Math 442, Partial Differential Equations, Spring 2015

Instructor: Junping Shi, Jones 117, phone: 221-2030, jxshix@wm.edu

Meeting time and location: Tuesday and Thursday 2:00-3:20pm, Jones Hall 306

Web pages: http://jxshix.people.wm.edu/schedule-math442-spring2015.html (schedule, homework assignments, software, extra reading)

Office Hours: R 3:30-5pm, F 10:30-11:50 or by appointment. 

Textbook: Partial Differential Equations: An Introduction, 2nd Edition Walter A. Strauss 2008. (errata of the book)

Course Description: An introduction to partial differential equations. Waves, diffusion, and boundary value problems; Fourier analysis; harmonic functions; Green’s function and Green’s identity. Introduction to numerical methods for approximating solutions. We will cover selected sections from Chap 1-8, 10 and 12 in the textbook.

Prerequisites: Math 111, Math 112, Math 211, Math 212/213, Math 302.You should be familiar with material in Appendix 1-3 in textbook.

Computer and Calculators: Computer demonstrations will be given in classes sometimes. Computer software Maple/Matlab/Mathematica (Wolfram Alpha) will be used in some homework assignments and possibly in your semester project. 

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 March, and late April. 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 for every lecture, and it will be available from http://jxshix.people.wm.edu/schedule-math442-spring2015.html. Homework will be collected weekly and usually they are due on Friday 5pm. You can request extension for 2 homework without any penalty. The problems are from textbook or from the instructors, and some problems may involve writing simple Maple/Matlab 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 or study a topic from textbook which is not covered in the lectures. Student can select their own article(s) or topic as long as approved by the instructor, otherwise a list of possible articles/topics will be chosen by the instructor (available in February). The project is to read and understand the articles/topics, 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. The project report is eligible to become a Math 300 paper.