ACM 101/AM 125b/CDS 140a, Winter 2013: Difference between revisions
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{{warning|This page is out of date. Please refer to the [[CDS 140a]] page for the latest information}} | |||
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* Katheryn Broersma (CDS), katheryn@caltech.edu | * Katheryn Broersma (CDS), katheryn@caltech.edu | ||
* Vanessa Jönsson (CDS), vjonsson@caltech.edu | * Vanessa Jönsson (CDS), vjonsson@caltech.edu | ||
* Office hours: | * Office hours: Fridays, 11-12 in 314 ANB; Mondays, 12-1 in 243 ANB | ||
* [https://piazza.com/caltech/winter2013/cds140 Piazza] | * [https://piazza.com/caltech/winter2013/cds140 Piazza] | ||
|} | |} | ||
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=== Lecture Schedule === | === Lecture Schedule === | ||
{| width=100% border=1 cellpadding=5 | {| class="mw-collapsible " width=100% border=1 cellpadding=5 | ||
|- | |- | ||
| '''Date''' | | '''Date''' | ||
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Perko, 1.1-1.6<br> | Perko, 1.1-1.6<br> | ||
Optional: | Optional: | ||
* J&S, Ch 1 | * J&S, Ch 1; Sec 2.1-2.5 | ||
* | * Ver, Sec 5.1-5.2; 6.1-6.2 | ||
| [[CDS 140a Winter 2013 Homework 1|HW 1]] <br> Due: 15 Jan (Tue) | | [[CDS 140a Winter 2013 Homework 1|HW 1]] <br> Due: 15 Jan (Tue) | ||
|- valign=top | |- valign=top | ||
| Line 55: | Line 56: | ||
* Stability theory | * Stability theory | ||
* Linear systems with inputs (nonhomogeneous systems) | * Linear systems with inputs (nonhomogeneous systems) | ||
* Boundary value problems | * Boundary value problems (if time) | ||
| Perko, 1.7-1.10 + notes | | Perko, 1.7-1.10 + notes | ||
| [[CDS 140a Winter 2013 Homework 2|HW 2]] <br> Due: 22 Jan (Tue) | | [[CDS 140a Winter 2013 Homework 2|HW 2]] <br> Due: 22 Jan (Tue) | ||
|- valign=top | |- valign=top | ||
| 22 Jan <br> 24 Jan <br> | | 22 Jan <br> 24 Jan <br> RMM | ||
| Nonlinear differential equations | | Nonlinear differential equations | ||
* Existence and uniqueness | * Existence and uniqueness | ||
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| [[CDS 140a Winter 2013 Homework 3|HW 3]] <br> Due: 29 Jan (Tue) | | [[CDS 140a Winter 2013 Homework 3|HW 3]] <br> Due: 29 Jan (Tue) | ||
|- valign=top | |- valign=top | ||
| 29 Jan <br> 31 Jan <br> DGM | | 29 Jan* <br> 31 Jan <br> DGM | ||
| Behavior of differential equations | | Behavior of differential equations | ||
* Stable and unstable manifolds | * Stable and unstable manifolds | ||
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| | [[CDS 140a Winter 2013 Homework 4|HW 4]] <br> Due: 5 Feb (Tue) | | | [[CDS 140a Winter 2013 Homework 4|HW 4]] <br> Due: 5 Feb (Tue) | ||
|- valign=top | |- valign=top | ||
| 5 Feb <br> 7 Feb <br> | | 5 Feb* <br> 7 Feb <br> DGM | ||
| Non-hyperbolic differential equations | | Non-hyperbolic differential equations | ||
* Lyapunov functions | * Lyapunov functions | ||
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| [[CDS 140a Winter 2013 Homework 5|HW 5]] <br> Due: 12 Feb (Tue) | | [[CDS 140a Winter 2013 Homework 5|HW 5]] <br> Due: 12 Feb (Tue) | ||
|- valign=top | |- valign=top | ||
| 12 Feb <br> 14 Feb* <br> | | 12 Feb <br> 14 Feb* <br> DGM | ||
| Hamiltonian systems | | Hamiltonian systems | ||
* Gradient and Hamiltonian systems | * Gradient and Hamiltonian systems | ||
| Line 96: | Line 97: | ||
* Applications | * Applications | ||
| Perko 2.14 + notes | | Perko 2.14 + notes | ||
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/L6-Hamiltonian.pdf Scanned lecture notes] | |||
* [http://www.cds.caltech.edu/~macmardg/courses/cds140a/MarsdenMechSystems.pdf Marsden, Mechanical systems] | |||
