Lebedev Leonid P's Books

Applications Of Tensor Analysis In Continuum Mechanics

By: Victor A Eremeyev,Michael J Cloud,Leonid P Lebedev

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Applications Of Tensor Analysis In Continuum Mechanics

By: Victor A Eremeyev,Michael J Cloud,Leonid P Lebedev

A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.

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426

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World Scientific

Published Date

ISBN 10

9813238984

ISBN 13

9789813238985

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 Mathematics at the 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 stage the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them.

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256

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400901690

ISBN 13

9789400901698

Calculus Of Variations And Functional Analysis, The: With Optimal Control And Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud

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Calculus Of Variations And Functional Analysis, The: With Optimal Control And Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud

This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of “the calculus of variations”) and more modern topics (under the heading of “optimal control”). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.

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435

Publisher

World Scientific

Published Date

ISBN 10

9814485179

ISBN 13

9789814485173

Functional Analysis in Mechanics

By: Leonid P. Lebedev,Iosif I. Vorovich,Michael J. Cloud

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Functional Analysis in Mechanics

By: Leonid P. Lebedev,Iosif I. Vorovich,Michael J. Cloud

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics. Reviews of first edition: "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. ... Detailed solutions of the exercises are provided in an appendix." (L’Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises ... test the reader’s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

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316

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461458684

ISBN 13

9781461458685

Advanced Engineering Analysis: The Calculus Of Variations And Functional Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

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Advanced Engineering Analysis: The Calculus Of Variations And Functional Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study.

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500

Publisher

World Scientific

Published Date

ISBN 10

9814397547

ISBN 13

9789814397544

Introduction To Mathematical Elasticity

By: Leonid P Lebedev,Michael J Cloud

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Introduction To Mathematical Elasticity

By: Leonid P Lebedev,Michael J Cloud

This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability.Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems.

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317

Publisher

World Scientific

Published Date

ISBN 10

9814467790

ISBN 13

9789814467797

Foundations of Micropolar Mechanics

By: Victor A. Eremeyev,Leonid P. Lebedev,Holm Altenbach

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Foundations of Micropolar Mechanics

By: Victor A. Eremeyev,Leonid P. Lebedev,Holm Altenbach

The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the constitutive modeling, i.e. constitutive inequalities, symmetry groups, acceleration waves, etc.

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145

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642283535

ISBN 13

9783642283536

Inequalities

With Applications to Engineering

By: Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev

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Inequalities

With Applications to Engineering

By: Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev

This book offers a concise introduction to mathematical inequalities for graduate students and researchers in the fields of engineering and applied mathematics. It begins by reviewing essential facts from algebra and calculus and proceeds with a presentation of the central inequalities of applied analysis, illustrating a wide variety of practical applications. The text provides a gentle introduction to abstract spaces, such as metric, normed and inner product spaces. It also provides full coverage of the central inequalities of applied analysis, such as Young's inequality, the inequality of the means, Hölder's inequality, Minkowski's inequality, the Cauchy–Schwarz inequality, Chebyshev's inequality, Jensen's inequality and the triangle inequality. The second edition features extended coverage of applications, including continuum mechanics and interval analysis. It also includes many additional examples and exercises with hints and full solutions that may appeal to upper-level undergraduate and graduate students, as well as researchers in engineering, mathematics, physics, chemistry or any other quantitative science.

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Page Count

249

Publisher

Springer

Published Date

ISBN 10

3319053116

ISBN 13

9783319053110

Approximating Perfection

A Mathematician's Journey into the World of Mechanics

By: Leonid P. Lebedev,Michael J. Cloud

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Approximating Perfection

A Mathematician's Journey into the World of Mechanics

By: Leonid P. Lebedev,Michael J. Cloud

This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

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233

Publisher

Princeton University Press

Published Date

ISBN 10

0691168261

ISBN 13

9780691168265

Tensor Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

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Tensor Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems.This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells.The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems — most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book.

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378

Publisher

World Scientific

Published Date

ISBN 10

9814464503

ISBN 13

9789814464505

Tensor Analysis

By: L. P. Lebedev,Michael J. Cloud

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Tensor Analysis

By: L. P. Lebedev,Michael J. Cloud

Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuumdescription. This concise text offers a straightforward treatment ofthe subject suitable for the student or practicing engineer

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208

Publisher

World Scientific

Published Date

ISBN 10

9812564462

ISBN 13

9789812564467

Tensor Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

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Tensor Analysis With Applications In Mechanics

By: Leonid P Lebedev,Michael J Cloud,Victor A Eremeyev

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378

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World Scientific

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9814464503

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9789814464505

Applications Of Tensor Analysis In Continuum Mechanics

By: Victor A Eremeyev,Michael J Cloud,Leonid P Lebedev

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Applications Of Tensor Analysis In Continuum Mechanics

By: Victor A Eremeyev,Michael J Cloud,Leonid P Lebedev

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426

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World Scientific

Published Date

ISBN 10

9813238984

ISBN 13

9789813238985

Inequalities

With Applications to Engineering

By: Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev

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Inequalities

With Applications to Engineering

By: Michael J. Cloud,Byron C. Drachman,Leonid P. Lebedev

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Page Count

249

Publisher

Springer

Published Date

ISBN 10

3319053116

ISBN 13

9783319053110

Foundations of Micropolar Mechanics

By: Victor A. Eremeyev,Leonid P. Lebedev,Holm Altenbach

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Foundations of Micropolar Mechanics

By: Victor A. Eremeyev,Leonid P. Lebedev,Holm Altenbach

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145

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Springer Science & Business Media

Published Date

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3642283535

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9783642283536

Functional Analysis in Mechanics

By: Leonid P. Lebedev,Iosif I. Vorovich,Michael J. Cloud

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Functional Analysis in Mechanics

By: Leonid P. Lebedev,Iosif I. Vorovich,Michael J. Cloud

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310

Publisher

Springer

Published Date

ISBN 10

1461458692

ISBN 13

9781461458692

Approximating Perfection

A Mathematician's Journey into the World of Mechanics

By: Leonid P. Lebedev,Michael J. Cloud

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Approximating Perfection

A Mathematician's Journey into the World of Mechanics

By: Leonid P. Lebedev,Michael J. Cloud

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Page Count

234

Publisher

Princeton University Press

Published Date

ISBN 10

1400873258

ISBN 13

9781400873258

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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