Integral and Discrete Transforms with Applications and Error Analysis

Abdul Jerri

• Publisher: CRC Press
• Year: 2021
• eBook ISBN: 9781000147520
• Edition: 1
• Topic: Mathematics
• Subtopic: Functional Analysis
• Index: Mathematics

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

• Cover
• Half Title
• Series
• Title Page
• Copyright Page
• Dedication
• Preface
• Guide to Course Adoption
• Table of Contents
• Chapter 1 Compatible Transforms
• Chapter 2  Integral Transforms
• Chapter 3  Finite Transforms—Fourier Series and Coefficients
• Chapter 4  Discrete Transforms
• Appendix A Basic Second-Order Differential Equations and Their (Series) Solutions—Special Functions
• Appendix Β Mathematical Modeling of Partial Differential Equations—Boundary and Initial Value Problems
• Appendix C Tables of Transforms
• Bibliography
• Index of Notations
• Subject Index