This course will be an introduction to interpolation and approximation of data and functions by polynomials, piecewise polynomials, and trigonometric series. Practical aspects of implementation such as FFTs and the chebfun software will be covered. See Software for the course.
Spectral methods for solving differential equations will serve as the main motivating application, along with other approximation problems and a brief introduction to finite element methods.
Applied Math 584-5-6 or similar background is strongly recommended, along with programming experience in Matlab and/or Python and some knowledge of complex analysis.
Note that SIAM members can purchase these books directly from SIAM at a big discount, and that UW students can join SIAM free
L. N. Trefethen, Approximation Theory and Approximation Practice, SIAM 2013.
[Download m-files] (See this page also for errata.)
L. N. Trefethen, Spectral Methods in Matlab, SIAM 2000.
I hope to cover the following: