Difference between revisions of "ACM 101/AM 125b/CDS 140a, Winter 2011"
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===Announcements ===  ===Announcements ===  
* 02 Mar 2011: For those interested, we have posted an [[Media:cds140awi11CMTLimitCycleExample.pdfexample]] illustrating the use of CMT and Lyapunov functions.  
* 08 Feb 2011: [[Media:cds140awi11hw6.pdfHW #6]] is now posted; due 17 Feb 2011  
* 01 Feb 2011: [[Media:cds140awi11hw5newstyle.pdfHW #5]] is now posted; due 10 Feb 2011  * 01 Feb 2011: [[Media:cds140awi11hw5newstyle.pdfHW #5]] is now posted; due 10 Feb 2011  
* 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4HW #4]] is now posted; due 3 Feb 2011  * 25 Jan 2011: [[CDS 140a Winter 2011 Homework 4HW #4]] is now posted; due 3 Feb 2011  
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{ width=100% border=1 cellspacing=0 cellpadding=5  { width=100% border=1 cellspacing=0 cellpadding=5  
    
 '''Date'''   '''Date'''  
 '''Topic'''   '''Topic'''  
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 4 Jan <br> 6 Jan   4 Jan <br> 6 Jan  
 Linear Differential Equations I   Linear Differential Equations I  
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 [[CDS 140a Winter 2011 Homework 1HW 1]]   [[CDS 140a Winter 2011 Homework 1HW 1]]  
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 11 Jan <br> 13 Jan   11 Jan <br> 13 Jan  
 Linear Differential Equations II   Linear Differential Equations II  
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 [[CDS 140a Winter 2011 Homework 2HW 2]]   [[CDS 140a Winter 2011 Homework 2HW 2]]  
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 18 Jan <br> 20 Jan   18 Jan <br> 20 Jan  
 Nonlinear differential equations   Nonlinear differential equations  
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 [[CDS 140a Winter 2011 Homework 3HW 3]]   [[CDS 140a Winter 2011 Homework 3HW 3]]  
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 25 Jan <br> 27 Jan   25 Jan <br> 27 Jan  
 Behavior of differential equations   Behavior of differential equations  
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 Perko, 2.72.10   Perko, 2.72.10  
* [[Media:cds140awi11Week4Notes.pdfSome notes]]  * [[Media:cds140awi11Week4Notes.pdfSome notes]]  
* [[Media:cds140awi11InvManRemark.pdfRemark on invariant manifolds]]  
  [[CDS 140a Winter 2011 Homework 4HW 4]]    [[CDS 140a Winter 2011 Homework 4HW 4]]  
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 1 Feb* <br> 3 Feb*   1 Feb* <br> 3 Feb*  
 Nonhyperbolic differential equations   Nonhyperbolic differential equations  
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* [[Media:cds140awi11Week5Notes.pdfNotes on Lyapunov]]  * [[Media:cds140awi11Week5Notes.pdfNotes on Lyapunov]]  
* [[Media:cds140awi11Week5NotesCMT.pdfNotes on Center Manifold]]  * [[Media:cds140awi11Week5NotesCMT.pdfNotes on Center Manifold]]  
* [[Media:cds140awi11CMTLimitCycleExample.pdfAn Example (Center Manifold / Limit Cycle)]]  
 [[Media:cds140awi11hw5newstyle.pdfHW 5]]   [[Media:cds140awi11hw5newstyle.pdfHW 5]]  
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 8 Feb* <br> 10 Feb   8 Feb* <br> 10 Feb  
 Hamiltonian systems   Hamiltonian systems  
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* Applications  * Applications  
 Perko 2.14 + notes   Perko 2.14 + notes  
 [[Media:cds140awi11hw6.pdfHW 6]]  * [[Media:cds140awi11Week6NotesHamGrad.pdfGradient and Hamiltonian Systems]]  
* [[Media:cds140awi11Week6NotesLagHamSum.pdfLagrangian, Summary]]  
 [[Media:cds140awi11hw6.pdfHW 6]]  
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 15 Feb <br> 17 Feb <br> 22 Feb  
 15 Feb <br> 17 Feb  
 Limit cycles   Limit cycles  
* Limit sets and attractors  * Limit sets and attractors  
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* Poincare' map  * Poincare' map  
* Bendixson criterion for limit cycles in the plane  * Bendixson criterion for limit cycles in the plane  
 Perko, 3.   Perko, 3.13.5, 3.9  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L71_orbits15Feb11.pdf Lecture notes on orbits and attractors]  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L72_limitcycles17Feb11.pdf Lecture notes on limit cycles]  
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L73_bfs_oscillators.pdf BFS notes on oscillators]  
 [[CDS 140a Winter 2011 Homework 7HW 7]]  
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   24 Feb <br> 1 Mar <br> 3 Mar  
 Bifurcations   Bifurcations  
* Structural stability  * Structural stability  
* Bifurcation of equilibrium points  * Bifurcation of equilibrium points  
* Hopf bifurcation  * Hopf bifurcation  
 Perko 4.14.4   Perko 4.14.4 + notes  
* [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/L82_bifurcations01Mar11.pdf Lecture notes on bifurcations]  
 [[CDS 140a Winter 2011 Homework 8HW 8]]  
*  
*  
  
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 8 Mar <br>   8 Mar <br>  
 Course review   Course review  
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== Old Announcements ==  == Old Announcements ==  
[[Category:Courses]] 
Latest revision as of 04:55, 27 June 2021
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
 02 Mar 2011: For those interested, we have posted an example illustrating the use of CMT and Lyapunov functions.
 08 Feb 2011: HW #6 is now posted; due 17 Feb 2011
 01 Feb 2011: HW #5 is now posted; due 10 Feb 2011
 25 Jan 2011: HW #4 is now posted; due 3 Feb 2011
 18 Jan 2011: HW #3 is now posted; due 27 Jan 2011
 11 Jan 2011: HW #2 is now posted; due 20 Jan 2011
 6 Jan 2011: Office hours for HW #1 will be on 10 Jan (Mon) from 46 pm in 235 ANB; office hours for future weeks will be on Wednesdays from 122 in 235 ANB
 6 Jan 2011: Course ombuds: Jeff Amelang and Matanya Horowitz
 3 Jan 2011: HW #1 is now posted; due 11 Jan 2011
 14 Nov 2010: web page creation
Lecture Schedule
Date  Topic  Reading  Homework 
4 Jan 6 Jan 
Linear Differential Equations I

Perko, 1.11.6

HW 1 
11 Jan 13 Jan 
Linear Differential Equations II

Perko, 1.71.10 + notes  HW 2 
18 Jan 20 Jan 
Nonlinear differential equations

Perko, 2.12.6  HW 3 
25 Jan 27 Jan 
Behavior of differential equations

Perko, 2.72.10  HW 4 
1 Feb* 3 Feb* 
Nonhyperbolic differential equations

Perko, 2.112.13  HW 5 
8 Feb* 10 Feb 
Hamiltonian systems

Perko 2.14 + notes  HW 6 
15 Feb 17 Feb 22 Feb 
Limit cycles

Perko, 3.13.5, 3.9  HW 7 
24 Feb 1 Mar 3 Mar 
Bifurcations

Perko 4.14.4 + notes  HW 8 
8 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. 
Grading
The ﬁnal grade will be based on homework and a ﬁnal exam:
 Homework (75%)  There will be 9 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.