Math 4541 AU&AG Dynamics and
Bifurcation I. Fall 2017
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Schedule: 9:30 - 10:45 am TR
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Classroom: Skiles 270
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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: 1:30 - 3 pm M & 4:05 - 4:40 pm T
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Final exam schedule (tentative): Dec. 14th (Thu.) 8 -- 10:50 am
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Syllabus
Instructor: Chongchun
Zeng
Prerequisites: MATH 2552 (formerly 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, 3rd ed.
by Morris Hirsch, Stephen Smale & Robert Devaney
Topics: In
this semester, we will discuss topics among:
- 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 50%, 1 midterm 26%, 6 homework assignments 4% each.
- Exams: The final will be 2 hours and 50 minutes. The 75-minute midterm will
be given (tentatively, subject to change) during the lecture on Thu. 10/5. 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 (see below). 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. The exact homework collecting dates are:
9/5 (Tue.), 9/19(Tue.), 10/3(Tue.), 10/17(Tue.), 10/31(Tue.), 11/14(Tue.)
- 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. 9/5):
- Assigned on Tue. 8/22: Chp. 1., 1, 2(bd), 3(c), 4
- Assigned on Thu. 8/24: Chp. 1., 7, 10, 13, 14
- Assigned on Thu. 8/31: Chp. 2., 1(bd)
- Sketch of some solutions
- Homework Assignment #2 (due Tue. 9/19):
- Assigned on Tue. 9/5: Chp 2., 2(c), 5, 6, 7, 9, 14
- Assigned on Thu. 9/7: Chp 3., 1, 2(iii, vi)
- Assigned on Tue. 9/14: none.
- Sketch of some solutions
- Homework Assignment #3 (due Tue. 10/3)
- Assigned on Tue. 9/19: Chp3., 4, 6, 9, 12, 16, 2(iii, vi)(bc)
- Assigned on Thu. 9/21: Chp 4., 1, 2, 5, 8
- Assigned on Tue. 9/26: none.
- Assigned on Thu. 9/28: none.
- Sketch of some solutions
- Homework Assignment #4 (due Tue. 10/17):
- Homework Assignment #5 (due date extended toThu. 11/2):
- Assigned on Tue. 10/17: Chp 5., 8(b), 10, 13, 15
- Assigned on Tue. 10/19: none.
- Assigned on Tue. 10/24: none.
- Assigned on Thu. 10/26: none.
- Sketch of some solutions
- Homework Assignment #6 (due Tue. 11/14):
- Assigned on Tue. 10/31: Chp 6., 1(ac), 2, 3
- Assigned on Thu. 11/2: Chp 6., 5, 7, 8
- Assigned on Tue. 11/7: Chp 6., 11
- Assigned on Thu. 11/9: Chp. 6, 15
- Sketch of some solutions
- Homework recommended but not colelcted:
- assigned on Thu. 11/16: Chp 6, 12(efi)
- Assigned on Tue. 11/21: Chp 7., 1(ce), 2, 4, 5, 7
- Assigned on Tue. 11/28: Chp 8. 1(i, ii, iv), 2, 3, 5, 9, 10