Linear Integral Equations (Applied Mathematical Sciences Book 82) 3rd Edition by Rainer Kress (PDF)

Description

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 Hahn–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 methodsReviews 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)

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have not read much of this book. I am writing my review as a warning to others of what I’ve experienced.This is a “real” math book. It is not like Wazwaz, or a book specifically targeted towards scientists and engineers. Not to say that s&e would not be able to get anything out of this text, as the author attempts to give a background on Functional Analysis in his first chapter. The author states that calculus is all that is required to read this text. Perhaps that may be true if you learned calculus more rigorously. The reader should be familiar with the ideas of vector spaces, epsilon delta proofs, infimum supremum, etc. I would say a more realistic background is Linear Algebra and Real Analysis I. Perhaps the reader could read this text without LA and RA, but it will definitely be a struggle and you will have difficulty with the exercises (especially since there are no solutions).Overall I would say that the text is written in a semi-modern way. The author does occasionally reiterate theorems and/or definitions in his own words for further understanding. But examples are nonexistent, problems are scarce and their solutions are nonexistent. That begin said if you do have the required background to read the text, then the proofs are clear and the author states what he is doing and then does it. There is hardly ever any pondering and wondering what is going on as the author is very blatant in his language.I would prefer more examples to exemplify the theory. I do not think that this is much to ask for since the prerequisites are only calculus right?The problems are at the end of the chapter, and not sprinkled within the text. I tend to dislike this, but it is just preference. The problems are also not plentiful whatsoever. There are only a handful of problems in any given chapter (literally only 5 per chapter). How is the reader supposed to learn the subject that this author is so passionate about with such a limited amount of exercises? There should be plenty ranging in difficulty!And no solutions? Perhaps the reason why the author neglected to include solutions is because there are so few problems to begin with!?This book’s focus is on theorems, proofs, etc. (theory). This is not a book on how to solve integral equations like the books written by Wazwaz. I do not think his text would give sufficient background to read this book either. But I recommend Wazwaz anyways for some context and motivation for what you are learning.For the background of LA and RA I can recommend this book. If not, then perhaps learn the subject of analysis using a text of your choice. There are plenty of great MODERN texts to choose from. For an easy path you can use Speight, for a difficult path use Tao, for a comprehensive modern take on the subject use Zorich!

⭐It is a difficult book even I am a graduate in math. If you are interested in the field, I recommend you to buy. But if for general reading, most may not understand.

⭐Great book about integral equations. Inside you have everything. Very good introduction to functional analysis and to methods for integral equations, there are some great chapters about inverse problems and regularization…After this book you need just some introduction to numerical methods and you will know everything you need to know about integral equations.

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