MA573 - Qualitative Differential Equations - Fall 2014Lecture: MWF 10:00-11:00am in PSY
B39Contact Information:Instructor: Margaret Beck Office: MCS 233 Phone: 617-358-3314 Email: mabeck -at- math.bu.edu Office Hours: M 1:00-2:30pm and W 4:00-5:30pm |

Announcements will be made in class and posted here as needed.

- A .pdf file of the syllabus can be found here.

- Textbook: "Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering," by Steven H. Strogatz. The BU library entry for this book is here.
- Grading policy: grades will be based on homework (40%), one midterm (30%), and the final exam (30%).
- Extra help: if you need some, please ask me! Also see the syllabus for other ways to get help.

- HW1 (assigned Fri Sept 5, due Fri Sept 12 at 10am): 2.2.3, 2.2.4, 2.2.8, 2.2.9, 2.2.10, 2.4.4, 2.4.5, 2.6.2
- HW2 (assigned Fri Sept 12, due Mon Sept 22 at 10am): 3.1.5, 3.4.6-3.4.9, 3.4.16, 3.6.2, 3.6.3, 3.7.2, 3.7.4
- HW3 (assigned Wed Sept 24, due Fri Oct 3 at 10am): 4.3.3, 4.5.1, 5.1.9, 5.1.10de, 5.2.2, 5.2.3, 5.2.5, 5.3.4
- HW4 (assigned Fri Oct 3, due Fri Oct 17 at 10am): 6.1.4, 6.1.8, 6.1.9,
6.1.12, 6.1.13, 6.2.2, 6.3.6, 6.3.10, 6.5.2, 6.5.11, 6.6.3

Note: two of the exercises ask you to plot a phase plane using a computer. Feel free to use any software you like. A very basic way to do this is to follow the instructions here. - HW5 (assigned Mon Oct 20, due Wed Oct 29): 7.1.3, 7.1.8, 7.2.4, 7.2.9, 7.2.12, 7.3.3
- HW6 (assigned Wed Oct 29, due Fri Nov 7): 7.5.5, 7.6.3, 7.6.5, 7.6.13 (up to order epsilon only), 7.6.18
- HW7 (assigned Mon Nov 10, due Mon Nov 24) is here.
- HW8 (assigned Mon Dec 1, due Wed Dec 10): 9.2.2, 9.2.4, 9.3.1, 9.3.8, 9.4.2, 10.1.12, 10.5.1

Unless otherwise noted, these are optional. I've just put them here in case you're interested.

- Spruce budworm paper, relevant for Cpt 2 on bifurcations in 1D: [.pdf]
- Synchronization in fireflies, relevant for Cpt 3 on dynamics on the circle: [.pdf]
- Lorenz's original paper: [.pdf]

**Midterm**: This will be during class-time on Friday, October 17. The midterm will cover chapters 1-6 of Strogatz, except for 6.8 on index theory. The questions on the midterm will be similar to in-class examples and to problems from the HW assignements.**Final**: This will be Wednesday, December 17, from 9-11am in our usual classroom. It will be cummulative, covering all the material we've covered this semester. The questions will be similar to in-class examples, problems from the HW assignments, and problems from the midterm.

- Homework assignments are a key aspect of this course. Although you may
work together on these, it is important that you understand the solutions
yourself and write up your solutions on your own. Homework grades will be
assigned as follows:
- Typically problems will each be graded on a six-point scale (adapted from Chad Topaz, Macalester College). Four points will be assigned for mathematical content, and two for communication. Mathematical correctness is important for obvious reasons. Communication is also extrememly important. If you make an important scientific discovery but cannot explain it to anyone, then your discovery is essentially worthless.
- Mathematical Content points: (4) Solution is 100% correct; (3) Solution demonstrates a good understand of the problem, although some details are incorrect or missing; (2) Solution contains some good ideas, but is largely incorrect; (1) A nontrivial effort was made; (0) No progress towards the solution has been demonstrated.
- Communication points: In order to obtain any of these points, you must receive at least two mathematical content points. (2) The solution is clearly written and justified in sufficient detail; (1) The solution is readable, but some details are missing and/or difficult to follow; (0) The solution is essentially unreadable and/or lacking in many details.
- Plagiarism: This is obviously unacceptable. Since you may work together on the HW problems, it is essential that your write-ups are your own, and that you understand everything that you have written in your solution. If I believe that you are simply copying another's work, I may ask you to come to my office and explain to me the details of your solution (without looking at any books/notes). If you are unable to explain what you have written, I will assume you did not do the work yourself and give you zero points for that assignment. If the problem persists, further action may be warranted.

- Exams: exam questions will be graded with the same philosophy as the HW problems, although the details of the grading structure may differ.