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Other titles in the Mathematical and Analytical Techniques with Applications to series:

Inverse Problems: Mathematical and Analytical Techniques with Applications to Engineering (Mathematical and Analytical Techniques with Applications to)

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Inverse Problems: Mathematical and Analytical Techniques with Applications to Engineering (Mathematical and Analytical Techniques with Applications to) Cover

 

Synopses & Reviews

Publisher Comments:

Inverse problems are the problems that consist of finding an unknown property of an object or a medium from the observation or a response of this object or a medium to a probing signal. Thus the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.) objects immersed in water (submarines, fish) and in many other situations. This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter. New results include recovery of a potential from I-function and applications to classical and new inverse scattering and spectral problems, study of inverse problems with"incomplete data", study of some new inverse problems for parabolic and hyperbolic equations, discussion of some non-overdetermined inverse problems, a study of inverse problems arising in the theory of ground-penetrating radars, development of DSM (dynamical systems method) for solving ill-posed nonlinear operator equations, comparison of the Ramm's inversion method for solving fixed-energy inverse scattering problem with the method based on the Dirichlet-to-Neumann map, derivation of the range of applicability and error estimates for Born's inversion, a study of some integral geometry problems, including tomography, inversion formulas for the spherical means, proof of the invertibility of the steps in the Gel'fand-Levitan and Marchenko inversion procedures, derivation of the inversion formulas and stability estimates for the multidimensional inverse scattering problems with fixed-energy noisy discrete data, new uniqueness and stability results in obstacle inverse scattering, formulation and a solution of an inverse problem of radiomeasurements, methods for finding small inhomogeneities from surface scattering data.

Synopsis:

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Table of Contents

Introduction.- Methods of soliving ill-posed problems.- One-dimensional inverse scattering and spectral problems.- Inverse obstacle scattering.- Stability of the solution to 3D Inverse scattering problems with fixed-energy data.- Non-uniqueness and uniqueness results.- Inverse problems of potential theory and other inverse source problems.- Non-overdetermined inverse problems.- Low-frequency inversions.- Wave scattering by small bodies of arbitrary shapes.- The Pompeiu problem.- Bilbliographical Notes.- References.- Index.

Product Details

ISBN:
9780387231952
Author:
Ramm, Alexander G.
Publisher:
Springer Science+Business Media
Author:
Ramm, A. G.
Subject:
Engineering - General
Subject:
Applied
Subject:
Computer Graphics - General
Subject:
Engineering mathematics
Subject:
Inverse problems (Differential equations)
Subject:
Computer graphics
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Theoretical, Mathematical and Computational Physics
Subject:
Image Processing and Computer Vision
Subject:
ordinary differential equations
Subject:
Engineering-General Engineering
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Mathematical and Analytical Techniques with Applications to Engineering
Publication Date:
20041216
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
462
Dimensions:
235 x 155 mm 1830 gr

Related Subjects

Computers and Internet » Graphics » General
Engineering » Engineering » General Engineering
Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Applied

Inverse Problems: Mathematical and Analytical Techniques with Applications to Engineering (Mathematical and Analytical Techniques with Applications to) New Hardcover
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Product details 462 pages Springer Science+Business Media - English 9780387231952 Reviews:
"Synopsis" by , Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
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