Math 4541 Dynamics and
Bifurcation I. Fall 2011
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Schedule: 1:35 pm - 2:55
pm TR
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Classroom: Skiles 254
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Office: Skiles 102A
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Phone: 404-894-4750
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Email:
zengch@math.gatech.edu
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Webpage: www.math.gatech.edu/~zengch
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Office hours: 9:35--10:55 T & 3:05--4:25 R
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Final schedule (tentative): Dec. 15th (Thu.) 2:50--5:40
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Syllabus
Instructor: Chongchun
Zeng
Prerequisites: MATH 2403 or permission of the instructor
Participation: Attendence
in
classes is mandatory. Students are expected to read the materials
before and/or
after the classes. It is suggested that you start to work on
homework
problems right after they are assigned.
Text book: Differential
Equations, Dynamical Systems & An Introduction to Chaos / 2nd ed.
by Morris Hirsch, Stephen Smale & Robert Devaney
Topics: In
this semester, we will study:
- First order equations
- Linear systems
- Nonlinear systems:
- Existence and uniqueness of solutions
- equilibria and bifurcations
- global nonlinear techniques
- closed orbits and limit sets
- Applications
Grades: 1
final exam 55%, 1 midterm 33%, 6 homework assignments 12%.
- Exams: The final will be 2 hours and 50 minutes. The 80-minute midterm will
be given during a lecture in late Spet. which will be announced at
least 9 days in advance. The exams are "closed book" and "closed
notes". You will be allowed to bring with you a one page (8.5 X 11,
both sides) "cheat sheet" with anything you want written on it. Please
write your exam solutions in ink and circle
the final answer of each problem in a box with no corrections inside.
Writing exams in pencil would automatically forfeit your right to argue
for credits after the exam is given back to you. There will be no
make-up for a missed exam, except under provable impossibility to
attend the exam.
- Homework: Homework will be assigned at the end of each lecture and
then put on this webpage in the below. You may discuss the homework
problems with other students in this class, but you
should write down the solutions and complete the homework independently.
The homework will be collected roughly every 2 weeks. On each
collecting day, the homework is due in the classroom at the beginning
of the lecture. The corresponding assignment includes all the problems
assigned before that collecting day and after the previous assignments.
Some selected problems from each assignment will be graded and the
score will be given based on both the graded problems and the
completion of the whole assignment. Due to the holiday schedules, the
specific homework collecting dates are:
9/6 (Tue.), 9/20(Tue.), 10/4(Tue.), 10/20(Thu.), 11/3(Thu.), 11/17(Thu.)
- Letter grade: in general, the letter grade
will be given based on the total score (homework + midterm + final) in
a curved fashion with the following exceptions:
- Total score 90/100 or above will always be an A
- Total score 60/100 or above will always be a C
or higher.
Homework assignments:
- Homework Assignment #1 (due Tue. 9/6):
- Assigned on Thu. 8/23: Chp 1. 1, 2(b)(d), 3(c), 4, 7, 10, 13, 14
- Assigned on Tue. 8/30: Chp 2. 1(b), 2(c), 5, 6, 7, 9, 14
- Partial solutions of HW#1 -- Part A
- Partial solutions of HW#1 -- Part B
- Partial solutions of HW#1 -- Part C
- Homework Assignment #2 (due Tue. 9/20):
- Assigned on Tue. 9/6: Chp 3. 1, 2(iii) (iv), 4, 6, 9, 12, 16
- Assigned on Tue. 9/13: Chp 4. 1, 2, 5, 8
- Announcement: The first midterm: Thu. 9/22, covering Chapter 1 --4.
- Homework Assignment #3 (due Tue. 10/4):
- Assigned on Tue. 9/27: Chp 5. 2d, 4, 5de, 6, 7, 8b
- Homework Assignment #4 (due Thu. 10/20):
- Assigned on Tue. 10/4: Chp 5. 10,.13, 15
- Assigned on Tue. 10/11: Chp 6. 1ac, 2, 3, 5, 7, 8, 11
- Homework Assignment #5 (due Thu. 11/3):
- Assigned on Thu. 10/20: Chp. 6 12(efi), 15
- Assigned on Thu. 10/27: Chp. 7 1ce, 2, 4, 5, 7
- Homework Assignment #6 (due Thu. 11/17):
- Assigned on Thu. 11/10: Chp. 8 1(i, ii, iv), 2, 3, 5, 9, 10
- Homework not to be collected:
- Chp. 9 1bd, 3, 4, 5
- Chpt. 9 6, 7bc, 8abd, 9