Tensors Geometry And Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 50,6 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.

Author : Joseph M. Landsberg
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 44,5 Mb
Release : 2012
Category : Matrices
ISBN : 0821884816

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Tensors: Geometry and Applications by Joseph M. Landsberg Pdf

Author : C. T. J. Dodson,Timothy Poston
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 42,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783642105142

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Tensor Geometry by C. T. J. Dodson,Timothy Poston Pdf

This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.

Author : C. E. Springer
Publisher : Courier Corporation
Page : 256 pages
File Size : 50,9 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486320915

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Tensor and Vector Analysis by C. E. Springer Pdf

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Author : C. T. J. Dodson,T. Poston
Publisher : Pitman Publishing
Page : 622 pages
File Size : 40,6 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015015605606

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Tensor Geometry by C. T. J. Dodson,T. Poston Pdf

Author : Nail H. Ibragimov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 197 pages
File Size : 44,8 Mb
Release : 2015-08-31
Category : Mathematics
ISBN : 9783110379501

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Tensors and Riemannian Geometry by Nail H. Ibragimov Pdf

This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 378 pages
File Size : 52,8 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

Author : Ivan Stephen Sokolnikoff
Publisher : Unknown
Page : 0 pages
File Size : 46,8 Mb
Release : 1951
Category : Electronic
ISBN : OCLC:253723474

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Tensor Analysis by Ivan Stephen Sokolnikoff Pdf

Author : Dipankar De
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 49,8 Mb
Release : 2022-05-24
Category : Mathematics
ISBN : 9781119795629

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Introduction to Differential Geometry with Tensor Applications by Dipankar De Pdf

INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student

Author : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 468 pages
File Size : 54,5 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198510594

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Tensors and Manifolds by Robert Wasserman Pdf

This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.

Author : K.K. Dube
Publisher : I. K. International Pvt Ltd
Page : 377 pages
File Size : 46,5 Mb
Release : 2013-12-30
Category : Mathematics
ISBN : 9789380026589

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Differential Geometry and Tensors by K.K. Dube Pdf

The purpose of this book is to give a simple, lucid, rigorous and comprehensive account of fundamental notions of Differential Geometry and Tensors. The book is self-contained and divided in two parts. Section A deals with Differential Geometry and Section B is devoted to the study of Tensors. Section A deals with: " Theory of curves, envelopes and developables. " Curves on surfaces and fundamental magnitudes, curvature of surfaces and lines of curvature. " Fundamental equations of surface theory. " Geodesics. Section B deals with: " Tensor algebra. " Tensor calculus. " Christoffel symbols and their properties. " Riemann symbols and Einstein space, and their properties. " Physical components of contravariant and covariant vectors. " Geodesics and Parallelism of vectors. " Differentiable manifolds, charts, atlases.

Author : Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210290

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Manifolds, Tensor Analysis, and Applications by Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu Pdf

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.

Author : I. S. Sokolnikoff
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 1951
Category : Electronic
ISBN : OCLC:729241083

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Tensor Analysis by I. S. Sokolnikoff Pdf

Author : Nazrul Islam
Publisher : New Age International
Page : 6 pages
File Size : 49,9 Mb
Release : 2006-12
Category : Tensor algebra
ISBN : 9788122418385

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Tensors and Their Applications by Nazrul Islam Pdf

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.

Author : Francisco Bulnes
Publisher : BoD – Books on Demand
Page : 142 pages
File Size : 44,8 Mb
Release : 2020-09-09
Category : Mathematics
ISBN : 9781839625558

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Advances on Tensor Analysis and their Applications by Francisco Bulnes Pdf

This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite dimensional operators, and more.