Applications Of Tensor Analysis
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Applications Of Tensor Analysis
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Author : A. J. McConnell
language : en
Publisher: Courier Corporation
Release Date : 1957-01-01
Applications Of Tensor Analysis written by A. J. McConnell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957-01-01 with Mathematics categories.
Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.
Tensor Analysis With Applications In Mechanics
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Author : Leonid P Lebedev
language : en
Publisher: World Scientific
Release Date : 2010-05-18
Tensor Analysis With Applications In Mechanics written by Leonid P Lebedev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-18 with Technology & Engineering categories.
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.
Vector And Tensor Analysis With Applications
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Author : A. I. Borisenko
language : en
Publisher: Courier Corporation
Release Date : 2012-08-28
Vector And Tensor Analysis With Applications written by A. I. Borisenko and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-28 with Mathematics categories.
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Applications Of Tensor Analysis In Continuum Mechanics
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Author : Victor A Eremeyev
language : en
Publisher: World Scientific
Release Date : 2018-07-10
Applications Of Tensor Analysis In Continuum Mechanics written by Victor A Eremeyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Technology & Engineering categories.
'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.
Tensor Analysis
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Author : Ivan Stephen Sokolnikoff
language : en
Publisher:
Release Date : 1964
Tensor Analysis written by Ivan Stephen Sokolnikoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
Tensor Calculus With Applications
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Author : Vladislav V Goldberg
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-29
Tensor Calculus With Applications written by Vladislav V Goldberg and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-29 with Science categories.
This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics.While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering.With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis.All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.
Principles And Applications Of Tensor Analysis
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Author : Matthew S Smith
language : en
Publisher:
Release Date : 2012-03-01
Principles And Applications Of Tensor Analysis written by Matthew S Smith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-01 with categories.
Application Of Tensor Analysis
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Author : A J (Albert Joseph) McConnell
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-09
Application Of Tensor Analysis written by A J (Albert Joseph) McConnell and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Advances On Tensor Analysis And Their Applications
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Author : Francisco Bulnes
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-09-09
Advances On Tensor Analysis And Their Applications written by Francisco Bulnes and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-09 with Mathematics categories.
This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite dimensional operators, and more.
Application Of Tensor Analysis
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Author : A. J. McConnell
language : en
Publisher:
Release Date : 1947
Application Of Tensor Analysis written by A. J. McConnell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1947 with categories.