# Math 645 ODEs and Dynamical Systems

Instructor: Matthew Dobson
Class meeting: MWF 11:15am-12:05pm LGRT 141
Course Text: Differential Dynamical Systems by James Meiss (either edition is fine)
Office hours: T 1p-2p, W 2:30p-3:30p F 9a-10a or e-mail me to make an appointment.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194

### Course Structure and Grading Policies:

• The course will cover chapters 1-6 with additional topics from chapters 8 and 9 as time permits and according to student interest.
• There will be six or seven homework assignments during the semester. You are encouraged to work together.
• There will be an in-class midterm on Nov 1 and a final exam on Dec 20.
• The ideas will be illustrated using numerical schemes and students are expected to participate and present results in class
• The course grade will be a combination of course participation (10%), homework assignments (45%), midterm (20%) and final (25%).
• Please speak to me at least one week in advance if you need special exam accommodation or if you need a make-up exam.
• Late policy: Homework is due at the beginning of class on the due date. Late homework is not accepted except: each student may submit one homework assignment up to one week late. This is meant to cover any unforeseen absence from class. If you will miss class for a religious observance or for a university activity on the day of an exam or homework due date, you must contact me one week before the missed class to arrange for making up the work.
• Last day to drop with no record is Monday, Sept 18th. Last day to withdraw with a W is Thursday, October 19th.

Article about instability for non-Autonomous linear systems with negative spectra from SIAM Review
See the system in action.

Some additional material on bifurcation by E. Doedel, with numerical methods for finding the bifurcations Lecture Notes and Slides

### Homework

Homework 1. Due 9/29.
Ch1: 2, 7, 8. Ch 2: 1.
Also, find equilibria and stability for
x' = (1 - 2x + y) cosh(x + sin(y))
y' = (1 + x - 2y) sinh(x + y)

Homework 2. Due 10/13. Numbers for revised edition. Older edition in parentheses
Ch 2: 14, 16, 19 (14, 16, 19)
Ch 3: 7, 10 ( 5, 8 ).

Homework 3. Due 11/6. Numbers are for revised 2017 edition. Older 2007 edition numbers in parentheses
Note one problem has been moved to HW 4
Ch 4: 1b, 4 a,b,c, 8 (1b, 4 a,b,c, 8).

Homework 4. Due 11/15. Numbers are for revised 2017 edition. Older 2007 edition numbers in parentheses
Ch 4: 12,17,18 (12,16,17)

Homework 5. Due 12/1. Numbers are the same for both editions.
Ch 5: 1
Ch 6: 12

Homework 6. Due 12/11. Numbers are the same for both editions
Ch 8: 1 a,c,e. 3, 15 a, b.

### Exams

Midterm 1 will be in class on 11/1/2017.

The final exam will be 12/20/2017 10:30-12:30 in LGRT 141.