2010 Spring MATH 225-01

Bulletin Course Description
Approximation theory: Fourier series, orthogonal polynomials, interpolating polynomials and splines. Numerical differentiation and integration. Numerical methods for ordinary differential equations: finite difference methods for initial and boundary value problems, and stability analysis. Introduction to finite element methods. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)

Title SCIENTIFIC COMPUTING II
Department MATH
Course Number225
Section Number 01
Primary Instructor Bouzarth,Elizabeth L
Course Homepage www.math.duke.edu/~bouzarth/math225

Synopsis of course content
This course will develop theoretical topics and computational techniques that are fundamental in many areas of mathematics, engineering, and scientific research applications. Topics will include approximation of functions, numerical differentiation and integration, and solutions of initial value and boundary value problems for ordinary differential equations. If time permits, numerical partial differential equations will be introduced. Error analysis and formulation of convergent mathematical schemes will be used to derive stable, reliable, efficient, and accurate numerical methods for large classes of problems.
Textbooks
An Introduction to Numerical Analysis, 2d Edition,
by Kendall E. Atkinson
Assignments
Weekly problem sets will include theory, analysis and computational projects.
Exams
There will be a midterm and a final.
Grade to be based on
Course grade will be based on the problem sets and tests.