Advanced Methods in Applied Mathematics

Math 781-001

Fall 2009

This is the web page http://math.gmu.edu/~wanner/courses/m781f09/index.html
It will be updated regularly and always contain the latest information on the course.

General Information:

Instructor: Thomas Wanner
Office: Room 205, ST1
E-mail: twanner@gmu.edu
Web Page: http://math.gmu.edu/~wanner/
Phone: (703) 993-1472
Fax: (703) 993-1491
Office hours: T 5:00-6:00pm, F 11:00am-12:00, and by appointment

Lectures: R 7:20-10:00pm, Room 242, ST1
Prerequisites: A thorough knowledge of multi-variable calculus and elementary differential equations is assumed. Also, familiarity with the theorem-proof style of presentation is important.
Textbook: No textbook is required, several relevant books are listed on the syllabus page.

Important Links:

Syllabus:

This course introduces several important methods that are used throughout applied mathematics. These include dimensional analysis and scaling, regular perturbation theory, singular perturbation theory, bifurcation theory, and (time permitting) stochastic modeling. This course will develop and apply these mathematical tools in current scientific fields, such as biology, materials science, or financial mathematics, in the context of ordinary and partial differential equations. A more detailed syllabus can be found here. It will be updated weekly.

Homework Assignments:

Homework problems will be assigned once a week and posted on the homework page. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.

Grading Policy:

Your final grade in the course will be determined from graded homework assignments, your performance in a midterm exam, a comprehensive final exam (dates and details to be announced), and your attendance and class participation. Weights for these items will be distributed approximately according to the following schedule:

Homework Midterm Exam Final Exam Attendance
30% 30% 30% 10%

Thomas Wanner, September 3, 2009.