ACM 101/AM 125b/CDS 140a, Winter 2011
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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
- 14 Nov 2010: web page creation
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. |
Lecture Schedule
| Week | Date | Topic | Reading | Homework | |||||
| 1 | 4 Jan 6 Jan |
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| 2 | 11 Jan 13 Jan |
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3 | 18 Jan? 20 Jan |
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| 4 | 25 Jan 27 Jan |
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| 5 | 1 Feb* 3 Feb |
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| 6 | 8 Feb 10 Feb |
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| 7 | 15 Feb 17 Feb |
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| 8 | 22 Feb 24 Feb |
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| 9 | 1 Mar 3 Mar |
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10 | 8 Mar |
Grading
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.
- 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.
