MATH 610-600: Numerical Methods for PDE's, Spring 2010

General Information:

References:

Course Description:

This is a one semester course on numerical methods for partial differential equations. The course will focus on the finite element method for elliptic problems but will also include the basic techniques of finite differences and finite volumes. Parabolic and hyperbolic problems will also be considered. The more basic components of the course will be illustrated in computer programming assignments.

MATH 609 and MATH 610 provide background material for the Qualifying Exam in Numerical Analysis . MATH 610 also provides background for the numerical analysis portion of the Combined Applied Analysis/Numerical Analysis Qualifying Exam.

Course Outline:

Elliptic problems.
Variational formulation.
The Ritz-Galerkin method.
Finite element approximation of one dimensional problems.
Numerical integration.
Finite difference methods of one dimensional problems.
Finite volume approximation of one dimensional problems.
Two-dimensional elliptic problems.
Examples of finite elements.
Error estimates and regularity.
Computational considerations.
The finite difference method.
Some non-conforming methods, Strang's Lemmas.
Parabolic problems.
Semi-discrete FEM approximation.
Fully-discrete FEM approximation.
Approximation by finite differences.
Finite volume methods.

Grading Policy:

Your MINIMUM grade will be A, B, C, or D, for averages of 90%, 80%, 65%, or 50%, respectively.

Prerequisites:

Math 609, Math 641 or a course with some real analysis and basic mathematical skills involving calculus and linear algebra (vector and inner product spaces).

Other information.

ADA Statement: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact the Department of Student Life, Disability Services Office, in Room B116 of Cain Hall or call 862-4570.

Aggie Honor Statement: An Aggie does not lie, cheat, or steal or tolerate those who do. Upon accepting admission to Texas A&M University, a student immediately assumes a commitment to uphold the Honor Code, to accept responsibility for learning, and to follow the philosophy and rules of the Honor System. Students will be required to state their commitment on examinations, research papers, and other academic work. Ignorance of the rules does not exclude any member of the TAMU community from the requirements or the processes of the Honor System. For additional information please visit: http://www.tamu.edu/aggiehonor/