Instructor: Junping Shi, Jones 100B,
phone: 221-2030, jxshix@wm.edu
Office Hours: TR 10:00-11:00am, W 14:00-15:00pm or by appointment.
Meeting Times and places: Tuesday and Thursday
Course Webpage: http://jxshix.people.wm.edu/schedule-math441-fall2021.html
Course
Description:
Math 441 provides an in-depth discussion of qualitative analysis of ordinary
differential equations (ODEs). In Math 441, material to be covered linear
systems of ODEs, nonlinear systems; dynamical systems, existence/uniqueness of
solutions; phase plane analysis; bifurcation; limit cycles; Poincare-Bendixson
theory; Discrete dynamical systems; Chaos theory. Applications to physics,
engineering, economics, chemistry, and biology will be discussed throughout the
courses.
Prerequisites: Math 111/131, Math 112/132, Math 211, Math 212/213 and Math 302.
Textbook: Strogatz,
Steven (2015). Nonlinear dynamics and chaos: with applications to physics,
biology, chemistry, and engineering. (2nd edition) Westview
Press. We plan to cover most of Chapters 1-3, 5-8 and some parts of
Chapter 4, and Chapter 9-10 if time allows.
Add/Drop
deadline:
September 10 (Friday), Withdraw deadline: November 1(Monday)
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:
|
|
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.
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. You do not need to know how to code in Matlab prior to this class.
Matlab is available on all university network computers. You can download
Matlab to your personal computer by using your university account. https://www.wm.edu/offices/it/services/software/licensedsoftware/mathstats/matlabstud/index.php
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 Matlab 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. These 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.
Mental
and Physical Well Being: William & Mary recognizes that students have many
different responsibilities and can face challenges that make learning
difficult. There are many resources available at W&M to help
students. Asking for help is a sign of courage and strength. Please
reach out to me if you or someone you know are facing problems inside or
outside the classroom, and I will do my best to guide you to
appropriate resources on campus. Those resources
include:
--For psychological/emotional stress, there is the W&M
Counseling Center (757-221-362), 240 Gooch Dr. 2nd floor, https://www.wm.edu/offices/wellness/counselingcenter/).
Services are free and confidential.
--For physical/medical concerns, there is the W&M Health
Center (757-221-4386), 240 Gooch Drive, https://www.wm.edu/offices/wellness/healthcenter/
--For other additional support or resources, please contact
the Dean of Students by submitting a care report (757-221-2510) or by email at deanofstudents@wm.edu https://www.wm.edu/offices/deanofstudents/services/caresupportservices/index.php