An Introduction To Inverse Problems In Physics PDF Download
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| Author | : Mohsen Razavy |
| Publisher | : World Scientific |
| Total Pages | : 387 |
| Release | : 2020-05-21 |
| Genre | : Science |
| ISBN | : 9811221685 |
Download An Introduction To Inverse Problems In Physics Book in PDF, ePub and Kindle
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.
| Author | : Alemdar Hasanov Hasanoğlu |
| Publisher | : Springer |
| Total Pages | : 261 |
| Release | : 2017-07-31 |
| Genre | : Mathematics |
| ISBN | : 331962797X |
Download Introduction to Inverse Problems for Differential Equations Book in PDF, ePub and Kindle
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.
| Author | : M. Bertero |
| Publisher | : CRC Press |
| Total Pages | : 366 |
| Release | : 2020-08-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9781439822067 |
Download Introduction to Inverse Problems in Imaging Book in PDF, ePub and Kindle
This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.
| Author | : Global Express Ltd. Co. |
| Publisher | : CRC Press |
| Total Pages | : 736 |
| Release | : 2000-03-21 |
| Genre | : Mathematics |
| ISBN | : 9780824719876 |
Download Methods for Solving Inverse Problems in Mathematical Physics Book in PDF, ePub and Kindle
Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.
| Author | : Andreas Kirsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2011-03-24 |
| Genre | : Mathematics |
| ISBN | : 1441984747 |
Download An Introduction to the Mathematical Theory of Inverse Problems Book in PDF, ePub and Kindle
This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.
| Author | : Z.S. Agranovich |
| Publisher | : Courier Dover Publications |
| Total Pages | : 307 |
| Release | : 2020-05-21 |
| Genre | : Mathematics |
| ISBN | : 0486842495 |
Download The Inverse Problem of Scattering Theory Book in PDF, ePub and Kindle
This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.
| Author | : Vladimir Gavrilovich Romanov |
| Publisher | : BRILL |
| Total Pages | : 260 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 9789067640565 |
Download Inverse Problems of Mathematical Physics Book in PDF, ePub and Kindle
| Author | : Charles W. Groetsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 159 |
| Release | : 2013-12-14 |
| Genre | : Technology & Engineering |
| ISBN | : 3322992020 |
Download Inverse Problems in the Mathematical Sciences Book in PDF, ePub and Kindle
Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.
| Author | : Khosrow Chadan |
| Publisher | : SIAM |
| Total Pages | : 206 |
| Release | : 1997-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898713870 |
Download An Introduction to Inverse Scattering and Inverse Spectral Problems Book in PDF, ePub and Kindle
Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.
| Author | : Jennifer L. Mueller |
| Publisher | : SIAM |
| Total Pages | : 349 |
| Release | : 2012-11-30 |
| Genre | : Mathematics |
| ISBN | : 1611972337 |
Download Linear and Nonlinear Inverse Problems with Practical Applications Book in PDF, ePub and Kindle
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
