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This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, 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 itself. Problems are included at the end of each chapter.

For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahnâ€“Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods

Reviews of earlier editions:

"This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution."

(Math. Reviews, 2000)

"This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)

- Series:
**Applied Mathematical Sciences 82** - Author:
**Rainer Kress (auth.)** - Year:
**2014** - Publisher:
**Springer-Verlag New York** - Language:
**English** - ISBN:
**978-1-4614-9592-5,978-1-4614-9593-2**

- File size:
**3 444 522** - Format:
**pdf**

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Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathemati...

This book presents the author's new method of two-stage maximization of likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, i...

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 equ...

The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. ItÂ introduces theÂ singular integral equations and their applications to researchers as well as graduate students of this fascinatin...

Hypersingular formulation of crack problems offers certain advantages in fracture analysis, such as having the unknown functions in the formulation directly related to the crack opening displacement and allowing for easy extraction of the crack tip stress...

This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems...

Definition of field through 1960, emphasizing work of PoincarĂ©, Liapounoff, PainlevĂ©, and Goursat. 137 problems.topics covered include differential equations of the first order, the Riccati equation and existence theorems, second order equations, elliptic...

INTRODUCTION TO THE THEORY OF LINEAR DIFFERENTIAL EQUATIONS BY E. G. C. PODJLE Fellow of New College, Oxford OXFORD AT THE CLARENDON PRESS 193d Oui, 1 oeuvre sort plus belle Dune forme au travail Rebelle, Vers, marbre, onyx, email TH. GAUTIEB iZmaux et Ca...

Honig C.S. Volterra Stieltjes-integral equations (NH 1975)(ISBN 0444108505)(169s)...

Design creative characters inspired by real people. Let Mike Mattesi show you how to use life drawing to discover the poses, features and personalities which form the basis of character and then build, develop and 'PUSH' your drawings to new heights of dr...

Praise for Working with Female Offenders"Encyclopedic in scope and full of very relevant work drawn from the fields of biology, psychology, criminology, and corrections, this book is a must-read for those working with girl and women offenders."â€”Meda Chesn...

Among the welter of books on critical pedagogy, this volume will be especially valued for its direct focus on early years and elementary educators. Benefiting from the considered views of two veteran teachers of critical pedagogy, the volume is far more t...

Drawing on her experiences as a Buddhist teacher in the tradition of Thich Nhat Hanh, Annabelle Zinser developed meditation and mindfulness practices for a variety of everyday situations and the transformation of emotional challenges. In short chapters th...

"Chomsky is a global phenomenon . . . he may be the most widely read American voice on foreign policy on the planet."â€”The New York Times Book Review"Ilan PappĂ© is Israel's bravest, most principled, most incisive historian."â€”John PilgerDescribed by a UN fa...

â€śIt is fun to figure out the puzzle of how children go about making sense of mathematics and then how to help teachers help kids.â€ťÂ John A. Van de Walle, Late of Virginia Commonwealth University Â This is the philosophy behind Elementary and Mi...

The articles in this volume describe problems and methods relevant to a better understanding of the pathogenesis of several diseases. The unifying theme is experimental pathology at sub-cellular levels, with emphasis on molecular cell pathology. The text ...

The role of nutrition in improving quality of life and combating disease is undeniable - and researchers from different disciplines are bringing their perspectives to bear on this fundamental topic. The 4-volume Encyclopedia of Human Nutrition, Third Edit...

"The most influential thinker, in my life, has been the psychologist Richard Nisbett. He basically gave me my view of the world." -Malcolm Gladwell, New York Times Book ReviewScientific and philosophical concepts can change the way we solve problems by he...