blue>9 May@12p</font>
| Distributions, Frobenius theorem || {{cds202-sp13 pdf|caltech/MTA-ch4.pdf|MTA 4.2, 4.4}}
| {{cds202-sp13 pdf|hw5.pdf|HW 5}}
|- valign=top
| 7 || 13 May (M) <br> 15 May (W)
| Lie groups and Lie algebras || {{cds202-sp13 pdf|caltech/MTA-ch5.pdf|MTA 5.1-5.2}}
| {{cds202-sp13 pdf|hw6.pdf|HW 6}}
|- valign=top
| 8 || 20 May<font color=blue>@4p</font> <br> 22 May (W)
| Applications of Lie groups || {{cds202-sp13 pdf|caltech/MTA-ch5.pdf|MTA 5.3}} + [http://www.cds.caltech.edu/~murray/preprints/cds94-014.pdf KM94]
| {{cds202-sp13 pdf|hw7.pdf|HW 7}}
|- valign=top
| 9 || 29 May (W) <br> 31 May (F)
| Differential forms || {{cds202-sp13 pdf|caltech/MTA-ch6.pdf|MTA 6.1-6.2}}, {{cds202-sp13 pdf|caltech/MTA-ch7.pdf|7.1-7.3}}  
| {{cds202-sp13 pdf|hw8.pdf|HW 8}}
|- valign=top
| 10 || 3 Jun (M) <br> 5 Jun (W)
| Integration on manifolds, exterior derivative || {{cds202-sp13 pdf|caltech/MTA-ch7.pdf|MTA 7.4-7.5}}, {{cds202-sp13 pdf|caltech/MTA-ch8.pdf|8.1-8.3}}
| {{cds202-sp13 pdf|hw9.pdf|HW 9}}
|}
|}


=== Course Text ===
=== Course Text ===
The primary course text is the third edition of ''Manifolds, Tensor Analysis, and Applications'':
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).
* Marsden, Ratiu and Abraham, {{cds202-sp13 pdf|caltech/MTA-frontback.pdf|Manifolds, Tensor Analysis, and Applications}} (only available to students enrolled in course).
In addition, students may find the following textbooks useful:
In addition, students may find the following textbooks useful:
* Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, Revised second edition, 2002.
* Boothby, An Introduction to Differential Manifolds and Riemannian Geometry, Revised second edition, 2002.
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=== Grading ===
=== Grading ===
The final grade will be based on homework and a final exam:
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.
* 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 (likely N hours over a 4-8N hour period).  
* 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).  


Latest revision as of 15:27, 2 June 2013

This is the homepage for ACM/CDS 202 (Geometry of Nonlinear Systems) for Spring 2013.

Instructor:

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

Lectures and course mailing list:

Teaching Assistant:

  • Katie Broersma

Office hours/recitations:

  • Recitations: TBD

Course Description

ACM/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 Date Topic Reading Homework
1 3 Apr (W) Course introduction, scheduling Mur94-NAS None
 
2		 5 Apr (F)
10 Apr (W) 		Point set topology MTA, 1.1-1.5 HW 1
 
3		 12 Apr (F)
15 Apr (M) 		Manifolds, maps, tangent spaces MTA 2.3-2.4, 3.1-3.3,
Boothby II.1-II.3, III.1-III.3 		HW 2
4 24 Apr (W)
26 Apr (F) 		Immersions, submersions, inverse function theorem MTA 2.5, 3.5 HW 3
5 29 Apr (M)
1 May (W) 		Tangent bundle, vector fields, flows MTA 3.5, 4.1-4.2 HW 4
6 6 May (M)
10 May (F)
9 May@12p 		Distributions, Frobenius theorem MTA 4.2, 4.4 HW 5
7 13 May (M)
15 May (W) 		Lie groups and Lie algebras MTA 5.1-5.2 HW 6
8 20 May@4p
22 May (W) 		Applications of Lie groups MTA 5.3 + KM94 HW 7
9 29 May (W)
31 May (F) 		Differential forms MTA 6.1-6.2, 7.1-7.3 HW 8
10 3 Jun (M)
5 Jun (W) 		Integration on manifolds, exterior derivative MTA 7.4-7.5, 8.1-8.3 HW 9

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 (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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