[PDF] Tensors eBook

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 40,83 MB
Release : 2011-12-14
Category : Mathematics
ISBN : 0821869078

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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.

Author : Anadi Jiban Das
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 48,65 MB
Release : 2007-10-05
Category : Science
ISBN : 0387694692

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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.

Author : Siegfried Hess
Publisher : Springer
Page : 449 pages
File Size : 23,84 MB
Release : 2015-04-25
Category : Science
ISBN : 331912787X

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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.

Author : David Lovelock
Publisher : Courier Corporation
Page : 402 pages
File Size : 50,61 MB
Release : 2012-04-20
Category : Mathematics
ISBN : 048613198X

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Incisive, self-contained 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. Includes problems.

Author : Juan R. Ruiz-Tolosa
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 18,71 MB
Release : 2005-12-08
Category : Computers
ISBN : 3540270663

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This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 15,32 MB
Release : 2021-06-16
Category : Mathematics
ISBN : 9811241031

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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 : Nils K. Oeijord
Publisher : iUniverse
Page : 144 pages
File Size : 27,72 MB
Release : 2005-05-25
Category : Mathematics
ISBN : 0595801722

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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.

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 40,79 MB
Release : 2015
Category : Mathematics
ISBN : 142141564X

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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 : Rutherford Aris
Publisher : Courier Corporation
Page : 322 pages
File Size : 41,73 MB
Release : 2012-08-28
Category : Mathematics
ISBN : 048613489X

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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.

Author : Richard L. Bishop
Publisher : Courier Corporation
Page : 290 pages
File Size : 25,81 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486139239

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DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div