Provides a broad survey of integral equation methods in scattering theory, including both the direct and inverse problems. Presents a mathematical treatment of acoustic and electromagnetic waves. Covers basic properties of solutions to the Helmholtz and Maxwell equations. Includes discussions on the Riesz-Fredholm theory of compact operations, entire functions of a complex variable, univalent function theory, improperly posed problems, and weak compactness.

Integral Equation Methods in Scattering Theory (Pure & Applied Mathematics)

Science & Math

Colton, David

Kress, Rainer

Mathematics

wiley

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.

Integral Equation Methods in Scattering Theory

Colton, David L.

Krieger Pub. Co

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory.
Review of earlier editions:
“Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.”
SIAM Review, September 1994
“This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.”
Mathematical Intelligencer, June 1994

Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences, 93)

Computers & Technology

Computer Science

Springer

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 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)

Linear Integral Equations (Applied Mathematical Sciences, 82)

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) 

This classic book provides a rigorous treatment of the Riesz-Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and Hölder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations.
 Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and Hölder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
 Audience: Integral Equation Methods in Scattering Theory can be used as a supplemental text in a graduate course on scattering theory or inverse problems and will also be of interest to research scientists in mathematics, physics, and engineering.
 Contents: Preface to the Classics Edition; Preface; Symbols; Chapter 1: The Riesz-Fredholm Theory for Compact Operators; Chapter 2: Regularity Properties of Surface Potentials; Chapter 3: Boundary-Value Problems for the Scalar Helmholtz Equation; Chapter 4: Boundary-Value Problems for the Time-Harmonic Maxwell Equations and the Vector Helmholtz Equation; Chapter 5: Low Frequency Behavior of Solutions to Boundary-Value Problems in Scattering Theory; Chapter 6: The Inverse Scattering Problem: Exact Data; Chapter 7: Improperly Posed Problems and Compact Families; Chapter 8: The Determination of the Shape of an Obstacle from Inexact Far-Field Data; Chapter 9: Optimal Control Problems in Radiation and Scattering Theory; References; Index.

Integral Equation Methods in Inverse Scattering Theory (Classics in Applied Mathematics)

Society for Industrial and Applied Mathematics

The inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. 
In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.

The inverse scattering problem is central to many areas of science and&nbsp;technology such as radar, sonar, medical imaging, geophysical exploration&nbsp;and nondestructive testing. This book is devoted to the mathematical and&nbsp;numerical analysis of the inverse scattering problem for acoustic and&nbsp;electromagnetic waves.&nbsp; In this fourth edition, a number of significant additions have been made including a new chapter&nbsp;on transmission eigenvalues and a new section on the impedance boundary condition where particular&nbsp;attention has been made to the generalized impedance boundary condition and to&nbsp;nonlocal impedance boundary conditions. Brief&nbsp;discussions on the generalized linear sampling method, the method of&nbsp;recursive linearization, anisotropic media and the use of target signatures&nbsp;in inverse scattering theory have also been added.

Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences)

At the Conference in Oberwolfach organized by Prof. R. Kress and Prof. J. Wick questions on mathematical methods of plasmaphysics were being dealt with. This book contains the papers presented at this Conference by the following mathematicians and physicists: Klaus Elsässer, K. Graf Finck von Finckenstein, R.J. Gribben, E.J. Parkes, R. Keil, K. Knorr/M. Mond, S. Kuhn, H. Schamel, G. Spindler, B. Steffen, P. Vachenauer, J. Vogel, H.U. Schmidt/ R. Wegmann, J. Denavit, H. Neunzert/J. Wick, and Sh. Kaniel.

Mathematical Methods of Plasmaphysics: Proceedings of a Conference held in Oberwolfach, September 16-22, 1979 (Methoden und Verfahren der mathematischen Physik)

Wick, Joachim

Peter Lang GmbH, Internationaler Verlag der Wissenschaften

See the best price to sell, buy, or rent books by Kress, Rainer. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Kress, Rainer

See the best price to sell, buy, or rent books by Kress, Rainer. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Integral Equation Methods in Scattering Theory (Pure & Applied Mathematics)

Integral Equation Methods in Scattering Theory

Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences, 93)

Linear Integral Equations (Applied Mathematical Sciences, 82)

Linear Integral Equations (Applied Mathematical Sciences, 82)

Integral Equation Methods in Inverse Scattering Theory (Classics in Applied Mathematics)

Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences, 93)

Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences)

Mathematical Methods of Plasmaphysics: Proceedings of a Conference held in Oberwolfach, September 16-22, 1979 (Methoden und Verfahren der mathematischen Physik)