Math 4542 AU&AG Dynamics and
Bifurcation II. Spring 2018

Schedule: 9:30 - 10:45 am TR |
Classroom: Skiles 269 |

Office: Skiles 102A |
Phone: 404-894-4750 |

Email: zengch@math.gatech.edu |
Webpage: |

Office hours: 10:05 - 11am W & 12:30 - 1:25pm R |
Final exam schedule (tentative): May 3rd (Thu.) 11:30 -- 2:20 |

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:

- A brief review of a.) the linear theory and b.) basic properties of nonlinear systems.

- Nonlinear systems:
- equilibria and bifurcations
- global nonlinear techniques
- closed orbits and limit sets
- Applications
- Math biology
- Mechanics,
- Circuits.
- Discrete dynamics systems.

*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 Tue. 2/27. 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 inand__ink__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__circle__make-up for a missed exam, except under provable impossibility to attend the exam.__no__

*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 studentsbut you should write down the solutions and complete the homework__in this class__,__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:

1/23 (Tue.), 2/6(Tue.), 2/20(Tue.), 3/6(Tue.), 3/27(Tue.), 4/10(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__

__Homework assignments:__

- Homework Assignment #1 (due Tue. 1/23):
- Assigned on Tue. 1/9: P72, 5(a); P136, 6; P137, 12; P138, 15; P157, 7

- Assigned on Thu. 1/11: Chp. 8, 1(ii, iii), 2
- Sketch of solutions to some homework problems

- Homework Assignment #2 (due Tue. 2/6):
- Assigned on Tue. 1/23: Chp 8. 1(iv)
- Assigned on Thu. 1/25: Chp 8. 3
- Assigned on Tue. 1/30: Chp 8. 5, 9, 10
- Sketch of solutions to some homework problems

- Homework Assignment #3 (due Tue. 2/20):
- Assigned on Tue. 2/6: Chp 9. 1(bd), 3, 4
- Assigned on Tue. 2/13: Chp. 9, 5, 6
- Assigned on Thu. 2/15: Chp 9., 7bc
- Sketch of solutions to some homework problems
- Homework Assignment #4 (due Tue. 3/6):
- Assigned on Tue. 2/20: Chp. 9, 8abd, 9

- Assigned on Thu. 2/22: Chp. 10, 1(ac)
- Assigned on Thu. 3/1: Chp. 10, 4
- Sketch of solutions to some homework problems
- Homework Assignment #5 (due Tue. 3/27):
- Assigned on Tue, 3/6: Chp. 10, 2, 5, 6
- Assigned on Tue. 3/13: Chp. 10, 7, 9
- Sketch of solutions to some homework problems
- Homework Assignment #6: (due Tue. 4/10):
- Assigned on Tue. 3/27: Chp. 11, 1, 2
- Assigned on Thu. 3/29: Chp. 11, 4
- Assigned on Thu. 4/5: Chp. 11, 6
- Sketch of solutions to some homework problems
- Recommended problems (not required):
- Assigned on Tue. 4/10: Chp. 13, 1
- Assigned on Tue. 4/17: Chp. 13, 2, 3, 5, 7