Catalogue Description. 172. Numerical Partial Differential Equations. (4) Finite difference methods for the numerical solution of hyperbolic and parabolic partial differential equations; finite difference and finite element methods for elliptic partial differential equations.

Course Description. Scientists often model physical systems with partial differential equations (“PDEs”). Analytic solutions exist only for the most elementary PDEs; the rest must be tackled with numerical methods. These can roughly be broken into two types: the finite difference and the finite element methods. The finite difference method approximates the solution of a PDE at a number of points in space. The finite element method attempts to find the best approximate solution to a PDE among some finite set of simple functions. In the end, both methods require solution of a set of linear equations. After an introduction to PDEs in general, we will look at each method, including theoretical and practical aspects, consistency, stability and convergence.

Grading Policy. It is my belief that any grading scheme will be disagreeable to some student; the best grading scheme one can hope for is one that is agreeable to the majority, and applies equally to all students.

Grading in this class will be based upon performance in homeworks, on a programming project, and two examinations. The final quarter grade is subdivided as follows: Homework: 30%; Project: 10%; Exams: 30% each. It is expected that the exams will be challenging, and grades will be curved.

The dates and times for the exams are listed in this syllabus: The first exam is Friday, April 29, in class. The second exam is during the final exam period for the class, Monday June 6, at 11:30am. There is also an optional comprehensive final exam during the final exam period, in addition to the second exam. The purpose of the optional final is to allow students to make up for poor performance on the first exam.

If you have known conflicts with either of these exams, I encourage you to notify me immediately. Legitimate, documented, excuses for missing an exam will be dealt with individually.

Homework. It is expected, and encouraged, that students will work together on the homeworks. This saves time (yours and mine), builds leadership, and encourages cooperation. Each student must submit their own homework, written in their own hand (please no printouts, photocopies or faxes). Please list on your homework the names of the other students you worked with.

A number of the homework problems ask you to write a program in FORTRAN. You may do this if you wish, but I encourage you to instead write the program in Matlab (or even better, the free Matlab clone Octave). If you choose to write in Matlab, do not use Matlab’s finite difference toolkit or otherwise “cheat” by using Matlab’s high-level functions. It should be clear from the wording of the problem what you are supposed to program; if not, ask me. You may talk to one another about programming assignments, but you should write your own programs. Please do not share code.

Project. The project will consist of a longer programming assignment. You will be able to choose from a limited number of different projects. Please do not consult one another for your project, and do not share code.

Getting Help. I encourage you to attend my office hours, and those of the TA (if this class is ultimately assigned one).

Academic Integrity Students are expected to adhere to the University’s Policy on Integrity of Scholarship, found in the UCSD general catalogue. Minimum punishment for cheating on a exam is a score of zero on that exam.

Course Webpage. The course page, http://scicomp.ucsd.edu/~spav/class/2005S-M172/ will include this syllabus and any updates, general announcements, handouts and other materials.

Course Schedule. The lecture schedule is tentative, but the exam schedule is exact. Section numbers are those of Numerical Treatment of Partical Differential Equations, except those on FEM, which are from Mathematics 172 Notes on the Finite Element Method.