Download or read book What Are Tensors Exactly written by Hongyu Guo and published by World Scientific. This book was released on 2021-06-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensors written by Anadi Jiban Das and published by Springer Science & Business Media. This book was released on 2007-10-05 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Download or read book The Very Basics of Tensors written by Nils K. Oeijord and published by iUniverse. This book was released on 2005-05-25 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor calculus is a generalization of vector calculus, and comes near of being a universal language in physics. Physical laws must be independent of any particular coordinate system used in describing them. This requirement leads to tensor calculus. The only prerequisites for reading this book are a familiarity with calculus (including vector calculus) and linear algebra, and some knowledge of differential equations.
Download or read book Vector and Tensor Analysis with Applications written by A. I. Borisenko and published by Courier Corporation. This book was released on 2012-08-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Student s Guide to Vectors and Tensors written by Daniel A. Fleisch and published by Cambridge University Press. This book was released on 2011-09-22 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
Download or read book An Introduction to Tensors and Group Theory for Physicists written by Nadir Jeevanjee and published by Birkhäuser. This book was released on 2015-03-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Tensors and Their Applications written by Nazrul Islam and published by New Age International. This book was released on 2006-12 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.
Download or read book Manifolds Tensors and Forms written by Paul Renteln and published by Cambridge University Press. This book was released on 2014 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Download or read book Covariant Physics written by Moataz Emam and published by Oxford University Press, USA. This book was released on 2021-02-21 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for 2nd and 3rd year undergraduate students using the fundamental principle of covariance as a basis for studying classical mechanics, electrodynamics, the special theory of relativity, and the general theory of relativity, before moving on to more advanced topics of field theory, differential forms, and modified theories of gravity.
Download or read book Tensor Spaces and Exterior Algebra written by Takeo Yokonuma and published by American Mathematical Soc.. This book was released on 1992 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Download or read book Tensors Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Download or read book Introduction to Vector and Tensor Analysis written by Robert C. Wrede and published by Courier Corporation. This book was released on 2013-01-30 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.
Download or read book Tensors Relativity and Cosmology written by Mirjana Dalarsson and published by Academic Press. This book was released on 2015-07-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tensors and Riemannian Geometry written by Nail H. Ibragimov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-08-31 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
