Spectral Methods : Algorithms Analysis and Applications Along with finite differences and finite elements spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems including in particular high order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications. Introduction Fourier Spectral Methods for Periodic Problems Orthogonol Polynomials and Related Approximation Results Second Order Two Point Boundary Value Problems Integral Equations High Order Differential Equations Problems in Unbounded Domains Multi Dimensional Domains Mathematical Preliminaries Basic iterative methods Basic time discretization schemes Instructions for routines in Matlab. .