Math 441, Nonlinear Dynamics, Fall 2022


Instructor: Junping Shi, Jones 117, phone: 221-2030,
Office Hours: WR 15:30-17:00pm, or by appointment.
Meeting Times and places:   Tuesday and Thursday 14:00-15:20pm, Boswell Hall 302

Course Webpage:

Course Description: Math 441 provides an in-depth discussion of qualitative analysis of ordinary differential equations (ODE. 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 12 (Monday), Withdraw deadline: October 31 (Monday)

Course Grade: Your final grade is calculated as follows: Homework 50%; Exams 40% (20% each); Project: 10%. The letter grade is assigned using the scale: A > 93 > A- > 90 > B+ > 87 > B > 83 > B- > 80> C+ > 77 > C > 73 > C- > 70 > D+ > 67 > D > 63 > D- > 60 > F

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.

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.

Attendance: Students are expected to attend lectures in the classroom if you are not sick.But if a student is tested positive for COVID-19 or has other temporary illness, the student needs to isolate and not attend in-person classes for at least five days. As soon as a student knows they will not be able to attend class in person (either because of having tested positive, having symptoms consistent with COVID, or other health matters), please email the instructor. In that case, the instructor will activate our mode of accommodating absences for your situation. Lecture notes of all classes will be shared with students, and if there is a group of students cannot attend classes, the instructor may use Zoom to broadcast classes from the classroom on a temporary basis.

Please note that testing positive for COVID or any other temporary illness is not considered a disability as defined by ADA guidelines and is not under the purview of W&Mís Student Accessibility Services (SAS). Thus, any questions should be addressed via email to the instructor.  

Honor Code: William & Mary has had an honor code since at least 1779. Academic integrity is at the heart of the university, and we all are responsible for upholding the ideals of honor and integrity.  The student-led honor system is responsible for resolving any suspected violations of the Honor Code, and I will report all suspected instances of academic dishonesty to the honor system. The Student Handbook ( includes your responsibilities as a student and the full Code. Your full participation and observance of the Honor Code is expected. To read the Honor Code, see

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Mental and Physical Well-Being: William & Mary recognizes that students juggle different responsibilities and can face challenges that make learning difficult.  There are many resources available at W&M to help students navigate emotional/psychological, physical/medical, material/accessibility concerns. Asking for help is a sign of courage and strength.  If you or someone you know is experiencing any of these challenges, we encourage you to reach out to the following offices:  

         For psychological/emotional stress, please consider reaching out to the W&M Counseling Center; or (757) 221-3620,  240 Gooch Dr., 2nd floor.  Services are free and confidential.  

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         For additional support or resources, please contact the Dean of Students by submitting a Care Report at; or by calling 757-221-2510, or by emailing  

         For a list of many other resources available to students, see Health and Wellness Resources for Students