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Integral Equations with Applications by Abdul Jerri [PDF]

### Introduction to Integral Equations with Applications by Abdul Jerri

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This book deals with the basic elements of the integral finite and dicrete transforms with emphasis on their use for solving boundary (and/or initial) value problems as well as facilitating the representation of signals and systems. The analysis of the discrete Fourier tranforms is stressed here because they represent a form for which an efficient means of computation, the well known fast Fourier Tranform (FFT) algorithm exists. However the discrete Fourier tranform is only an approximation to the Fourier integral or Fourier Series that we seek to compute.Thus we stresss the importance of detailed analysis of the errors incurred in this approxmation as preiude to taking advantage of the (efficient) FFT algorithm.
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.
(Abdul J. Jerri)

Book Detail :-
Title: Introduction to Integral Equations with applications
Edition:
Author(s): Abdul J. Jerri
Publisher: John Wiley & Sons
Series:
Year:
Pages: Short Preview 45
Type: PDF
Language: English
ISBN: 0824772938
Country: US

The author Abdul Jabbar Hassoon Jerri is an Iraqi American mathematician, most recognized for his contributions to Shannon Sampling Theory, It's Generalizations, Error Analysis, and Historical Reviews, and in particular his establishment in 2002 of the journal Sampling Theory in Signal and Image Processing (STSIP-ISSN 1530-6429) with over thirty top international experts as its editors, besides establishing its Sampling Publishing, also his contribution to the general understanding of the Gibbs Phenomenon, where he wrote the first book ever on the subject, published by Springer - Verlag, then he followed it by editing another book on Advances in Gibbs Phenomenon published by Sampling Publishing.
Abdul Jerri earned a B.Sc. in Physics with honors at the University of Baghdad (1955) and M.S. in Physics from Illinois Institute of Technology (1960) in Chicago where he continued to work within the research group (1960–63) in Reactor Physics and Radiation streaming in Shelter Entrance ways. He also earned a Ph.D. in Mathematics from Oregon State University in 1967 with the dissertation title On Extensions of the Generalized Sampling Theorem.
Abdul Jerri commenced his tenure with the faculty of the Department of Mathematics and Computer Science at Clarkson University in Potsdam, NY (1967), where he worked from 1967 until his retirement as Professor Emeritus in 2002.
Abdul Jerri's career includes visiting positions at the American University in Cairo, where he established the Study Programs in Mathematics and Computer Science (1972–74). He was also the Director of the Graduate Mathematics Study Program at Kuwait University (1978–80).
He is the author of several other popular books: Introduction to Integral Equations with Applications, accompanied by a Students Solution Manual: Sampling Publishing,Introduction to Wavelets accompanied by a Students Solution Manual( The latter Manual was co-authored with Prof Masaru Kamada); Sampling Publishing. Other books include Integral and Discrete Transforms with Applications and Error Analysis: Marcel Dekker, and Linear Difference Equations with Discrete Transform Methods:Sp ringer-Verlag.
He had published over forty papers, with numerous lectures on his areas of research interest nationally and internationally. Jerri's main research interests include the areas of Integral and Discrete Transforms, Sampling Expansion and its Applications,History and Error Analysis, the Gibbs Phenomenon, Transform-Iterative Methods for Nonlinear Problems, and Operational Sum Methods for Difference Equations.
In his first workshop, he introduced the subject of Shannon Sampling Theory in four-one hour lectures. In 1997 workshop in Aveiro, Portugal, the Proceedings of the workshop was dedicated to jerri 65th birthday. Presently, he is working on writing a Tutorial review paper on the subject "Multidimensional sampling in Signal Processing. He is dedicating this paper for the occasion of the CENTENNIAL of the American Scientist of the century, the father of Information Theory, Claude Elwood Shannon.

