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Physical Components Of Tensors
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Book Synopsis Physical Components of Tensors by : Wolf Altman
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.
Book Synopsis A Note on Physical Components of Tensors by : Luigi Morino
Download or read book A Note on Physical Components of Tensors written by Luigi Morino and published by . This book was released on 1972 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tensor Calculus by : John Lighton Synge
Download or read book Tensor Calculus written by John Lighton Synge and published by Courier Corporation. This book was released on 1978-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an excellent classroom text, since it is clearly written, contains numerous problems and exercises, and at the end of each chapter has a summary of the significant results of the chapter." — Quarterly of Applied Mathematics. Fundamental introduction for beginning student 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, special types of space, relative tensors, ideas of volume, and more.
Book Synopsis Polyadics and Physical Components of Tensors by : Kent Gardner Stansberry
Download or read book Polyadics and Physical Components of Tensors written by Kent Gardner Stansberry and published by . This book was released on 1967 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Tensor Calculus by : Jacques L. Mercier
Download or read book An Introduction to Tensor Calculus written by Jacques L. Mercier and published by . This book was released on 1971 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Physical Properties of Crystals by : J. F. Nye
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.
Book Synopsis A Brief on Tensor Analysis by : J.G. Simmonds
Download or read book A Brief on Tensor Analysis written by J.G. Simmonds and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: When I was an undergraduate, working as a co-op student at North American Aviation, I tried to learn something about tensors. In the Aeronautical En gineering Department at MIT, I had just finished an introductory course in classical mechanics that so impressed me that to this day I cannot watch a plane in flight-especially in a tum-without imaging it bristling with vec tors. Near the end of the course the professor showed that, if an airplane is treated as a rigid body, there arises a mysterious collection of rather simple looking integrals called the components of the moment of inertia tensor. Tensor-what power those two syllables seemed to resonate. I had heard the word once before, in an aside by a graduate instructor to the cognoscenti in the front row of a course in strength of materials. "What the book calls stress is actually a tensor. . . ." With my interest twice piqued and with time off from fighting the brush fires of a demanding curriculum, I was ready for my first serious effort at self instruction. In Los Angeles, after several tries, I found a store with a book on tensor analysis. In my mind I had rehearsed the scene in which a graduate stu dent or professor, spying me there, would shout, "You're an undergraduate.
Book Synopsis Tensors and Their Applications by : Nazrul Islam
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.
Book Synopsis Vectors, Tensors and the Basic Equations of Fluid Mechanics by : Rutherford Aris
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.
Book Synopsis What Are Tensors Exactly? by : Hongyu Guo
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 Applied Elasticity written by J D Renton and published by Elsevier. This book was released on 2002-12-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987 Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approach Uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis
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.
Book Synopsis Vector and Tensor Analysis by : George E. Hay
Download or read book Vector and Tensor Analysis written by George E. Hay and published by Courier Corporation. This book was released on 1953-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Tensors for Physics by : Siegfried Hess
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.
Book Synopsis Cartesian Tensors in Engineering Science by : L. G. Jaeger
Download or read book Cartesian Tensors in Engineering Science written by L. G. Jaeger and published by Elsevier. This book was released on 2016-06-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cartesian Tensors in Engineering Science provides a comprehensive discussion of Cartesian tensors. The engineer, when working in three dimensions, often comes across quantities which have nine components. Variation of the components in a given plane may be shown graphically by a familiar construction called Mohr's circle. For such quantities it is always possible to find three mutually perpendicular axes, called principal axes, with respect to which the six ""paired up"" components are all zero. Such quantities are called symmetric tensors of the second order. The student may at this stage be struck by the fact that the physical quantities with which he normally deals have either one component, three components or nine components, being respectively scalars, vectors, and what have just been called second order tensors. The family of quantities having 1, 3, 9, 27, ... components does exist. It is the tensor family in three dimensions. The book discusses the ""tests"" a given quantity must pass in order to qualify as a member of the family. The products of tensors, elasticity, and second moment of area and moment of inertia are also covered. Although written primarily for engineers, it is hoped that students of various branches of physical science may find this book useful.
Book Synopsis Introduction to Vectors and Tensors by : Ray M. Bowen
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.
Book Synopsis Elements of Tensor Calculus by : André Lichnerowicz
Download or read book Elements of Tensor Calculus written by André Lichnerowicz and published by . This book was released on 1962 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
