AMATH 571
SLN 10220, MW 3:30-4:50, MGH 228

Spectral Methods


Instructor:

 Professor Randall J. LeVeque
Guggenheim 415C
tel: 685-3037
fax: 685-1440
rjl at amath.washington.edu
office hours: TBA

Important announcements, corrections, etc.

Homework assignments

Additional reading, references, etc.

Course Description

Analysis and application of spectral methods for the numerical solution of differential equations. Fourier methods and the FFT; collocation methods; polynomial interpolation and Chebyshev series; approximation theory and spectral accuracy; boundary conditions.

Spectral methods are an extremely powerful class of methods for solving differential equations and other problems in applied mathematics, and should be part of everyone's toolbox of computational techniques.

Prerequisite: AMATH 584, AMATH 585, AMATH 586, or permission of instructor. The course will be largely self-contained and does not depend heavily on material from other courses, but a reasonable background in finite difference methods for differential equations is assumed, along with sufficient mathematical and computational sophistication.

Syllabus

Textbook and references

The main text will be "Spectral Methods in MATLAB" by L. N. Trefethen, published by SIAM. It will be available in the bookstore, but note that members of SIAM receive a 30% discount if you buy it online, and all UW students are eligible for free membership in SIAM, see The book contains many Matlab programs that can be downloaded from the book webpage. See also the errata page for corrections to some typos in the book.

Several other resources will be used for supplementary material on topics not covered in this book.

The books of Trefethen, Fornberg, and Hesthaven & Gottlieb & Gottlieb are on reserve in the Engineering library. You may wish to refer to some of these for more background. In particular, I recommend as an excellent general reference.

Grading

The course will be graded based on several homework assignments, involving both analysis and computing, a final project, and class participation.