An Introduction To Tensor Analysis

Author : Bipin Singh Koranga,Sanjay Kumar Padaliya
Publisher : CRC Press
Page : 127 pages
File Size : 55,7 Mb
Release : 2022-09-01
Category : Mathematics
ISBN : 9781000795912

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An Introduction to Tensor Analysis by Bipin Singh Koranga,Sanjay Kumar Padaliya Pdf

The subject of Tensor Analysis deals with the problem of the formulation of the relation between various entities in forms which remain invariant when we pass from one system of coordinates to another. The invariant form of equation is necessarily related to the possible system of coordinates with reference to which the equation remains invariant. The primary purpose of this book is the study of the invariance form of equation relative to the totally of the rectangular co-ordinate system in the three-dimensional Euclidean space. We start with the consideration of the way the sets representing various entities are transformed when we pass from one system of rectangular co-ordinates to another. A Tensor may be a physical entity that can be described as a Tensor only with respect to the manner of its representation by means of multi-sux sets associated with different system of axes such that the sets associated with different system of co-ordinate obey the transformation law for Tensor. We have employed sux notation for tensors of any order, we could also employ single letter such A,B to denote Tensors.

Author : Pavel Grinfeld
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 47,8 Mb
Release : 2013-09-24
Category : Mathematics
ISBN : 9781461478676

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Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld Pdf

This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Author : Jan Arnoldus Schouten
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 55,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662129272

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Ricci-Calculus by Jan Arnoldus Schouten Pdf

This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic introduction to the kernel index method but also contained many notions that had come into prominence since 1923. For instance densities, quantities of the second kind, pseudo-quantities, normal Coordinates, the symbolism of exterior forms, the LIE derivative, the theory of variation and deformation and the theory of subprojective connexions were included. Now since 1938 there have been many new developments and so a book on RICCI cal culus and its applications has to cover quite different ground from the book of 1923. Though the purpose remains to make the reader acquainted with RICCI's famous instrument in its modern form, the book must have quite a different methodical structure and quite different applica tions have to be chosen. The first chapter contains algebraical preliminaries but the whole text is modernized and there is a section on hybrid quantities (quantities with indices of the first and of the second kind) and one on the many abridged notations that have been developed by several authors. In the second chapter the most important analytical notions that come before the introduction of a connexion aredealt with in full.

Author : Derek Frank Lawden
Publisher : Unknown
Page : 184 pages
File Size : 55,6 Mb
Release : 2013-08
Category : Electronic
ISBN : 1258787415

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An Introduction to Tensor Calculus and Relativity by Derek Frank Lawden Pdf

Author : James G. Simmonds
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 46,9 Mb
Release : 2012-10-31
Category : Mathematics
ISBN : 9781441985224

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A Brief on Tensor Analysis by James G. Simmonds Pdf

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

Author : Albert Potter Wills
Publisher : Unknown
Page : 0 pages
File Size : 43,8 Mb
Release : 1931
Category : Calculus of tensors
ISBN : LCCN:nun00509342

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Vector Analysis by Albert Potter Wills Pdf

Author : Robert C. Wrede
Publisher : Courier Corporation
Page : 418 pages
File Size : 55,8 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9780486137117

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Introduction to Vector and Tensor Analysis by Robert C. Wrede Pdf

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, and more. 1963 edition.

Author : Liqun Qi,Ziyan Luo
Publisher : SIAM
Page : 313 pages
File Size : 49,6 Mb
Release : 2017-04-19
Category : Mathematics
ISBN : 9781611974744

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Tensor Analysis by Liqun Qi,Ziyan Luo Pdf

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?

Author : Richard L. Bishop,Samuel I. Goldberg
Publisher : Courier Corporation
Page : 288 pages
File Size : 44,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139234

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Tensor Analysis on Manifolds by Richard L. Bishop,Samuel I. Goldberg Pdf

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

Author : A. I. Borisenko,I. E. Tarapov
Publisher : Courier Corporation
Page : 288 pages
File Size : 40,7 Mb
Release : 2012-08-28
Category : Mathematics
ISBN : 9780486131900

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Vector and Tensor Analysis with Applications by A. I. Borisenko,I. E. Tarapov Pdf

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 244 pages
File Size : 48,5 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"

Author : Leonard Lovering Barrett
Publisher : Unknown
Page : 48 pages
File Size : 48,7 Mb
Release : 1956
Category : Calculus of tensors
ISBN : UOM:39015065698568

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An Introduction to Tensor Analysis by Leonard Lovering Barrett Pdf

Author : John G. Papastavridis
Publisher : Routledge
Page : 435 pages
File Size : 54,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351411622

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Tensor Calculus and Analytical Dynamics by John G. Papastavridis Pdf

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Author : Louis Brand
Publisher : Unknown
Page : 472 pages
File Size : 52,9 Mb
Release : 1947
Category : Calculus of tensors
ISBN : UCAL:B4248870

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Vector and Tensor Analysis by Louis Brand Pdf

Author : Ray M. Bowen,Chao-cheng Wang
Publisher : Springer
Page : 224 pages
File Size : 46,7 Mb
Release : 1976-05-31
Category : Mathematics
ISBN : UOM:39015017127955

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Introduction to Vectors and Tensors by Ray M. Bowen,Chao-cheng Wang Pdf

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.