Tensors

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Tensors

Author : Anadi Jiban Das
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 40,5 Mb
Release : 2007-10-05
Category : Science
ISBN : 9780387694696

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Tensors by Anadi Jiban Das Pdf

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.

Tensors, Differential Forms, and Variational Principles

Author : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 55,7 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131986

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Tensors, Differential Forms, and Variational Principles by David Lovelock,Hanno Rund Pdf

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.

Tensors: Geometry and Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 40,7 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

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Tensors: Geometry and Applications by J. M. Landsberg Pdf

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.

From Vectors to Tensors

Author : Juan R. Ruiz-Tolosa,Enrique Castillo
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 46,9 Mb
Release : 2005-12-08
Category : Computers
ISBN : 9783540270669

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From Vectors to Tensors by Juan R. Ruiz-Tolosa,Enrique Castillo Pdf

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.

Energy Momentum Tensors

Author : Robert Hermann
Publisher : Math-Sci Press
Page : 132 pages
File Size : 48,5 Mb
Release : 1973
Category : Mathematics
ISBN : 0915692031

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Energy Momentum Tensors by Robert Hermann Pdf

Tensors for Physics

Author : Siegfried Hess
Publisher : Springer
Page : 449 pages
File Size : 45,9 Mb
Release : 2015-04-25
Category : Science
ISBN : 9783319127873

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Tensors for Physics by Siegfried Hess Pdf

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.

Tensors made easy

Author : Giancarlo Bernacchi
Publisher : Lulu.com
Page : 184 pages
File Size : 40,9 Mb
Release : 2019-09-10
Category : Calculus of tensors
ISBN : 9781326230975

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Tensors made easy by Giancarlo Bernacchi Pdf

--New September 2019 revised edition --A friendly and non-formal approach to a subject of abstract mathematics that has important applications in physics, especially in General Relativity, but also in other fields. The purpose of the book is mainly didactic and requires a minimum of mathematical background (calculus, partial derivatives included). See also enlarged edition ""Tensors made easy with SOLVED PROBLEMS""

Tensor Calculus

Author : John Lighton Synge,Alfred Schild
Publisher : Courier Corporation
Page : 340 pages
File Size : 46,5 Mb
Release : 1978-01-01
Category : Mathematics
ISBN : 0486636127

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Tensor Calculus by John Lighton Synge,Alfred Schild Pdf

"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.

Tensor Analysis with Applications in Mechanics

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 378 pages
File Size : 52,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814313995

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Tensor Analysis with Applications in Mechanics by L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev Pdf

1. Preliminaries. 1.1. The vector concept revisited. 1.2. A first look at tensors. 1.3. Assumed background. 1.4. More on the notion of a vector. 1.5. Problems -- 2. Transformations and vectors. 2.1. Change of basis. 2.2. Dual bases. 2.3. Transformation to the reciprocal frame. 2.4. Transformation between general frames. 2.5. Covariant and contravariant components. 2.6. The cross product in index notation. 2.7. Norms on the space of vectors. 2.8. Closing remarks. 2.9. Problems -- 3. Tensors. 3.1. Dyadic quantities and tensors. 3.2. Tensors from an operator viewpoint. 3.3. Dyadic components under transformation. 3.4. More dyadic operations. 3.5. Properties of second-order tensors. 3.6. Eigenvalues and eigenvectors of a second-order symmetric tensor. 3.7. The Cayley-Hamilton theorem. 3.8. Other properties of second-order tensors. 3.9. Extending the Dyad idea. 3.10. Tensors of the fourth and higher orders. 3.11. Functions of tensorial arguments. 3.12. Norms for tensors, and some spaces. 3.13. Differentiation of tensorial functions. 3.14. Problems -- 4. Tensor fields. 4.1. Vector fields. 4.2. Differentials and the nabla operator. 4.3. Differentiation of a vector function. 4.4. Derivatives of the frame vectors. 4.5. Christoffel coefficients and their properties. 4.6. Covariant differentiation. 4.7. Covariant derivative of a second-order tensor. 4.8. Differential operations. 4.9. Orthogonal coordinate systems. 4.10. Some formulas of integration. 4.11. Problems -- 5. Elements of differential geometry. 5.1. Elementary facts from the theory of curves. 5.2. The torsion of a curve. 5.3. Frenet-Serret equations. 5.4. Elements of the theory of surfaces. 5.5. The second fundamental form of a surface. 5.6. Derivation formulas. 5.7. Implicit representation of a curve; contact of curves. 5.8. Osculating paraboloid. 5.9. The principal curvatures of a surface. 5.10. Surfaces of revolution. 5.11. Natural equations of a curve. 5.12. A word about rigor. 5.13. Conclusion. 5.14. Problems -- 6. Linear elasticity. 6.1. Stress tensor. 6.2. Strain tensor. 6.3. Equation of motion. 6.4. Hooke's law. 6.5. Equilibrium equations in displacements. 6.6. Boundary conditions and boundary value problems. 6.7. Equilibrium equations in stresses. 6.8. Uniqueness of solution for the boundary value problems of elasticity. 6.9. Betti's reciprocity theorem. 6.10. Minimum total energy principle. 6.11. Ritz's method. 6.12. Rayleigh's variational principle. 6.13. Plane waves. 6.14. Plane problems of elasticity. 6.15. Problems -- 7. Linear elastic shells. 7.1. Some useful formulas of surface theory. 7.2. Kinematics in a neighborhood of [symbol]. 7.3. Shell equilibrium equations. 7.4. Shell deformation and strains; Kirchhoff's hypotheses. 7.5. Shell energy. 7.6. Boundary conditions. 7.7. A few remarks on the Kirchhoff-Love theory. 7.8. Plate theory. 7.9. On Non-classical theories of plates and shells

