MAT6932-003 Theory of Ordinary Differential Equations

Instructor:

Dr. Wen-Xiu Ma, Office: PHY310, Phone: 974-9563.

Office Hours and Location:

TR4:00-5:30pm (tentative) or by appointment, PHY310.

Course Objectives:

Upon completing the course, the student should be able to understand the fundamental concepts, techniques and theories in the theory of ordinary differential equations, and employ the Lie techniques to perform analysis and computation of solutions to ordinary differential equations.

Prerequisites:

MAS3105 Linear Algebra, MAP2302 Differential Equations, MAA5307 Real Analysis, MAP5317 Ordinary Differential Equations or equivalent.

Course Text:

- A. G. Kartsatos, Advanced Ordinary Differential Equations, Mancorp Publishing, 1993.

- P. E. Hydon, Symmetry Methods for Differential Equations, Cambridge University Press, 2000.

- Main Topics include existence and uniqueness theorems, linear systems, perturbed linear systems, Floquet theory, stability, Lyapunov functions, Lie symmetries, discrete symmetries, Noether's theorem, the Euler-Lagrange equation, Lie groups of transformations, invariant solutions, etc.

- Notes or tapes of class lectures are not permitted for purposes of sale.

Homework Assignments:

- There will be seven homework assignments for the course. All designed exercises will help you to develop your skills and your ability to apply the techniques you have learned to concrete situations.

- You are required to do all homework exercises. Doing exercises is the best way to deepen your understanding of the topics and to convince yourself that you understand them.

- Homework assigned in Week 4 and Week 8 will be collected on Thursday, September 25 and Thursday, October 23 (tentative), respectively.

Examinations:

- There will be three examinations.

• Exam 1. Week 6 - Thursday, October 2 (tentative).
• Exam 2. Week 11 - Thursday, November 6 (tentative).
• Final exam. 1:00pm-3:00pm, Thursday, December 11 (tentative) in PHY108.

The contents covered by the exams will be announced in class. The final exam will be comprehensive.

- Attendance for examinations is mandatory. No make-up exams will be given except in the most extenuating of circumstances. If you are sick, a note signed by the physician indicating that you were physically unable to attend class is necessary in order to postpone the exam. A receipt from the infirmary is not a valid excuse. Any sort of excuse must be documented in some manner (prayer cards, tow truck receipts, subpoenas, etc.). You must contact the instructor prior to the exam if circumstances warrant that you cannot attend. If you do not, you will be given a zero on the exam.

- The instructor reserves the right to give a different exam to students requiring a make-up.

Grading Policy:

- Regular and punctual attendance in classes is important and required. It will contribute towards 5% of your final score.

NB: Students who anticipate the necessity of being absent from class due to the observation of a major religious observance must provide notice of the date(s) to the instructor, in writing, by the second class meeting.

- Each of the first two exams accounts for 25%. The final exam accounts for 35%. Homework accounts for 10% plus 5% as bonus points. Your final score will be computed by these weights, the maximum being 105.

- A plus/minus grading system will be used for the course. Course letter grades will be decided based on final scores as follows: 90 for A-, 75 for B-, 65 for C-, 50 for D-, 0-49 for F, etc., and other letter grades will be assigned accordingly.

Blackboard Website:

The Blackboard course web site can be entered via the university web single sign-on portal at myUSF Online, from which all supplementary materials will be available for download. There is also a discussion board at the Blackboard course web site, administrated by the instructor.

Links to Related Sites:

"If you look around, you can see a lot." "Farther along, we'll know all about it. Farther along, we'll understand why?"
• Orientation Sessions offered by the USF Tampa Campus Library
• Internet Resources on Ordinary Differential Equations at Math Forum: Ordinary Differential Equations
• MacTutor History of Mathematics Archive at University of St Andrews, Scotland
• Check out the netLibrary eBook: What Is Mathematics, Really?
• The Origin of Zero at What is the origin of zero?
• The Number Pi at The Pi Page
• The USF Math Club Home Page
• MAA Florida Section Site at St. Petersburg College

If you have questions or suggestions, please leave your messages at mawx@math.usf.edu