Math 441, Ordinary Differential Equations II, Fall 2013


Instructor: Junping Shi, Jones 117, phone: 221-2030, jxshix@wm.edu
Office Hours: TR 3:30-4:30pm, W 1:30-2:30pm or by appointment.
Meeting Times and places:   Tuesday and Thursday 2:00-3:20pm, Jones Hall 113

Course Webpage:  http://jxshix.people.wm.edu/schedule-math441-fall2013.html

Course Description: Math 441 provides an in-depth discussion of qualitative analysis of ordinary differential equations. In Math 441, material to be covered linear systems of ODEs, nonlinear systems; dynamical systems, existence/uniqueness of solutions; phase plane analysis; bifurcation; Poincare-Bendixson theory. Discrete dynamical systems. Applications to physics, engineering, economics, chemistry, and biology will be discussed throughout the courses.

Prerequisites: Math 111, Math 112, Math 211, Math 212 and Math 302.

Textbook:
Strogatz, Steven (1994). Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering. Perseus Books.
We plan to cover most of Chapters 1-3, 5-8 and some parts of Chapter 4, and Chapter 9-10 if time allows. 

Computer and Calculators: Computer demonstrations will be given in classes sometimes. Computer software Matlab will be used in some homework assignments and possibly in your semester project. Maple is available on all university network computers, please visit webpage http://www.wm.edu/IT/labs/ for lab information. You can download Matlab to your personal computer by using your university account.

Email address: jxshix@wm.edu I find that email is a good way to leave messages, but it is not a good way to get help on your homework. For help with the mathematics in this course, I encourage you to visit me in my office. If you miss class, do not send me email asking for answers to questions that were covered in class.

Course Grade:

Test #1 20%
Test #2 20%
Homework 40%
      Project     20%
Total 100%
Percentage Letter grade
90-100 A
80-90 B
70-80 C
60-70 D
below 60 F
Your letter grade will be calculated according to the formula above. Scores of tests, homework and project will be available on Blackboard website once they are available. A possible extra credit up to 5% will be awarded by the instructor(extra credit point in tests, challenging homework problems, creative project, etc.)

Tests and Final Exam: We will have two take-home exams during the semester and there is no final exam. The two take-home exams will take place around early-mid October, and late November to early December. The exams must be completed by the students individually in one week. Books, notes and computer can be used in exams.

Homework: Homework will be assigned every week, and it will be available from course webpage. Homework will be collected weekly during the semester. The problems are from textbook or from the instructors, and some problems may involve writing simple Maple or other computer  programs. Students are encouraged to discuss homework problems with each other or with the instructor. No late homework will be accepted for any reason.

Project: A semester long project is to read one or several articles related to one of subjects in the course. This articles will be from recent issues of journals on applied mathematics. (like SIAM Journal on Applied Mathematics, Applied Mathematics and Computation,  Physica D: Nonlinear Phenomena, Journal of Computational and Applied Mathematics, etc.) Student can select their own article(s) as long as approved by the instructor, otherwise a list of possible articles will be chosen by the instructor. The list of articles will be available in early October. The project is to read and understand the articles, perform detail calculation omitted in articles, sometime write computer programs which generate graphs in the articles, and put these together into a new article which should be understandable to another math major student. The project is to be done individually, but students are encouraged to discuss with each other or with the instructor. Student can also choose one problem of his/her own interest, and use techniques/knowledge learned in this course to solve the problem.