MATH 815: Topics in Numerical Analysis:

Numerical Solution of Partial Differential Equations

Spring 2008

Department of Mathematical Sciences, UWM

Lecture Time and Place

2:00 PM - 3:15 PM, Tuesday and Thursday, EMS Room E416

Instructor

Dr. Dexuan Xie
Office: EMS-489
Telephone:   (414) 229-3528
E-mail: dxie@uwm.edu
Homepage:   http://www.uwm.edu/~dxie/
Office Hours:    10:00 AM - 11:30 AM, Tuesday and Thursday.

Textbook

Class notes will be used in the course based on the following reference books:

Finite Difference Schemes and Partial Differential Equations (2nd ed.), by John C. Strikweda, SIAM 2004.
Numerical Solution of Partial Differential Equations (2nd ed.), by K. W. Morton and D. F. Mayers, Cambridge 2005.
The Mathematical Theory of Finite Elements (2nd ed.),by Susanne Brenner and Ridgway Scott, Springer, 2002
Numerical Analysis, Richard L. Burden and J. Douglas Faires, 8th edition, Thomson, Brooks/Cole, 2005.

Course Overview

This course will discuss basic numerical methods for solving hyperbolic, parabolic, and elliptical partial differential equations in one and two dimensional space. It covers both finite difference and finite element methods. Basic numerical techniques such as explicit, implicit and ADI approaches will be discussed. Classic and advanced iterative methods such as the SOR method, the multigrid method, and preconditioned conjugate gradient method will be studied for solving the system of linear algebraic equations that arises from finite difference and finite element approximations to the partial differential equation.

Prerequisite

The course is proper for graduate students who demand to learn numerical techniques for solving partial differential equations.

Grading

The grade will be based on your class attendance (10 %) and homeworks (90 %). Three homework assignments (each 30 %) will be collected and graded.

Attendance:

There is no provision for absences due to vacations, family outings and other social activities, other special plans and appointments, etc. Absences due to illness require a medical excuse on Physician's letterhead, signed by the physician.

Important Dates

·             January 22: First day of classes.

·             February 21: Homework 1 due.

·             February 18: Lat day to drop course without W on record.

·             March 14: Last day to drop or withdraw.

·             March 16 to 23: Spring Recess.

·             April 3: Homework 2 due.

·             May 8 : Last day of classes.

·             May 15: Homework 3 due.

Statement of Academic Misconduct

The university has a responsibility to promote academic honesty and integrity

and to develop procedures to deal effectively with instances of academic

dishonestly. Students are responsible for the honest completion and

representation of their work, for the appropriate citation of sources, and for

respect of others' academic endeavors. Further information can be found at http://www.uwm.edu/Dept/Acad_Aff/policy/academicmisconduct.html.

Statement of Sexual Harassment

Sexual harassment is reprehensible and will not be tolerated by the

University. It subverts the mission of the University and threatens the careers,

educational experience, and well being of students, faculty and staff. The

University will not tolerate behavior between or among members of the University

community which creates an unacceptable working environment.