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Tensor CalculusFundamental 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. read more Hide

Cartesian TensorsThis undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and... read more Hide

Tensor Properties of SolidsTensor Properties of Solids presents the phenomenological development of solid state properties represented as matter tensors in two parts: Part I on equilibrium tensor properties and Part II on transport tensor properties. Part I begins with an introduction to tensor notation, transformations, algebra, and calculus together with the matrix representations. Crystallography, as it relates to tensor properties of crystals, completes the background treatment. A generalized treatment of solidstate... read more Hide

Applications of Tensor AnalysisStandard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers. read more Hide

Vector and Tensor Analysis with ApplicationsConcise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Workedout problems and solutions. 1968 edition. read more Hide

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A Student's Guide to Vectors and TensorsVectors and tensors are among the most powerful problemsolving 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... read more Hide

Susceptibility Tensors for Nonlinear OpticsSusceptibility Tensors for Nonlinear Optics is a unique and invaluable reference book with accompanying software. Starting from basic principles, the book presents a detailed introduction to the concept of optical susceptibilities of crystalline media. Substantial appendices include useful tables of third, fourth, and fifthrank susceptibility tensors for major nonlinear optical effects. Integral to the book is an entirely original TURBO RANK software package (compatible with PCs running MSDOS... read more Hide

Vectors and Tensors in Engineering and PhysicsVectors and Tensors in Engineering and Physics develops the calculus of tensor fields and uses this mathematics to model the physical world. This new edition includes expanded derivations and solutions, and new applications. The book provides equations for predicting: the rotations of gyroscopes and other axisymmetric solids, derived from Euler's equations for the motion of rigid bodies; the temperature decays in quenched forgings, derived from the heat equation; the deformed shapes of twisted rods... read more Hide

Introduction to Diffusion Tensor ImagingThe concepts behind diffusion tensor imaging (DTI) are commonly difficult to grasp, even for magnetic resonance physicists. To make matters worse, a many more complex higherorder methods have been proposed over the last few years to overcome the now wellknown deficiencies of DTI. In Introduction to Diffusion Tensor Imaging: And Higher Order Models, these concepts are explained through extensive use of illustrations rather than equations to help readers gain a more intuitive understanding of the... read more Hide

Tensor and Vector AnalysisConcise and userfriendly, this collegelevel text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics.Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in threespace, transformation of coordinates in space and differentiation, tensor algebra... read more Hide

An Introduction to Linear Algebra and TensorsEminently readable and completely elementary, this treatment begins with linear spaces and ends with analytic geometry. Additional topics include multilinear forms, tensors, linear transformation, eigenvectors and eigenvalues, matrix polynomials, and more. More than 250 carefully chosen problems appear throughout the book, most with hints and answers. 1972 edition. read more Hide

Introduction to Vector and Tensor AnalysisA broad introductory treatment, this volume 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, fundamental notions in nspace, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition. read more Hide

Tensors, Differential Forms, and Variational Principles by David Lovelock & Hanno Rund, ISBN 9780486658407Tensors, Differential Forms, and Variational Principles

Introduction to Tensor Calculus, Relativity and CosmologyElementary introduction pays special attention to aspects of tensor calculus and relativity that students find most difficult. Contents include tensors in curved spaces and application to general relativity theory; black holes; gravitational waves; application of general relativity principles to cosmology. Numerous exercises. Solution guide available upon request. 1982 edition. read more Hide

An Introduction to Tensors and Group Theory for PhysicistsAn Introduction to Tensors and Group Theory for Physicists provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calculations with the abstract but more conceptual formulation found in many mathematical texts, the work will... read more Hide

The ScalarTensor Theory of GravitationThe scalartensor theory of gravitation is one of the most popular alternatives to Einstein's theory of gravitation. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of BransDicke theory. Topics covered include the cosmological constant problem, time variability of coupling constants, higher dimensional spacetime, branes and conformal transformations. The authors emphasise the physical... read more Hide

Tensors, Relativity, and CosmologyThis book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved spacetime, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy... read more Hide

Differential Tensor Algebras and their Module CategoriesThis volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras... read more Hide

Conformal Field Theories and Tensor CategoriesThe present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at theBeijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics... read more Hide

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New Developments in the Visualization and Processing of Tensor Fields by David H. Laidlaw & Anna Vilanova, ISBN 9783642273421New Developments in the Visualization and Processing of Tensor Fields

Tensors, Differential Forms, and Variational PrinciplesIncisive, selfcontained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments. read more Hide

General Relativity 3: Astrophysics with Tensor CalculusAll of modern astrophysics and cosmology stands on the foundation of General Relativity that is best expressed in tensors. This book, and its sequel, General Relativity 4: Astrophysics & Cosmology, present the clearest, most comprehensible, and most complete introduction to the tensor calculus of differential topology, which Einstein used to explain the cosmos. Derivations that are difficult to find elsewhere, are all collected here and explained in detail. This book presents all the principle tensors... read more Hide

Visualization and Processing of Tensors and Higher Order Descriptors for MultiValued DataArising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for MultiValued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties.Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current... read more Hide

Lectures on Tensor Categories and Modular FunctorsThis book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3dimensional topological quantum field theory, and 2dimensional modular functors (which naturally arise in 2dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the WessZuminoWitten modular functor. The idea that these topics... read more Hide

Tensor Algebra and Tensor Analysis for EngineersThere is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided... read more Hide

Tensor Analysis and Elementary Differential Geometry for Physicists and EngineersTensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics, and cybernetics.This book comprehensively presents topics, such as braket notation, tensor analysis, and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous... read more Hide

Introduction to Vector and Tensor Analysis by Robert C. Wrede, ISBN 9780486618791DescriptionText for advanced undergraduate and graduate students covers the algebra, differentiation, and integration of vectors, and the algebra and analysis of tensors, with emphasis on transformation theory read more Hide

Tensor Norms and Operator Ideals by A. Defant, K. Floret, ISBN 9780080872872DescriptionThe three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms... read more Hide
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20140829 17:22:34.101062