Table of Contents

Preface; 1. Differentiation matrices; 2. Unbounded grids: the semidiscrete Fourier transform; 3. Periodic grids: the DFT and FFT; 4. Smoothness and spectral accuracy; 5. Polynomial interpolation and clustered grids; 6. Chebyshev differentiation matrices; 7. Boundary value problems; 8. Chebyshev series and the FFT; 9. Eigenvalues and pseudospectra; 10. Time-stepping and stability regions; 11. Polar coordinates; 12. Integrals and quadrature formulas; 13. More about boundary conditions; 14. Fourth-order problems; Afterword; Bibliography; Index.

Promotional Information

This is the only book on spectral methods built around MATLAB programs.

About the Author

Lloyd N. Trefethen is Professor of Numerical Analysis at Oxford University, UK. His previous book, Numerical Linear Algebra (with David Bau, III) is one of SIAM's bestsellers.

Reviews

'A brief, intuitive, and excellent introductory textbook of spectral methods. Readers with basic experience of finite difference methods can easily get to the core knowledge of spectral methods through this book. Those MATLAB scripts for examples in the book are very useful for both teaching and research.' Professor Tzyy-Leng Allen Horng, Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan 'This book is a very nice addition to the collection of books on spectral methods, from a totally different angle. It should attract more students and researchers to the powerful spectral methods.' Chi-Wang Shu, Mathematics of Computation 'What a great book! I sat down to read through it last month, and it's so inspiringly lean with such great examples that I can't resist using it this term for 18.336 [Numerical Methods for PDEs].' Peter Mucha, Massachusetts Institute of Technology 'This is a charming book, beautifully written, easy to understand without sacrificing accuracy. The idea of using MATLAB is brilliant and will appeal to the students and the other readers.' David Gottlieb, Ford Foundation Professor of Applied Mathematics, Brown University 'Fascinating mathematics, intriguing graphics, and beautiful MATLAB codes.' Cleve Moler, Chairman and Chief Scientist, The MathWorks, Inc. "The book's succinct style and the understanding that is gained by parsing and experimenting with MATLAB routines allow for a large number of fundamental concepts to be conveyed in a few pages... I recommend this book highly; it is clear, concise, and dense with interesting and exciting examples. It is an appropriate text for an introductory class on the subject and also includes many ideas and explanations that are appealing to a broader research audience." -Paul Milewski, University of Wisconsin, SIAM Review, Vol. 43, No. 3, pp.541-581.