What Are Tensors Exactly?

Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 47,6 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031

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What Are Tensors Exactly? by Hongyu Guo Pdf

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.

Tensor Calculus for Physics

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 44,8 Mb
Release : 2015
Category : Mathematics
ISBN : 9781421415642

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Tensor Calculus for Physics by Dwight E. Neuenschwander Pdf

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"

Introduction to General Relativistic and Scalar-tensor Cosmologies

Author : Marcelo Samuel Berman
Publisher : Nova Publishers
Page : 284 pages
File Size : 40,6 Mb
Release : 2007
Category : Mathematics
ISBN : 1600210139

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Introduction to General Relativistic and Scalar-tensor Cosmologies by Marcelo Samuel Berman Pdf

This book offers an introduction to General Relativity and its mathematical tools, together with an introduction to relativistic and scalar-tensor cosmologies. Part I deals with Tensor Calculus. Part II introduces General Relativity Theory, while Part III deals with Relativistic Cosmology. In Part IV we work Scalar-Tensor theories, concentrating in Cosmological Models. In the last chapters, the cosmological models presented, become more and more sophisticated, including some new cases, never published elsewhere, in which all fundamental "constants" are made to vary, with the age of the Universe, namely, the gravitational, the cosmological, the coupling Brans-Dicke "constants", the speed of light, Planck's "fine -structure "constant" alpha" etc. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students, to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.

Vectors, Tensors and the Basic Equations of Fluid Mechanics

Author : Rutherford Aris
Publisher : Courier Corporation
Page : 320 pages
File Size : 49,7 Mb
Release : 2012-08-28
Category : Mathematics
ISBN : 9780486134895

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Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris Pdf

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.

Vector and Tensor Analysis

Author : Eutiquio C. Young
Publisher : CRC Press
Page : 519 pages
File Size : 55,9 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781482277265

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Vector and Tensor Analysis by Eutiquio C. Young Pdf

Revised and updated throughout, this book presents the fundamental concepts of vector and tensor analysis with their corresponding physical and geometric applications - emphasizing the development of computational skills and basic procedures, and exploring highly complex and technical topics in simplified settings.;This text: incorporates transformation of rectangular cartesian coordinate systems and the invariance of the gradient, divergence and the curl into the discussion of tensors; combines the test for independence of path and the path independence sections; offers new examples and figures that demonstrate computational methods, as well as carify concepts; introduces subtitles in each section to highlight the appearance of new topics; provides definitions and theorems in boldface type for easy identification. It also contains numerical exercises of varying levels of difficulty and many problems solved.

Matrix and Tensor Decompositions in Signal Processing, Volume 2

Author : Gérard Favier
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 43,7 Mb
Release : 2021-08-31
Category : Technology & Engineering
ISBN : 9781786301550

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Matrix and Tensor Decompositions in Signal Processing, Volume 2 by Gérard Favier Pdf

The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.