Integral and Discrete Transforms with Applications and Error Analysis  book cover
1st Edition

Integral and Discrete Transforms with Applications and Error Analysis

ISBN 9780824782528
Published June 11, 1992 by CRC Press
848 Pages

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Book Description

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Table of Contents

Part 1 Compatible transforms: the method of separation of variables and the integral transforms; compatible transforms; classification of the transforms; comments on the inverse transforms - tables of the transforms; the compatible transform and the adjoint problem; constructing the compatible transforms for self-adjoint problems - second-order differential equations; the nth-order differential operator. Part 2 Integral transforms: Laplace transforms; Fourier exponential transforms; boundary and initial value problems - solutions by Fourier transforms; signals and linear systems - representation in the Fourier (spectrum) space; Fourier sine and cosine transforms; higher-dimensional Fourier transforms; the Hankel (bessel) tranforms; Laplace transform inversion; other important integral transforms. Part 3 Finite transforms - Fourier series and coefficients: Fourier (trigonometric) series and general orthogonal expansion; Fourier sine and cosine transforms; Fourier (exponential) transforms; Hankel (bessel) transforms; classical orthogonal polynomial transforms; the generalized sampling expansion; a remark on the transform methods and nonlinear problems. Part 4 Discrete transforms; discrete Fourier transforms; discrete orthogonal polynomial transforms; bessel-type poisson summation formula (for the Bessel-Fourier series and Hankel transforms). Appendix A: basic second-order differential equations and their (series) solutions - special functions. Appendix B: mathematical modeling of partial differential equations - boundary and initial value problems. Appendix C: tables of transforms.

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