Product Description
Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations.This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems.Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory.Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations.

By Chapter 7 the momentum has built until we are looking at problems on the frontier.Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability.Chapter 8 presents a solid foundation for the theory of functional differential equations.Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated.

Key Features:

- Smooth transition from ordinary differential equations to integral and functional differential equations.

- Unification of the theories, methods, and applications of ordinary and functional differential equations.

- Large collection of examples of Liapunov functions.

- Description of the history of stability theory leading up to unsolved problems.

- Applications of the resolvent to stability and periodic problems.

1. Smooth transition from ordinary differential equations to integral and functional differential equations.
2. Unification of the theories, methods, and applications of ordinary and functional differential equations.
3. Large collection of examples of Liapunov functions.
4. Description of the history of stability theory leading up to unsolved problems.
5. Applications of the resolvent to stability and periodic problems. ... Read more

Product Description
This book presents the subject of integral equations in an accessible manner for a variety of applications. Emphasis is placed on understanding the subject while avoiding the abstract and compact theorems. A distinctive feature of the book is that it introduces the recent powerful and reliable developments in this field, which are not covered in traditional texts. The newly developed decomposition method, the series solution method and the direct computation method are thoroughly implemented, which allows the topic to be far more accessible. The book also includes some of the traditional techniques for comparison.

Using the newly developed methods, the author successfully handles Fredholm and Volterra integral equations, singular integral equations, integro-differential equations and nonlinear integral equations, with promising results for linear and nonlinear models. Many examples are given to introduce the material in a clear and thorough fashion. In addition, many exercises are provided to build confidence, ease and skill in using the new methods.

This book may be used as a text for advanced undergraduates and graduate students in mathematics and scientific areas, and as a work of reference for research study of differential equations and numerical analysis. ... Read more

Customer Reviews (2)

What I was looking for
A little background.I am taking an inverse problem graduate level course, which makes use of Gelfand-Levitan equations, Marchenko equations, etc.I had never studied integral equations, and I was looking to get an intuitive understanding of how to solve and approach the G-L and Marchenko equations.One of the main problems I was having was understanding the notation of the G-L equations.This book gave me a lot of the basics that I was missing in how to solve Fredholm and Volterra equations and also where some of the more advanced theory came from.So, I would recommend this book as a great introduction to integral equations, as the name suggests.

For a more theoretical approach, I would first go through Abdul Jerri's book on integral equations, and then, if you want to learn some applications or more theory, I would recommend books by Chadan, Sabatier, Marchenko, etc.

A really wonderful book !
This was almost my first book which I had read about integral equations. The real advantage of it is that this book is not an abstract one, but really teaches you several practical equation solving methods and contains lots of examples and exercises with the answers provided at the end of the book. Simply great !
... Read more

Product Description
Authoritative, well-written basic treatment of extremely useful mathematical tool. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, Types of Singular or Nonlinear Integral Equations, more. Advanced undergraduate to graduate level. Exercises. Bibliography.
... Read more

Customer Reviews (1)

Satisfied purchaser.
Excellent prioe on Integral Equations book.It was in excellent condition and was shipped in a timely manner.Really appreciate the shipper/seller in this transaction. Great used book purchase through Amazon! ... Read more

Product Description
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener–Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. With 300 additional pages, this edition covers much more material than its predecessor.

New to the Second Edition

•          New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions

•          More than 400 new equations with exact solutions

•          New chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs

•          Additional examples for illustrative purposes

To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations. ... Read more

Customer Reviews (4)

It is a unique book!
This is an outstanding work, devoted to integral equations (linear and nonlinear), can be considered as a unique book: it contains a vast number of integral equations (>2500!!!) with corresponding analytical solutions (including new author's results) and a large collection of solving methods (analytical and numerical) appropriate for a given class of integral equations with illustrative examples.

Book recommended for modelling research
I am a chemical and petroleum engineer modelling flow in porous media. This book was extremelly useful for me to formulate flow problems allowing for analytical solutions.
Sicerely
Dr Carageorgos

Excellent book for engineering scientists
The book is highly recommended for engineers who use analytical models. The book contains several explicit formula and solutions allowing to avoid cumbersome numerical calculations. This feature is particularly important for solution of inverse problems, adjustment of the model to the data, for optimization, where solution of forward problem is used in algorithms for numerous times.

