An Introduction To Tensor Calculus
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Introduction To Tensor Analysis And The Calculus Of Moving Surfaces
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Author : Pavel Grinfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-24
Introduction To Tensor Analysis And The Calculus Of Moving Surfaces written by Pavel Grinfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-24 with Mathematics categories.
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.
An Introduction To Tensor Analysis
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Author : Bipin Singh Koranga
language : en
Publisher: CRC Press
Release Date : 2022-09-01
An Introduction To Tensor Analysis written by Bipin Singh Koranga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Science categories.
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.
Ricci Calculus
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Author : Jan Arnoldus Schouten
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Ricci Calculus written by Jan Arnoldus Schouten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Tensor Calculus For Physics
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Author : Dwight E. Neuenschwander
language : en
Publisher: JHU Press
Release Date : 2015
Tensor Calculus For Physics written by Dwight E. Neuenschwander and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
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 Tensor Calculus And Continuum Mechanics
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Author : John Henry Heinbockel
language : en
Publisher:
Release Date : 1996
Introduction To Tensor Calculus And Continuum Mechanics written by John Henry Heinbockel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Tensor Calculus And Analytical Dynamics
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Author : John G. Papastavridis
language : en
Publisher: Routledge
Release Date : 2018-12-12
Tensor Calculus And Analytical Dynamics written by John G. Papastavridis and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Mathematics categories.
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.
An Introduction To Tensor Calculus
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Author : Derek F. Lawden
language : en
Publisher: Courier Corporation
Release Date : 2012-03-07
An Introduction To Tensor Calculus written by Derek F. Lawden and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-07 with Science categories.
This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.
Tensor Calculus
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Author : J. L. Synge
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Tensor Calculus written by J. L. Synge and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Fundamental introduction 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, more.
An Introduction To Differential Geometry With The Use Of Tensor Calculus
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Author : Luther Pfahler Eisenhart
language : en
Publisher: Read Books Ltd
Release Date : 2011-03-23
An Introduction To Differential Geometry With The Use Of Tensor Calculus written by Luther Pfahler Eisenhart and has been published by Read Books Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-23 with Mathematics categories.
Since 1909, when my Differential Geometry of Curves and Surfaces was published, the tensor calculus, which had previously been invented by Ricci, was adopted by Einstein in his General Theory of Relativity, and has been developed further in the study of Riemannian Geometry and various generalizations of the latter. In the present book the tensor calculus of cuclidean 3-space is developed and then generalized so as to apply to a Riemannian space of any number of dimensions. The tensor calculus as here developed is applied in Chapters III and IV to the study of differential geometry of surfaces in 3-space, the material treated being equivalent to what appears in general in the first eight chapters of my former book with such additions as follow from the introduction of the concept of parallelism of Levi-Civita and the content of the tensor calculus. Of the many exercises in the book some involve merely direct application of the text, but most of them constitute an extension of it. In the writing of the book I have received valuable assistance and criticism from Professor H. P. Robertson and from my students, Messrs. Isaac Battin, Albert J. Coleman, Douglas R. Crosby, John Giese, Donald C. May, and in particular, Wayne Johnson. The excellent line drawings and half-tone illustrations were conceived and executed by Mr. John H. Lewis.