University of Illinois at 
Urbana-Champaign

Math 489. Differential Equations II
Section E13
Fall 2006

Instructor
Zoi Rapti
366 Altgeld Hall
Phone: (217) 333-6625
Email: zrapti@math.uiuc.edu

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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