Instructors: Dr. Sharon Crook & Dr. William Bray
Dr. Crook's office hours are MT 10-11 and by appointment.
Office: 323 Neville Hall, 581-3919, Sharon.Crook@umit.maine.edu
Dr. Bray's office hours are MWF 9-10, W 2-3 and by appointment.
Office: 220 Neville Hall, 581-3932, bray@math.umaine.edu
Prerequisites: MAT 259 or the permission of the instructor
Text: Steven Strogatz, Nonlinear Dynamics and
Chaos with Applications to Physics, Biology, Chemistry, and Engineering,
Perseus Books,1994.
Description: This course is designed for students of
mathematics and the sciences. We will study the nature and behavior
of solutions of linear and nonlinear systems of differential equations.
All concepts will be explored using theoretical mathematical analysis
and reinforced through the use of applications and computer software.
Topics covered will include the following:
One-dimensional flows: existence, uniqueness, fixed
points, stability analysis, bifurcations, and oscillators
Two-dimensional flows: linear systems, the phase
plane, fixed points and linearization, limit cycles, Poincare-Bendixson
theorem, relaxation oscillators, weakly nonlinear oscillators, and
bifurcations
Chaos: Lorenz equations, fixed points, the logistic
map, fractals, and strange attractors
Applications will come from various areas of physics, biology,
chemistry and engineering including population dynamics, biophysics,
chemical reactions, circuit physics, pattern formation, biochemistry
and many more.
Grading: Tests: 50%
Projects: 30%
Final Exam: 20%
Policy: Attendance is required and no make-up work is
allowed without the prior approval of the instructor and an official
University or Doctor's excuse.
Tentative Syllabus
| WED | 1/22 | Class Introduction, 2.0,
2.1 |
Read Chapter 1 and 2.1 |
| FRI | 1/24 | 2.2, 2.3, 2.4 |
2.2:1,5,7,8,13 2.3:1,3
2.4:1,3,7,8 |
| MON | 1/27 | 2.5, 2.6, 2.8 |
2.5:3,4,6 2.6:1,2 2.8:6,7 |
| WED | 1/29 | 3.0, 3.1 |
3.1:1,3,5 |
| FRI | 1/31 | Problems and 3.2 |
3.2:1,2,3,4 & 6 (optional) |
| MON | 2/3 | 3.4, parts of 3.7 |
3.4: 1-10 (suggested) ,14 Project
1 assigned |
| WED | 2/5 | 4.0, 4.1, 4.2 |
4.1:1,2,4,6,9(2.6.2) 4.2: 1,3 |
| FRI | 2/7 | 4.3 |
4.3:3,5,7,9,10 |
| MON | 2/10 | Problems from Chapter
3 |
|
| WED |
2/12 |
Chapter 5 |
5.1:3-6 5.2:1,2,3-9 |
| FRI |
2/14 | Discussion of Matrix Solutions |
|
| MON | 2/17 | Review and 6.0, 6.1, 6.2 |
Study for Exam |
| WED |
2/19 | Exam 1 |
|
| FRI | 2/21 | 6.3, 6.4 |
6.1:1,3,5,8,9,10,11 6.2:1 6.3:1,3,5,7,13
,16 |
| MON | 2/24 | Topics from 6.5,6.6 |
6.5:1,2 either 6,15,16,17 or 19 6.6:1,3,4 |
| WED | 2/26 | 6.8 |
6.8:2,4,6,7,8 |
| FRI | 2/28 | 7.0,7.1,7.2 |
Project 2 Assigned 7.1:1,3,5,8
7.2:1,2,4,6,10,12 |
| MON | 3/3 | 7.3 |
7.3:1,2,3,6,8 |
| WED | 3/5 | 7.5 |
7.5:1,3,6,7 |
| FRI | 3/7 | 7.6 |
7.6:14,18 |
| MON | 3/10 | Spring Break |
|
| MON | 3/24 | Presentations |
|
| WED | 3/26 | Presentations |
|
| FRI | 3/28 | Exam 2 |
|
| MON | 3/31 | 8.0,8.1 |
|
| WED | 4/2 | 8.2 |
|
| FRI | 4/4 | 8.3 |
|
| MON | 4/7 | 8.4 |
|
| WED | 4/9 | 8.5 |
|
| FRI | 4/11 | 8.6 |
|
| MON | 4/14 | 8.7 |
|
| WED | 4/16 | Problem Day |
|
| FRI | 4/18 | 9.0,9.1(read),9.2 |
|
| MON | 4/21 | 9.3,9.4 |
|
| WED | 4/23 | 9.5 |
|
| FRI | 4/25 | 10.1-10.3 |
|
| MON | 4/28 | 10.3-10.4/10.5 |
|
| WED | 4/30 | Problem Day |
|
| FRI | 5/2 | Exam 3 |
|
| MON | 5/5 | Problems and Review |
|
| WED | 5/7 | Problems and Review |
|
| FRI | 5/9 | Problems and Review |
|
| MON | 5/12 |
Final Exam Week |