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Introduction to integral equations with applications

Author: Abdul J Jerri
Publisher: New York : Wiley, ©1999.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
"Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Abdul J Jerri
ISBN: 0471317349 9780471317340
OCLC Number: 40979823
Notes: "A Wiley-Interscience publication."
Description: xviii, 433 pages ; 24 cm
Contents: Integral Equations, Origin, and Basic Tools --
Various Problems as Integral Equations --
Classification of Integral Equations --
Some Important Identities and Basic Definitions --
Multiple Integrals Reduced to Single Integrals --
Generalized Leibnitz Formula --
Convergence of Integrals and Basic Definitions --
Laplace, Fourier, and Other Transforms --
The Laplace Transform --
Fourier Transforms --
Other Transforms --
Basic Numerical Integration Formulas --
Basic (Elementary) Integration Formulas --
The Smoothing Effect of Integration --
Interpolation of the Numerical Solutions of Integral Equations --
Review of Cramer's Rule --
Modeling of Problems as Integral Equations --
Population Dynamics --
Human Population --
Biological Species Living Together --
Control and Other Problems --
Mortality of Equipment and Rate of Replacement --
Mechanics Problems --
Hanging Chain --
Sliding a Bead Along a Wire: Abel's Problem --
Initial Value Problems Reduced to Volterra Integral Equations --
Boundary Value Problems Reduced to Fredholm Integral Equations --
Mixed Boundary Conditions: Dual Integral Equations --
Electrified Infinite Plane --
Electrified Disc --
Integral Equations in Higher Dimensions --
Schrodinger Equation as an Integral Equation in the Three-Dimensional Momentum Space --
Volterra Integral Equations --
Volterra Equations of the Second Kind --
Resolvent Kernel Method: Neumann Series --
Method of Successive Approximations (Iterations) --
Laplace Transform Method: Difference Kernel --
Volterra Integral Equations of the First Kind --
Volterra Integral Equation of the 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 of the Green's Function --
Nonhomogeneous Differential Equations --
Construction of the 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 --
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 Symmetric Kernel --
Homogeneous Fredholm Equations with Symmetric Kernel --
Solution of Fredholm Equations of the Second Kind with Symmetric Kernel --
Fredholm Integral Equations of the 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 Symmetric Kernels --
Ill-Posed Problems and the Fredholm Equation of the 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 Metric Spaces --
Contractive Mapping for Linear Fredholm Equations --
Contractive Mapping for Linear Volterra Equations --
Fixed Point Theorem of Banach --
Existence of the Solution for Linear Integral Equations --
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 --
The Hankel Transforms --
The Hankel Transform for the Electrified Disc --
The Finite Hankel Transform --
Green's Function for Various Boundary Value Problems --
Green's Functions in Terms of Simple Functions --
Green's Function in Terms of Special Functions.
Responsibility: Abdul J. Jerri.
More information:

Abstract:

"Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises."--Jacket.

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