<!-- | <!-- | ||
* [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]] | * [[Media:cds140a-wi11-Week6NotesHamGrad.pdf|Gradient and Hamiltonian Systems]] | ||
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| [[CDS 140a Winter 2013 Homework 6|HW 6]] <br> Due: 19 Feb (Tue) | | [[CDS 140a Winter 2013 Homework 6|HW 6]] <br> Due: 19 Feb (Tue) | ||
|- valign=top | |- valign=top | ||
| 19 Feb | | 19 Feb <br> 21 Feb* <br> 26 Feb <br> RMM | ||
| 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, 3.1-3.5, 3.9 | | Perko, 3.1-3.5, 3.7, 3.9 | ||
<!-- | <!-- | ||
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors] | * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-1_orbits-15Feb11.pdf Lecture notes on orbits and attractors] | ||
| Line 125: | Line 128: | ||
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* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity] | * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_parmsens-24Feb11.pdf Lecture notes on structural stability, parameter sensitivity] | ||
--> | |||
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity] | * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-1_bfs_sensitivity.pdf BFS notes on parameter sensitivity] | ||
<!-- | |||
* [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations] | * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L8-2_bifurcations-01Mar11.pdf Lecture notes on bifurcations] | ||
--> | --> | ||
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| align=right | [J&S] | | align=right | [J&S] | ||
| D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007. | | D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers, Fourth Edition. Oxford University Press, 2007. | ||
|- valign=top | |||
| align=right | [Ver] | |||
| F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Second Edition. Springer, 2006. | |||
|} | |} | ||
Latest revision as of 06:31, 11 November 2013
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Differential Equations and Dynamical Systems | |
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Instructors
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Teaching Assistants
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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, Poincaré-Bendixon theory, Poincaré maps. Introduction to simple bifurcations, including Hopf bifurcations, invariant and center manifolds.
Announcements
- 16 Dec 2012: set up Piazza page + added additional course info
- 23 Aug 2012: web page creation
Lecture Schedule
| Date | Topic | Reading | CollapseHomework |
| 8 Jan 10 Jan RMM |
Linear Differential Equations I
|
Perko, 1.1-1.6
|
HW 1 Due: 15 Jan (Tue) |
| 15 Jan 17 Jan RMM |
Linear Differential Equations II
|
Perko, 1.7-1.10 + notes | HW 2 Due: 22 Jan (Tue) |
| 22 Jan 24 Jan RMM |
Nonlinear differential equations
|
Perko, 2.1-2.6 | HW 3 Due: 29 Jan (Tue) |
| 29 Jan* 31 Jan DGM |
Behavior of differential equations
|
Perko, 2.7-2.10 | HW 4 Due: 5 Feb (Tue) |
| 5 Feb* 7 Feb DGM |
Non-hyperbolic differential equations
|
Perko, 2.11-2.13 | HW 5 Due: 12 Feb (Tue) |
| 12 Feb 14 Feb* DGM |
Hamiltonian systems
|
Perko 2.14 + notes | HW 6 Due: 19 Feb (Tue) |
| 19 Feb 21 Feb* 26 Feb RMM |
Limit cycles
|
Perko, 3.1-3.5, 3.7, 3.9 | HW 7 Due: 5 Mar (Tue) |
| 28 Feb 5 Mar 7 Mar* RMM |
Bifurcations
|
Perko 4.1-4.4 + notes | HW 8 Due: 12 Mar (Tue) |
| 12 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 one-week 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 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 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.