Sincerely,
Prof. Pavel Bedrikovetsky

Saved me a lot of time
I'm not a mathematician nor do I have many mathematician friends, but working on queueing theory during my master degree I started dealing with a bunch of integral equations. This book saved me weeks of looking around and reading to find the solution to Integral Equations that may or may not have a closed form solution. ... Read more

Product Description
A comprehensive, up-to-date, and accessible introduction to the numerical solution of a large class of integral equations, this book builds an important foundation for the numerical analysis of these equations. It provides a general framework for the degenerate kernel, projection, and Nyström methods and includes an introduction to the numerical solution of boundary integral equations (also known as boundary element methods).It is an excellent resource for graduate students and researchers trying to solve integral equation problems and for engineers using boundary element methods. ... Read more

Product Description
This book resulted from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter. For the second edition, in addition to corrections and adjustments throughout the text, as well as an updated reference section, new topics have been added. ... Read more

Customer Reviews (1)

The right place to look.
Integral equations has become (I don't know why) a somewhat misterious subject. I've heard physicists say "I have enough with differential equations. Why to study more complicated types of equations?", or"I have enough trouble with differential equations; please don't tellme there's something else", and even "Why to study integralequations? What are they good for?".

The subject of integralequations is a natural part of analysis which serves to connect severalrelated topics (complex analysis, harmonic analysis, potential theory,differential equations,...) and to use all the power thus gained to solveimportant boundary value problems of mathematics and physics.

Everyoneinterested in mathematical physics should get a thorough training inintegral equations, and this book is the right place to start. Using amodern and comprehensive language, the author exposes the most importanthighlights of the theory, up to the numerical aspect, and puts the readerin the track to current research.

The contents of the book are: Normedspaces, bounded and compact operators, the Riesz theory, dual systems andFredholm theory, regularizations in dual systems, potential theory,singular integral equations, Sobolev spaces, the heat equation, operatorapproximations, degenerate kernel approximation, quadrature methods,projection methods, iterative solution and stability, equations of thefirst kind, Tikhonov regularization, regularization by discretization,inverse scattering theory.

Includes motivation for each topic, excercisesfor each chapter, and extensive references. Suitable for graduate studentsand advanced undergraduates with a strong background in real and complexanalysis.

Please take a look to the rest of my reviews (just click on myname above). ... Read more

Product Description
Written for students of mathematics and the physical sciences, this superb treatment offers modern mathematical techniques for setting up and analyzing problems. Topics include elementary modeling, partial differential equations of the first order, potential theory, parabolic equations, much more. Prerequisites are a course in advanced calculus and basic knowledge of matrix methods.
... Read more

Customer Reviews (4)

a classic text in applied mathematics
This is one of the finest textbooks on applied mathematics.It is appropriate for a wide range of levels and disciplines.A moderately paced graduate class can finish most of the chapters in a full year.The first two chapters cover material that is difficult to find elsewhere and nowhere is it better handled.The real boon to this book is the constant integration of physical reasoning with solid mathematical theory.To be sure, many of the more complicated ideas are only mentioned, but the later chapters pick these up and go much further. It covers basic heat and wave applications, but also Brownian motion and gas dynamics.A solid calculus background is needed, which includes vector calculus and convergence issues.Eigenvalues and some functional analysis are needed.Many books on elementary partial differential equations spend all their time on the big three: heat, wave and Laplace.This is too low a level for any graduate class and doesn't create the excitement other applications provide.On the other hand, this book is accessible to many people.Often, graduate texts are thoroughly awash with Sobolev spaces and weak convergence and the physical problem, i.e., the actual model, is all but ignored.This classic text is the bridge between elementary and advanced applied mathematics.In some respects, it is self-contained.Guenther and Lee have written an indispensable book.

Partial Differential Equations of Mathematical Physics & Integral Equations
Book came in excellent condition and was shipped quickly.Highly recommend this seller.

