ACM 101b/AM 125b/CDS 140a, Winter 2014: Difference between revisions
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'''Teaching Assistants''' | '''Teaching Assistants''' | ||
* | * Katie Broersma (CDS) | ||
* | * Vanessa Jonsson (CDS) | ||
* | * Office hours: Tue, 3:30-4:30, 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 2.1-2.5 | * J&S, Ch 1; Sec 2.1-2.5 | ||
* Ver, Sec 5.1-5.2; 6.1-6.2 | * Ver, Sec 5.1-5.2; 6.1-6.2 | ||
| [[CDS 140a Winter 2014 Homework 1|HW 1]] <br> Due: | | [[CDS 140a Winter 2014 Homework 1|HW 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, 1.7-1.10 + notes | | Perko, 1.7-1.10 + notes | ||
| [[CDS 140a Winter 2014 Homework 2|HW 2]] <br> Due: | | [[CDS 140a Winter 2014 Homework 2|HW 2]] <br> Due: 22 Jan (Wed) | ||
|- valign=top | |- valign=top | ||
| 21 Jan <br> 23 Jan | | 21 Jan <br> 23 Jan | ||
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* Linearization | * Linearization | ||
| Perko, 2.1-2.6 | | Perko, 2.1-2.6 | ||
| [[CDS 140a Winter 2014 Homework 3|HW 3]] <br> Due: | | [[CDS 140a Winter 2014 Homework 3|HW 3]] <br> Due: 29 Jan (Wed) | ||
|- valign=top | |- valign=top | ||
| 28 Jan <br> 30 Jan | | 28 Jan <br> 30 Jan | ||
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* [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]] | * [[Media:cds140a-wi11-InvManRemark.pdf|Remark on invariant manifolds]] | ||
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| | [[CDS 140a Winter 2014 Homework 4|HW 4]] <br> Due: | | | [[CDS 140a Winter 2014 Homework 4|HW 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:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]] | * [[Media:cds140a-wi11-CMTLimitCycleExample.pdf|An Example (Center Manifold / Limit Cycle)]] | ||
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| [[CDS 140a Winter 2014 Homework 5|HW 5]] <br> Due: | | [[CDS 140a Winter 2014 Homework 5|HW 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:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]] | * [[Media:cds140a-wi11-Week6NotesLagHamSum.pdf|Lagrangian, Summary]] | ||
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| [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: | | [[CDS 140a Winter 2014 Homework 6|HW 6]] <br> Due: 19 Feb (Wed) | ||
|- valign=top | |- valign=top | ||
| 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/L7-3_bfs_oscillators.pdf BFS notes on oscillators] | * [http://www.cds.caltech.edu/~murray/courses/cds140/wi11/caltech/L7-3_bfs_oscillators.pdf BFS notes on oscillators] | ||
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| [[CDS 140a Winter 2014 Homework 7|HW 7]] <br> Due: | | [[CDS 140a Winter 2014 Homework 7|HW 7]] <br> Due: 5 Mar (Wed) | ||
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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] | ||
--> | --> | ||
| [[CDS 140a Winter 2014 Homework 8|HW 8]] <br> Due: | | [[CDS 140a Winter 2014 Homework 8|HW 8]] <br> Due: 12 Mar (wed) | ||
|- valign=top | |- valign=top | ||
| 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, Poincaré-Bendixon 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, 1.1-1.6
|
HW 1 Due: 15 Jan (Wed) |
14 Jan 16 Jan |
Linear Differential Equations II
|
Perko, 1.7-1.10 + notes | HW 2 Due: 22 Jan (Wed) |
21 Jan 23 Jan |
Nonlinear differential equations
|
Perko, 2.1-2.6 | HW 3 Due: 29 Jan (Wed) |
28 Jan 30 Jan |
Behavior of differential equations
|
Perko, 2.7-2.10 | HW 4 Due: 5 Feb (Wed) |
4 Feb 6 Feb |
Non-hyperbolic differential equations
|
Perko, 2.11-2.13 | 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, 3.1-3.5, 3.7, 3.9 | HW 7 Due: 5 Mar (Wed) |
27 Feb 4 Mar 6 Mar |
Bifurcations
|
Perko 4.1-4.4 + 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 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.