Difference between revisions of "ACM 101b/AM 125b/CDS 140a, Winter 2014"
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'''Teaching Assistants'''  '''Teaching Assistants'''  
−  *  +  * Katie Broersma (CDS) 
−  *  +  * Vanessa Jonsson (CDS) 
−  *  +  * Office hours: Tue, 3:304:30, 101 STH 
}  }  
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===Announcements ===  ===Announcements ===  
+  * 29 Dec 2013: updated course information  
* 4 Nov 2013: web page creation  * 4 Nov 2013: web page creation  
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* J&S, Ch 1; Sec 2.12.5  * J&S, Ch 1; Sec 2.12.5  
* Ver, Sec 5.15.2; 6.16.2  * Ver, Sec 5.15.2; 6.16.2  
−   [[CDS 140a Winter 2014 Homework 1HW 1]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 1HW 1]] <br> Due: 15 Jan (Wed) 
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 14 Jan <br> 16 Jan   14 Jan <br> 16 Jan  
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* Boundary value problems (if time)  * Boundary value problems (if time)  
 Perko, 1.71.10 + notes   Perko, 1.71.10 + notes  
−   [[CDS 140a Winter 2014 Homework 2HW 2]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 2HW 2]] <br> Due: 22 Jan (Wed) 
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 21 Jan <br> 23 Jan   21 Jan <br> 23 Jan  
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* Linearization  * Linearization  
 Perko, 2.12.6   Perko, 2.12.6  
−   [[CDS 140a Winter 2014 Homework 3HW 3]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 3HW 3]] <br> Due: 29 Jan (Wed) 
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 28 Jan <br> 30 Jan   28 Jan <br> 30 Jan  
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* [[Media:cds140awi11InvManRemark.pdfRemark on invariant manifolds]]  * [[Media:cds140awi11InvManRemark.pdfRemark on invariant manifolds]]  
>  >  
−    [[CDS 140a Winter 2014 Homework 4HW 4]] <br> Due:  +    [[CDS 140a Winter 2014 Homework 4HW 4]] <br> Due: 5 Feb (Wed) 
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 4 Feb <br> 6 Feb   4 Feb <br> 6 Feb  
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* [[Media:cds140awi11CMTLimitCycleExample.pdfAn Example (Center Manifold / Limit Cycle)]]  * [[Media:cds140awi11CMTLimitCycleExample.pdfAn Example (Center Manifold / Limit Cycle)]]  
>  >  
−   [[CDS 140a Winter 2014 Homework 5HW 5]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 5HW 5]] <br> Due: 12 Feb (Wed) 
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 11 Feb <br> 13 Feb   11 Feb <br> 13 Feb  
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* [[Media:cds140awi11Week6NotesLagHamSum.pdfLagrangian, Summary]]  * [[Media:cds140awi11Week6NotesLagHamSum.pdfLagrangian, Summary]]  
>  >  
−   [[CDS 140a Winter 2014 Homework 6HW 6]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 6HW 6]] <br> Due: 19 Feb (Wed) 
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 18 Feb <br> 20 Feb <br> 25 Feb   18 Feb <br> 20 Feb <br> 25 Feb  
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L73_bfs_oscillators.pdf BFS notes on oscillators]  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L73_bfs_oscillators.pdf BFS notes on oscillators]  
>  >  
−   [[CDS 140a Winter 2014 Homework 7HW 7]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 7HW 7]] <br> Due: 5 Mar (Wed) 
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<!  <!  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_parmsens24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_parmsens24Feb11.pdf Lecture notes on structural stability, parameter sensitivity]  
−  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_bfs_sensitivity.pdf BFS notes on parameter sensitivity]  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L81_bfs_sensitivity.pdf BFS notes on parameter sensitivity]  
−  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L82_bifurcations01Mar11.pdf Lecture notes on bifurcations]  * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L82_bifurcations01Mar11.pdf Lecture notes on bifurcations]  
>  >  
−   [[CDS 140a Winter 2014 Homework 8HW 8]] <br> Due:  +   [[CDS 140a Winter 2014 Homework 8HW 8]] <br> Due: 12 Mar (wed) 
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 11 Mar* <br>   11 Mar* <br> 
Revision as of 15:51, 29 December 2013
Differential Equations and Dynamical Systems  
Instructors

Teaching Assistants

Course Description
Analytical methods for the formulation and solution of initial value problems for ordinary differential equations. Basics in topics in dynamical systems in Euclidean space, including equilibria, stability, phase diagrams, Lyapunov functions, periodic solutions, PoincaréBendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.
Announcements
 29 Dec 2013: updated course information
 4 Nov 2013: web page creation
Lecture Schedule
Date  Topic  Reading  Homework 
7 Jan 9 Jan 
Linear Differential Equations I

Perko, 1.11.6

HW 1 Due: 15 Jan (Wed) 
14 Jan 16 Jan 
Linear Differential Equations II

Perko, 1.71.10 + notes  HW 2 Due: 22 Jan (Wed) 
21 Jan 23 Jan 
Nonlinear differential equations

Perko, 2.12.6  HW 3 Due: 29 Jan (Wed) 
28 Jan 30 Jan 
Behavior of differential equations

Perko, 2.72.10  HW 4 Due: 5 Feb (Wed) 
4 Feb 6 Feb 
Nonhyperbolic differential equations

Perko, 2.112.13  HW 5 Due: 12 Feb (Wed) 
11 Feb 13 Feb 
Hamiltonian systems

Perko 2.14 + notes  HW 6 Due: 19 Feb (Wed) 
18 Feb 20 Feb 25 Feb 
Limit cycles

Perko, 3.13.5, 3.7, 3.9  HW 7 Due: 5 Mar (Wed) 
27 Feb 4 Mar 6 Mar 
Bifurcations

Perko 4.14.4 + notes  HW 8 Due: 12 Mar (wed) 
11 Mar* 
Course review 
Textbook
The primary text for the course (available via the online bookstore) is
[Perko]  L. Perko, Differential Equations and Dynamical Systems, Third Edition. Springer, 2006. 
The following additional texts may be useful for some students (on reserve in SFL):
[J&S]  D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007. 
[Ver]  F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second Edition. Springer, 2006. 
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 approximately 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 48N 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 or from other external sources 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.