Book Description
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. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.

Review
‘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.