Randall J. LeVeque
rjl at amath.washington.edu
office hours: TBA
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.
Several other resources will be used for supplementary material on topics not covered in this book.