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• Read Online Introduction to Integral Equations with Applications by Abdul Jerri • Download PDF Integral & Discrete Transforms with Applications & Error Analysis by Abdul Jerri • Download PDF Linear Difference Equations with Discrete Transform Methods by Abdul J. Jerri • Download PDF The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations by Abdul J. Jerri  Join WhatsApp Group Join Telegram Group

Book Contents :-
Introduction to Integral Equations with applications written by Abdul J. Jerri cover the following topics.
1. Integral Equations, Origin, and Basic Tools
Various Problems as Integral Equations, Exercises, Classification of Integral Equations, Exercises, Some Important Identities and Basic Definitions (Multiple Integrals Reduced to Single Integrals, Generalized Leibnitz Formula, Convergence of Integrals and Basic Definitions), Exercises, Laplace, Fourier, and Other Transforms (The Laplace Transform, Fourier Transforms, Other Transforms), Exercises, Basic Numerical Integration Formulas (Basic (Elementary) Integration Formulas, The Smoothing Effect of Integration, Interpolation ofthe Numerical Solutions of Integral Equations, Review of Cramer's Rule), Exercises

2. Modeling of Problems as Integral Equations
Population Dynamics (Human Population, Biological Species Living Together), Exercises, Control and Other Problems (Mortality of Equipment and Rate of Replacement), Exercises, Mechanics Problems (Hanging Chain, Sliding a Bead Along aWire: Abel's Problem), Exercises, Initial Value Problems Reduced to Volterra Integral Equations, Exercises, Boundary Value Problems Reduced to Fredholm Integral Equations, Exercises, Mixed Boundary Conditions: Dual Integral Equations (Electrified Infinite Plane, Electrified Disc), Exercises, Integral Equations in Higher Dimensions (Schrödinger Equation as an Integral Equation in the Three-Dimensional Momentum Space)

Volterra Integral Equations
Volterra Equations ofthe Second Kind, Resolvent Kernel Method: Neumann Series, Method of Successive Approximations (Iterations), Laplace Transform Method: Dijference Kernel, Volterra Integral Equations ofthe First Kind, Volterra Integral Equation ofthe First Kind with a Difference Kernel—Laplace Transform Method, Numerical Solution of Volterra Integral Equations, Numerical Approximation Setting of Volterra Equations, The Green''s Function

Construction ofthe Green's Function
Nonhomogeneous Differential Equations, Construction ofthe Green's Function — Variation of Parameters Method, Orthogonal Series Representation of Green 's Function, Green''s Function in Two Dimensions, Fredholm Integral Equations and the Green's Function, Fredholm Integral Equations 209

Fredholm Integral Equations with Degenerate Kernel
Nonhomogeneous Fredholm Equations with Degenerate Kernel, Fredholm Alternative, Approximating a Kernel by a Degenerate One, Fredholm Integral Equations with Symmetrie Kernel, Homogeneous Fredholm Equations with Symmetrie Kernel, Solution of Fredholm Equations ofthe Second Kind with Symmetrie Kernel, Fredholm Integral Equations ofthe Second Kind, Method of Fredholm Resolvent Kernel, Method of Iterated Kernels, Some Basic Approximate Methods, Fredholm Integral Equations of the First Kind, Fredholm Equations of the First Kind with Symmetrie Kernels, Ill-Posed Problems and the Fredholm Equation ofthe First Kind, Numerical Solution of Fredholm Integral Equations, Numerical Approximation Setting of Fredholm Integral Equations, Homogeneous Fredholm Equations

Existence of the Solutions: Basic Fixed Point Theorems
Preliminaries: Toward a Contractive Mapping, Basic Definitions: Complete Metrie Spaces, Contractive Mapping for Linear Fredholm Equations, Contractive Mapping for Linear Volterra, Fixed Point Theorem of Banach, Existence ofthe Solution for Linear Integral, Existence of the Solution for Nonlinear Integral Equations, Existence of the Solution for Nonlinear Differential Equations

Higher Quadrature Rules for the Numerical Solutions
Higher Quadrature Rules of Integration with Tables, Higher Quadrature Rules for Volterra Equations, Higher Quadrature Rules for Fredholm Equations, Comments on Higher Quadrature Rules for Some Singular Fredholm Equations

Appendix A The Hankel Transforms
A.l The Hankel Transform for the Electrified Disc, The Finite Hankel Transform

Appendix B Green 's Functionfor Various Boundary Value Problems
B.l Green 's Functions in Terms of Simple Functions, B.2 Green 's Function in Terms of Special Functions

References
Index

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