I agree with the reader from CAL
The book skip too many steps and most of the time, the equation is presented without explanation...Don't waste money.

Book that dosn't make sense
This book is one of the worse I ever see representing the mathematics for physics, the mathematics and the physics both was not explained as it should, the authors are not familiar at all with the concept of physicsmake their material in the book related to this subject unclear and vague.The book has too many gaps as I see it has too many jumps when a physicalphenomena represented using mathematics. Physical concept was most of thetimes not even mention, and I believe that the author should stick onlywith mathematics since they try to explain physics they don't reallyfamiliar with. ... Read more

Product Description
In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another subject of the study is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included. ... Read more

Product Description

Product Description
Details the methods for solving electromagnetic wave problems using the integral equation formula. This text limits the use of mathematics to the level of standard undergraduate students and explains all the derivations and transformations of equations in detail. ... Read more

Product Description
This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. It guides the reader from the "basics" to the current state-of-the-art level of the field, describes important problems and directions for future research, and highlights methods.The analysis includes numerous exercises and applications to the modelling of physical and biological phenomena. ... Read more

Product Description
Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis.

Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'. ... Read more

Customer Reviews (1)

Physicists , Do yourself a favor and get this book or atleat check it out at the Library!
This is an excellent introduction to Differential and especially integral equations for physicists especially those than plan on going on to graduate school for physics. This book covers a material not covered in any other textbook at this undergrad/grad level. Very easy to follow and understand and the font and layout makes for an easy read, with lots of easy to follow examples and exercises. Can be used as an alternative to Arfken and Webber, although it does not cover as much material. The integral equation part can be skipped, since most undergraduates might not need this portion until graduate school. Can be followed with Sadri Hassanis larger (1100 page) "Mathematical Physics" for the move abstract concepts. ... Read more

Product Description
This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics. ... Read more

Customer Reviews (3)

No details, impossible to learn from
This book covers a huge range of topics.There are no details.I am unable to work the homework problems with the details provided in the text.I'm googling information and will purchase a few more textbooks so I can learn something.This book might be good as a reference book if you already know what you're doing.

new chap 19 on numerical inverse laplace transforms
Chapter 19 is an excellent modern review of the main numerical inverse Laplace transform methods in use today.It does a good job of tying together many of the methods into a unifyingtheoretical light.Pretty much the only modern review out there, it was written by Dr John Knight, who is a co-author of one of the more important numerical inverse methods (Fourier series method of de Hoog, Knight & Stokes).

The rest of the book is great too.

Great Introduction
This well written book teaches by example and will quickly make youproficient in the subject. Davies uses complex analysis to approach thesubject which provides a way to visualize the problems. ... Read more

Product Description
The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM's) have certain advantages over other procedures for solving such problems: BIEM's are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM's are also essential ingredients in boundary element methods, often used by scientists and engineers.However, BIEM's are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problems has been largely neglected in the literature-even when it is more than marginally different from that applied to the corresponding three-dimensional versions.This volume discusses three typical cases where such differences are clear: the Laplace equation (one unknown function), plane strain (two unknown functions), and the bending of plates with transverse shear deformation (three unknown functions). The author considers each of these with Dirichlet, Neumann, and Robin boundary conditions. He subjects each to a thorough investigation-with respect to the existence and uniqueness of regular solutions-through several BIEM's. He proposes suitable generalizations of the concept of logarithmic capacity for plane strain and bending of plates, then uses these to identify contours where non-uniqueness may occur. In the final section, the author compares and contrasts the various solution representations, links them by means of boundary operators, and evaluates them for their suitability for numeric computation. ... Read more

Customer Reviews (1)

Mathematics Major
I am utilizing it for an independent study as an undergraduate. It is concise and well written. I do not recommend it as a primary text. It serves as a great supplemental text for my Boundary Elements Method investigations. ... Read more

Product Description
This book gives a rigorous and practical treatment of integral equations and aims to tackle the solution of integral equations using a blend of abstract structural results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text, and it allows a thorough account to be given of many of the types of integral equation that arise, particularly in numerical analysis and fluid mechanics. Because it is not always possible to find explicit solutions to the problems posed, much attention is devoted to obtaining qualitative information and approximations and the associated error estimates. ... Read more

