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Spectral Methods in MATLAB is written by Lloyd N. Trefethen and published by SIAM. It's available with International Standard Book Number or ISBN identification 0898719593 (ISBN 10) and 9780898719598 (ISBN 13).
This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.