Spectral methods, as presented by Boyd, are techniques for numerically solving differential equations.  His book is a collection of A LOT of practical information presented mostly through a mathematical frame work.  Practical means different things to different people; in Boyd's case, he discusses the details of what happens in putting the mathematics to use (the pitfalls), and when each technique should be used.  Supporting numerical methods, such as matrix techniques, are discussed where needed.  Example computer code is scarce.  Worked examples are inconsistently used, and sometimes abstract.As a novice to the field, I found the level of presentation a notch too high to be able to put it to use.  It was more abstract than applied.  I'm not saying it is not informative, only that this is not a good first book on the topic.  I might get this as a second or third book.I give it 4 starts due to two complaints.  There are not a lot of illustrations, and moreover those that are included are often too simple or need more annotation.  A little more thought should go into them, and there should be a more of them for some of the more abstract topics.  Additional thought should go into the organization too.  Information at different levels of expertise are scattered throughout so you either (a) need to know the answers already, (b) skip ahead several chapters, or (c) go on an aside in another text.

Chebyshev and Fourier Spectral Methods: Second Revised Edition PDF

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