Download or read book Physical Components of Tensors written by Wolf Altman and published by CRC Press. This book was released on 2018-10-08 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory of physical and anholonomic components of tensors and applies the theory of dimensional analysis to tensors and (anholonomic) connections. This theory shows the relationship and compatibility among several existing definitions of physical components of tensors when referred to nonorthogonal coordinates. The book assumes a basic knowledge of linear algebra and elementary calculus, but revisits these subjects and introduces the mathematical backgrounds for the theory in the first three chapters. In addition, all field equations are also given in physical components as well. Comprised of five chapters, this noteworthy text: Deals with the basic concepts of linear algebra, introducing the vector spaces and the further structures imposed on them by the notions of inner products, norms, and metrics Focuses on the main algebraic operations for vectors and tensors and also on the notions of duality, tensor products, and component representation of tensors Presents the classical tensor calculus that functions as the advanced prerequisite for the development of subsequent chapters Provides the theory of physical and anholonomic components of tensors by associating them to the spaces of linear transformations and of tensor products and advances two applications of this theory Physical Components of Tensors contains a comprehensive account of tensor calculus, and is an essential reference for graduate students or engineers concerned with solid and structural mechanics.
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 Vectors Tensors and the Basic Equations of Fluid Mechanics written by Rutherford Aris and published by Courier Corporation. This book was released on 2012-08-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Download or read book Physical Properties of Crystals written by J. F. Nye and published by Oxford University Press. This book was released on 1985 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tensor Properties of Crystals Second Edition written by D Lovett and published by CRC Press. This book was released on 1999-01-01 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of single crystals for scientific and technological applications is now widespread in solid-state physics, optics, electronics, materials science, and geophysics. An understanding of the variation of physical properties with crystalline direction is essential to maximize the performance of solid-state devices. Written from a physical viewpoint and avoiding advanced mathematics, Tensor Properties of Crystals provides a concise introduction to the tensor properties of crystals at a level suitable for advanced undergraduate and graduate students. While retaining the successful basic format of the well-known first edition, this second edition brings the material up to date with the latest developments in nonlinear optics and modulated structures. Because of the increasing importance of nonlinear optics, a new chapter on optoelectronics has been added. This edition also includes a short discussion on incommensurate modulated structures in the final chapter because they are relevant to high temperature superconductors and to ferroelectric and ferromagnetic materials. The book extensively contains diagrams, worked examples, and problems with answers throughout.
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 Introduction to Vectors and Tensors written by Ray M. Bowen and published by Springer. This book was released on 1976-05-31 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
Download or read book Tensor Analysis on Manifolds written by Richard L. Bishop and published by Courier Corporation. This book was released on 2012-04-26 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
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 317 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 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 Tensors for Physics written by Siegfried Hess and published by Springer. This book was released on 2015-04-25 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.
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 Tensor Analysis and Continuum Mechanics written by Wilhelm Flügge and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Download or read book Tensor Calculus for Physics written by Dwight E. Neuenschwander and published by JHU Press. This book was released on 2015 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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"
Download or read book Quantities Units and Symbols in Physical Chemistry written by International Union of Pure and Applied Chemistry. Physical and Biophysical Chemistry Division and published by Royal Society of Chemistry. This book was released on 2007 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prepared by the IUPAC Physical Chemistry Division this definitive manual, now in its third edition, is designed to improve the exchange of scientific information among the readers in different disciplines and across different nations. This book has been systematically brought up to date and new sections added to reflect the increasing volume of scientific literature and terminology and expressions being used. The Third Edition reflects the experience of the contributors with the previous editions and the comments and feedback have been integrated into this essential resource. This edition has been compiled in machine-readable form and will be available online.
Download or read book Mathematical Techniques and Physical Applications written by J Killingbeck and published by Elsevier. This book was released on 2012-12-02 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Techniques and Physical Applications provides a wide range of basic mathematical concepts and methods, which are relevant to physical theory. This book is divided into 10 chapters that cover the different branches of traditional mathematics. This book deals first with the concept of vector, matrix, and tensor analysis. These topics are followed by discussions on several theories of series relevant to physics; the fundamentals of complex variables and analytic functions; variational calculus for presenting the basic laws of many branches of physics; and the applications of group representations. The final chapters explore some partial and integral equations and derivatives of physics, as well as the concept and application of probability theory. Physics teachers and students will greatly appreciate this book.
Download or read book Tensor Calculus written by J. L. Synge and published by Courier Corporation. This book was released on 2012-04-26 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