Product Description
Presenting a mathematical treatment of acoustic and electromagnetic waves, this text covers basic properties of solutions to the Helmholtz and Maxwell equations. It provides a broad survey of integral equation methods in scattering theory, including both the direct and inverse problems. Also included are discussions on the Riesz-Fredholm theory of compact operations, entire functions of a complex variable, univalent function theory, improperly posed problems, and weak compactness. ... Read more

Product Description
The purpose of this book is threefold: to be used for graduate courses on integral equations; to be a reference for researchers; and to describe methods of application of the theory. The author emphasizes the role of Volterra equations as a unifying tool in the study of functional equations, and investigates the relation between abstract Volterra equations and other types of functional-differential equations. ... Read more

Product Description
Written by leading numerical analysts, this state-of-the-art collection covers the design and implementation of programs for the multigrid method, which first came to prominence in the late 1970s.Now considered a significant computational tool, the multigrid method has allowed substantial progress in the development of efficient, robust methods for solving field equations, and has made accessible new areas of computation, such as three-dimensional simulation. Indeed, in many cases, this method allows a realization of optimal algorithms, whose computational work grows linearly with the number of unknowns in a system of equations.With contributions by internationally recognized experts such as Achi Brandt, Wolfgang Hackbusch, Pieter Wesseling and Ulrich Trottenberg. ... Read more

Product Description
From the reviews of the First Edition: "Extremely clear, self-contained text . . . offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquées.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. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration. Other features include:* A new section on integral equations in higher dimensions.* An improved presentation of the Laplace and Fourier transforms.* A new detailed section for Fredholm integral equations of the first kind.* A new chapter covering the basic higher quadrature numerical integration rules.* A concise introduction to linear and nonlinear integral equations.* Clear examples of singular integral equations and their solutions.* A student's solutions manual available directly from the author. ... Read more

Customer Reviews (4)

One of the best integral equations textbooks
The book represents a well-written and richly illustrated by examples textbook for those who want to be introduced to the topic... The book...might be very useful forengineers and students. Special features, distinguishing the book from others...are simple exposition, ample examples, anddetailed solution manual forthe exercises.
Highly recommended.

Student's Solution Manual to accompany Introduction to integral equations with Appls., Samp. Publ.69 Leroy St Potsdam NY13676
The Solutions manual can be found at:

http://www.amazon.com/exec/obidos/tg/detail/-/0967330106/qid=1141351808/sr=1-3/ref=sr_1_3/104-2033616-3607961?v=glance&s=books

It is the only solution manual for a book in integral equations with solutions to the exercises and many extra problems.

Published by a different publisher than Wiley and Sons, it is
Sampling Publishing
(...)

An excellent introduction.
Clearly written, this book offers to the non-specialist the theoretical framework as well as the numerical methods of the integral equations (IE). The book does not require strong skills in maths. It provides a useful classification of the IE. The link between IE and Boundary Value problems is clearly explicited.

The book is formed as following:
1/IE, origin and basic tools
2/Modeling of problems as IE
3/Volterra IE
4/Green's function
5/Fredholm IE
6/Existence of the solutions; Basic fixed point theorems
7/Higher quadrature rules for numerical solutions
A/Hankel transforms
B/GF for various Bounadry Value problems
Answers to exercises

This book is intended for absolute beginners in IE. It is effectively an excellent introduction to the world of IE (see also the Hochstadt). Readers more familiar with should turn to Estrada & Kanwal, or to Muskhelishvili.

Integral Equations
Since the 19th century, integral equations have been used to solve physical and engineering problems instead differential equations. Only on the beginning of 20th century the theory of this kind of equations were properly formalized by Fredholm. On this book, the integral equation problem is presented to the reader and tools for solving them are also provided. Several examples of practical applications are given in the areas of mathematic, physics and engineering. This book is particularly useful for those who want study the Boundary Element Method, with is based on integral equations. ... Read more