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This book provides the most comprehensive, up-to-date theory and state-of-the-art algorithms of spectral methods. It is written by the authors who pioneered the subject and who introduced spectral methods as a mainstream tool for scientific and engineering computation.
The last, and farthest-reaching, level requires the additional study of the material contained in the appendices, which enable the strongly motivated reader to explore further into the subject. This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics.
The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.
A companion to "Fundamentals in Single Domains", which discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in global basis functions. This book contains a survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries.
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