Matrices And Tensors In Physics

Author : A. W. Joshi
Publisher : New Age International
Page : 364 pages
File Size : 46,8 Mb
Release : 1995
Category : Mathematics
ISBN : 8122405630

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Matrices and Tensors in Physics by A. W. Joshi Pdf

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.

Author : A. W. Joshi
Publisher : Unknown
Page : 289 pages
File Size : 53,6 Mb
Release : 1984
Category : Calculus of tensors
ISBN : 0852264380

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Matrices and Tensors in Physics by A. W. Joshi Pdf

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 41,7 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642

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Tensor Calculus for Physics by Dwight E. Neuenschwander Pdf

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"

Author : Anonim
Publisher : Unknown
Page : 283 pages
File Size : 49,9 Mb
Release : 1975
Category : Electronic
ISBN : OCLC:48069997

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Matrices and Tensors in Physics by Anonim Pdf

Author : M. C. Jain
Publisher : Unknown
Page : 284 pages
File Size : 47,8 Mb
Release : 2018-04-30
Category : Technology & Engineering
ISBN : 1783323760

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Vector Spaces, Matrices and Tensors in Physics by M. C. Jain Pdf

Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.

Author : Nadir Jeevanjee
Publisher : Birkhäuser
Page : 305 pages
File Size : 51,6 Mb
Release : 2015-03-11
Category : Science
ISBN : 9783319147949

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An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee Pdf

The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

Author : George Garfield Hall
Publisher : Unknown
Page : 128 pages
File Size : 53,6 Mb
Release : 1963
Category : Calculus of tensors
ISBN : UVA:X001408793

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Matrices and Tensors by George Garfield Hall Pdf

Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 47,8 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042193

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Manifolds, Tensors and Forms by Paul Renteln Pdf

Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.

Author : Günter Ludyk
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 51,7 Mb
Release : 2013-06-12
Category : Science
ISBN : 9783642357985

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Einstein in Matrix Form by Günter Ludyk Pdf

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 50,9 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894

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Tensor Network Contractions by Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein Pdf

Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Author : J. F. Nye
Publisher : Oxford University Press
Page : 356 pages
File Size : 52,8 Mb
Release : 1985
Category : Mathematics
ISBN : 0198511655

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Physical Properties of Crystals by J. F. Nye Pdf

First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.

Author : John A. Eisele,Robert M. Mason
Publisher : John Wiley & Sons
Page : 360 pages
File Size : 40,5 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015623088

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Applied Matrix and Tensor Analysis by John A. Eisele,Robert M. Mason Pdf

Author : Sharma,Sharma Vinod K.
Publisher : PHI Learning Pvt. Ltd.
Page : 498 pages
File Size : 50,5 Mb
Release : 2009-12
Category : Science
ISBN : 9788120338661

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Matrix Methods and Vector Spaces in Physics by Sharma,Sharma Vinod K. Pdf

They have wide applications in a number of subjects ranging from solid state physics, solid/fluid mechanics to relativity and electromagnetics. This well-written book gives, in an easy-to-read style, a step-by-step and comprehensive understanding about the various concepts, theories and applications of vector spaces, matrices and tensors. The book equips the reader with the fundamental knowledge in such subjects as matrix theory, linear algebraic equations, applications of eigenvalues and eigenvectors, diagonalisation process, quadratic forms, Cartesian tensors and more.

Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 47,9 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031

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What Are Tensors Exactly? by Hongyu Guo Pdf

Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.

Author : George E. Hay
Publisher : Courier Corporation
Page : 210 pages
File Size : 53,5 Mb
Release : 1953-01-01
Category : Mathematics
ISBN : 9780486601090

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Vector and Tensor Analysis by George E. Hay Pdf

"Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.