Math 4541   Dynamics and Bifurcation I.   Fall 2014

Schedule: 12:05 pm - 1:25 pm  TR	Classroom: Skiles 246
Office: Skiles  102A	Phone: 404-894-4750
Email: zengch@math.gatech.edu	Webpage: www.math.gatech.edu/~zengch
Office hours: TR 9:35--10:55	Final schedule (tentative): Dec. 11th (Thu.) 11:30 am -- 2:20 pm

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.

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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 
• Planar systems
• Phase portraits
• Higher dimensions 
• Nonlinear systems:
• Existence and uniqueness of solutions
• equilibria and bifurcations
• global nonlinear techniques
• closed orbits and limit sets
• Applications

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Grades: 1 final exam 55%, 1 midterm 30%, 6 homework assignments 2.5% each.

• Exams: The final will be 2 hours and 50 minutes. The 80-minute midterm will be given (tentatively, subject to change) during the lecture on Thu. 9/25. 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. Due to the holiday schedules, the specific homework collecting dates are:

              9/2 (Tue.), 9/16(Tue.), 9/30(Tue.), 10/21(Tue.), 11/4(Tue.), 11/18(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:

1. Total score 90/100 or above will always be an A
2. Total score 60/100 or above will always be a C or higher.

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Homework assignments:

• Homework Assignment #1 (due Tue. 9/2):
• Assigned on Tue. 8/19:   Chp 1.  1, 2(b)(d), 3(c), 4
• Assigned on Tue. 8/26:   Chp 1.   7, 10, 13, 14
• Homework Assignment #2 (due Tue. 9/16):
• Assigned on Tue. 9/2: Chp 2.   1(b), 7, 14
• Assigned on Thu. 9/4: Chp. 2.   2(c), 5, 6, 9
• Assigned on Tue. 9/11: Chp. 3   1, 4, 6, 9, 12, 16
• Homework Assignment #3 (due Tue. 9/30):
• Assigned on Thu. 9/18: Chp. 4   1, 2, 5, 8
• Homework Assignment #4 (due Tue. 10/21):
• Assigned on Tue. 9/30: Chp. 5   2d, 4, 5de, 6, 7
• Assigned on Tue. 10/7: Chp. 5   8b, 10, 13, 15
• Homework Assignment #5 (due Tue. 11/4):
• Assigned on Tue. 10/21: Chp. 6   2, 3
• Assigned on Thu. 10/23: Chp. 6   1ac, 5, 7, 8, 11
• Assigned on Tue. 10/28: Chp. 6   12efi, 15
• Homework Assignment #6 (due Tue. 11/18):
• Assigned on Tue. 11/4: Chp. 7   1ce, 2, 4, 5, 7
• Assigned on Tue. 11/11: Chp. 8   1(i, ii, iv), 2
• Hoemwork not to be collected
• Assigned on Tue. 11/18: Chp. 8   3, 5, 9, 10
  

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