Tensor Calculus For Physics
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Tensor Calculus For Physics
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Author : Dwight E. Neuenschwander
language : en
Publisher: JHU Press
Release Date : 2015
Tensor Calculus For Physics written by Dwight E. Neuenschwander and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.--Gary White, editor of The Physics Teacher "American Journal of Physics"
An Introduction To Tensor Calculus
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Author : Derek F. Lawden
language : en
Publisher: Courier Corporation
Release Date : 2012-03-07
An Introduction To Tensor Calculus written by Derek F. Lawden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-07 with Science categories.
This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.
Tensor Calculus
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Author : J. L. Synge
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Tensor Calculus written by J. L. Synge and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.
Tensor Analysis For Physicists
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Author : Jan Arnoldus Schouten
language : en
Publisher: Courier Corporation
Release Date : 1989-01-01
Tensor Analysis For Physicists written by Jan Arnoldus Schouten and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Science categories.
This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.
Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds
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Author : Uwe Mühlich
language : en
Publisher: Springer
Release Date : 2017-04-18
Fundamentals Of Tensor Calculus For Engineers With A Primer On Smooth Manifolds written by Uwe Mühlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Science categories.
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Tensor Calculus With Applications
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Author : Goldberg Vladislav V
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-09-29
Tensor Calculus With Applications written by Goldberg Vladislav V 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.
Matrices And Tensors In Physics
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Author : A. W. Joshi
language : en
Publisher: New Age International
Release Date : 1995
Matrices And Tensors In Physics written by A. W. Joshi and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The First Part Of This Book Begins With An Introduction To Matrices Through Linear Transformations On Vector Spaces, Followed By A Discussion On The Algebra Of Matrices, Special Matrices, Linear Equations, The Eigenvalue Problem, Bilinear And Quadratic Forms, Kronecker Sum And Product Of Matrices. Other Matrices Which Occur In Physics, Such As The Rotation Matrix, Pauli Spin Matrices And Dirac Matrices, Are Then Presented. A Brief Account Of Infinite Matrices From The Point Of View Of Matrix Formulation Of Quantum Mechanics Is Also Included. The Emphasis In This Part Is On Linear Dependence And Independence Of Vectors And Matrices, Linear Combinations, Independent Parameters Of Various Special Matrices And Such Other Concepts As Help The Student In Obtaining A Clear Understanding Of The Subject. A Simplified Proof Of The Theorem That A Common Set Of Eigenvectors Can Be Found For Two Commuting Matrices Is Given. The Second Part Deals With Cartesian And General Tensors. Many Physical Situations Are Discussed Which Require The Use Of Second And Higher Rank Tensors, Such As Effective Mass Tensor, Moment Of Inertia Tensor, Stress, Strain And Elastic Constants, Piezoelectric Strain Coefficient Tensor, Etc. Einsteins Summation Convention Is Explained In Detail And Common Errors Arising In Its Use Are Pointed Out. Rules For Checking The Correctness Of Tensor Equations Are Given. This Is Followed By Four-Vectors In Special Relativity And Covarient Formulation Of Electrodynamics. This Part Comes To An End With The Concept Of Parallel Displacement Of Vectors In Riemannian Space And Covariant Derivative Of Tensors, Leading To The Curvature Tensors And Its Properties.Appendix I Has Expanded And Two New Appendices Have Been Added In This Edition.
Introduction To Tensor Calculus Relativity And Cosmology
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Author : Derek F. Lawden
language : en
Publisher:
Release Date : 2002
Introduction To Tensor Calculus Relativity And Cosmology written by Derek F. Lawden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Tensor Calculus For Engineers And Physicists
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Author : Emil de Souza Sánchez Filho
language : en
Publisher: Springer
Release Date : 2016-05-20
Tensor Calculus For Engineers And Physicists written by Emil de Souza Sánchez Filho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-20 with Technology & Engineering categories.
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.
An Introduction To Tensor Calculus And Relativity
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Author : Derek Frank Lawden
language : en
Publisher:
Release Date : 2013-08
An Introduction To Tensor Calculus And Relativity written by Derek Frank Lawden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08 with categories.