Instructor's Office Hours: M 5:00-6:00 PM, W 2:00-3:00 PM, and by appointment.
Section E13 meets: MWF 1:00-1:50 PM in 145 Altgeld Hall.
Textbook
Arrowsmith and Place, Dynamical Systems: Differential Equations, Maps and
Chaotic Behavior, 1st Edition, Chapman and Hall/CRC, 1996.
Lecture Coverage
Chapter 1: Introduction
Chapter 2: Linear systems
Chapter 3: Non-linear systems in the plane
Chapter 4: Flows on non-planar phase spaces (4.1.1, 4.1.2, 4.2.3, 4.3.1, 4.4.1)
Chapter 5: Applications I: planar phase spaces (5.1, 5.2, 5.3, 5.4)
Chapter 6: Applications II: non-planar phase spaces (6.1, 6.3.1, 6.3.3)
Homework
Homework will be assigned weekly. You should submit your homework in class.
However, if you miss a class, but want to hand in your homework, you must
bring it to my office by 3:00 PM on the due date. You can drop your two
lowest homework scores. The first assignment will be announced on August
30.
Assignments
HW1: due date 09/06/06, Chapter 1, problems 4 a and b, 6, 8, 13, 14.
Extra HW1 for E14: due date 09/06/06, Chapter 1, problems 15, 17, 18.
HW2: due date 09/15/06, Chapter 1, problems 19 b & d, 20 b & d, 23
Extra HW2 for E14: due date 09/15/06, Chapter 1, problems 29 b, 31.
HW3: due date 09/27/06, Chapter 1, problems 34 a, 35, Chapter 2,
problems 4, 5, 8, 9 a, c, d, f, j, 11
Extra HW3 for E14: due date 09/27/06, Chapter 1, problems 33, Chapter 2,
problems 3, 12.
HW4: due date 10/13/06, Chapter 2, problems 13 a, b, c, d & e (just state
their
type), 22 a & b, 23 a, b & d, 26 b, 29 d, 30, 33.
Extra HW4 for E14: due date 10/13/06, Chapter 2,
problems 14, 18, 28, 32 b.
HW5: due date 10/27/06, Chapter 3, problems 3, 5 a, b, c, d, 6, 10.
Extra HW5 for E14: due date 10/27/06, Chapter 3, problems 1 c, 2, 11.
HW6: due date 11/13/06, Chapter 3, problems 13 c & d, 14 c & d, 15 a,
22.
Extra HW6 for E14: due date 11/13/06, Chapter 3, problems 13 a & b,
14 a & b.
HW7: due date 11/29/06, Chapter 3, problems 24, 27, 30, 31, 37, 40 a,
42 a, c and e.
Extra HW7 for E14: due date 11/29/06, Chapter 3, problems 26, 28, 33,
42 b.
Make-Up Policy
Make-up exams will be given ONLY if you are excused for a
university related activity (e.g. university sporting event, marching band
trip, a required field trip in a course), or your absence is approved by the
Emergency Dean (in case of an illness, personal or family emergency).
If you are ill for an hour exam, contact me by e-mail BEFORE THE EXAM.
Grading Policy
Your grade will be based on homework, three hour exams and the
final exam. Your work should be readable and organized. All work must be
shown-a bare answer is not enough.
Weekly Homework 20%
Hour Exams 45%, (15% each)
Final Exam 35%
Exams
There will be 3 hour exams and a final exam.
Exam 1: Friday, September 29, 5-6 pm, room 147 AH.
Review for Exam 1: Thursday, September 28, 4-5 pm, room 147 AH.
The exam will cover Chapter 1 and sections 2.1 through 2.4 in the
textbook.
Exam 2: Friday, October 27, 1-1.50 pm, room 145 AH.
Review for Exam 2: Thursday, October 26, 4-5 pm, room 345 AH.
The exam will cover sections 5-7 from Chapter 2, sections 1-4 from
Chapter 3, and sections 1-2 from Chapter 5.
Exam 3: Friday, December 1, 1-1.50 pm, room 145 AH.
Review for Exam 3: Thursday, November 30, 4-5 pm, room 345 AH.
The exam will cover sections 5-9 from Chapter 3, and sections 4.1.1,
4.1.2 from Chapter 4.
Final Exam : 1:30-4:30, Wednesday, December 13, room 145 AH.
Review: Tuesday, December 12, 11:20am -1:10pm, room
TBA.
Coverage : Chapters 1-3, sections 4.1, 4.2.3, 4.3.1 and 4.4.4
from Chapter 4, sections 5.1.1, 5.1.4, 5.2 (exclude the circuit related
material), 5.4.1 from Chapter 5 , and sections
6.1, 6.3.1 and 6.3.3.
Topics : methods for the construction of
phase portraits in the plane, flows and evolution operators, linear
changes of variable, phase portraits for canonical systems in the
plane, classification of phase portraits, affine systems, systems of
dimension greater than two, local and global behavior of nonlinear
systems, linearization theorem and stability of fixed points, Liapunov
functions, non-simple fixed points, first integrals, limit points and
limit cycles, Poincare - Bendixson theory, non-hyperbolic fixed points,
flows on tori, mechanical oscilators, coupled oscillators, bifurcations.
HW problems : 4, 6 a and b from Chapter 4; 1, 2, 3 from Chapter 5;
7 from Chapter 6.
Scores
to check your scores click
here and then
select 'Score reports'.
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