Fall 2013 Course Syllabus - Mathematics 8023.001

Course: Mathematics 8023.001.
Course Title: Numerical Differential Equations I.
Time: TR 9:30-10:50.
Place: Wachman 617.
Instructor: Joshi, Sunnie.
Instructor Office: Wachman 544.
Instructor Email: sjoshi@temple.edu
Instructor Phone: 215-214-7588.
Course Web Page: https://math.temple.edu/~sjoshi/teaching.html
Office Hours: W 1:00-3:00.
Prerequisites: see course webpage.
Textbook: Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations - Steady State and Time Dependent Problems, SIAM, 2007.
Course Goals: This course will focus on numerical methods for ordinary and partial differential equations such as the Runge-Kutta Method, the finite difference methods, finite volume and finite element methods and spectral methods with specific emphasis on fundamental concepts such as stability, convergence and error analysis. It time permits, we will look at some application driven problems such as wave propagation and flow problems.
Topics Covered: Fundamentals of Numerical Methods - Stability, Convergence, Error Analysis. Finite Difference, finite Element Methods for Elliptic, Parabolic and Hyperbolic equations. Spectral Methods, ENO/WENO schemes.
Course Grading: The grading will be based on Homework problems (50%) and a class project (50%). The homework problems will be due every other week. The project grade involves a midterm report (20%) and a final report (50%), and a final presentation (30%). Due dates will be announced in class.
Exam Dates: TBD.
Attendance Policy: Attendance is expected.
Other References: L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, V. 19, American Mathematical Society, 1998 L.N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000 Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.

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Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:

• The first day of classes is Monday, August 26.
• Labor Day is Monday, September 2.
• The last day to drop/add (tuition refund available) is Monday, September 9.
• Thanksgiving is Thursday, November 28.
• The last day to withdraw (no refund) is Tuesday, October 22.
• The last day of classes is Wednesday, December 4.

During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.

The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.