Math 441, Applied Mathematics I, Fall 2009
Syllabus

Instructor: Professor Junping Shi
Office: Jones Hall 122
Office Hour: TWR2-3pm or by appointment
Phone: 221-2030
email: shij@math.wm.edu
Course Description

Math 441 and Math 442 is a two-semester sequence of introduction to basic methods in applied mathematics. Mathematical modeling, Analytical and Approximate methods of physical problems will be systematically discussed. In Math 441, material to be covered include dimensional analysis and scaling, perturbation methods, variational methods and bifurcation problems, and the course focuses on the analysis of mathematical models of ordinary differential equations. In Math 442, we concentrate on partial differential equations: we will introduce basic types of PDEs, eigenfunction expansions, integral transforms, waves, and diffusion equations, etc. Applications to physics, mechanics, chemistry, and biology will be discussed throughout the courses.

Course Webpage:  

Meeting Times and places:   Tuesday and Thursday 12:30-1:50pm, Morton 4

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

Textbook:
Applied mathematics, (3rd edition), By J. David Logan, John Wiley & Sons, Inc., 2006. This is the main textbook. We plan to cover Chapters 1-3 and some parts of Chapter 5 in Math 441, and Chapter 4, 6-8 in Math 442 next spring. In Math 442, we also use another book Partial Differential Equations for Scientists and Engineers, By Stanley Farlow, Dover Publishing.  

Computer and Calculators: Computer demonstrations will be given in classes sometimes. Computer software Maple/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.

Email address: shij@math.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 CourseInfo website (certainly you can only find your own scores) 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 for every lecture, and it will be available from course webpage under the link "Assignment"). 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 omited 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.