G.M.L. Gladwell's Books

Functional Analysis

Applications in Mechanics and Inverse Problems

By: Leonid P. Lebedev,Iosif I. Vorovich,G.M.L. Gladwell

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Functional Analysis

Applications in Mechanics and Inverse Problems

By: Leonid P. Lebedev,Iosif I. Vorovich,G.M.L. Gladwell

This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.

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Page Count

259

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402006675

ISBN 13

9781402006678

Inverse Problems in Scattering

An Introduction

By: G.M.L. Gladwell

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Inverse Problems in Scattering

An Introduction

By: G.M.L. Gladwell

Inverse Problems in Scattering exposes some of the mathematics which has been developed in attempts to solve the one-dimensional inverse scattering problem. Layered media are treated in Chapters 1--6 and quantum mechanical models in Chapters 7--10. Thus, Chapters 2 and 6 show the connections between matrix theory, Schur's lemma in complex analysis, the Levinson--Durbin algorithm, filter theory, moment problems and orthogonal polynomials. The chapters devoted to the simplest inverse scattering problems in quantum mechanics show how the Gel'fand--Levitan and Marchenko equations arose. The introduction to this problem is an excursion through the inverse problem related to a finite difference version of Schrödinger's equation. One of the basic problems in inverse quantum scattering is to determine what conditions must be imposed on the scattering data to ensure that they correspond to a regular potential, which involves Lebesque integrable functions, which are introduced in Chapter 9.

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369

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Springer Science & Business Media

Published Date

ISBN 10

9401120463

ISBN 13

9789401120463

Inverse Problems in Vibration

By: G.M.L. Gladwell

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Inverse Problems in Vibration

By: G.M.L. Gladwell

In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews

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Page Count

472

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Springer Science & Business Media

Published Date

ISBN 10

1402027214

ISBN 13

9781402027215

Inverse problems in vibration

By: G.M.L. Gladwell

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Inverse problems in vibration

By: G.M.L. Gladwell

The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theory is the determination of the natural frequencies (eigen frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties.

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Page Count

272

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401511780

ISBN 13

9789401511780

Inverse Problems in Scattering

An Introduction

By: G.M.L. Gladwell

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Inverse Problems in Scattering

An Introduction

By: G.M.L. Gladwell

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369

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ISBN 10

9401120463

ISBN 13

9789401120463

Contact Problems

The legacy of L.A. Galin

By: L. A. Galin

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Contact Problems

The legacy of L.A. Galin

By: L. A. Galin

L.A. Galin’s book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.

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Page Count

325

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Springer Science & Business Media

Published Date

ISBN 10

1402090439

ISBN 13

9781402090431

Functional Analysis

Applications in Mechanics and Inverse Problems

By: Leonid P. Lebedev,Iosif I. Vorovich,G.M.L. Gladwell

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Functional Analysis

Applications in Mechanics and Inverse Problems

By: Leonid P. Lebedev,Iosif I. Vorovich,G.M.L. Gladwell

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Page Count

254

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Springer

Published Date

ISBN 10

9401739641

ISBN 13

9789401739641

Book's by G.M.L. Gladwell

Functional Analysis

Functional Analysis

Inverse Problems in Scattering

Inverse Problems in Scattering

Inverse Problems in Vibration

Inverse Problems in Vibration

Inverse problems in vibration

Inverse problems in vibration

Inverse Problems in Scattering

Inverse Problems in Scattering

Contact Problems

Contact Problems

Functional Analysis

Functional Analysis

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