Tensor Analysis PDF Download
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Author | : Pavel Grinfeld |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2013-09-24 |
Genre | : Mathematics |
ISBN | : 1461478677 |
Download Introduction to Tensor Analysis and the Calculus of Moving Surfaces Book in PDF, ePub and Kindle
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 | : James G. Simmonds |
Publisher | : Springer Science & Business Media |
Total Pages | : 124 |
Release | : 2012-10-31 |
Genre | : Mathematics |
ISBN | : 1441985220 |
Download A Brief on Tensor Analysis Book in PDF, ePub and Kindle
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 | : Richard L. Bishop |
Publisher | : Courier Corporation |
Total Pages | : 288 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 0486139239 |
Download Tensor Analysis on Manifolds Book in PDF, ePub and Kindle
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author | : A. I. Borisenko |
Publisher | : Courier Corporation |
Total Pages | : 288 |
Release | : 2012-08-28 |
Genre | : Mathematics |
ISBN | : 0486131904 |
Download Vector and Tensor Analysis with Applications Book in PDF, ePub and Kindle
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 | : C. E. Springer |
Publisher | : Courier Corporation |
Total Pages | : 256 |
Release | : 2013-09-26 |
Genre | : Mathematics |
ISBN | : 048632091X |
Download Tensor and Vector Analysis Book in PDF, ePub and Kindle
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 | : Liqun Qi |
Publisher | : SIAM |
Total Pages | : 313 |
Release | : 2017-04-19 |
Genre | : Mathematics |
ISBN | : 1611974747 |
Download Tensor Analysis Book in PDF, ePub and Kindle
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 | : Bipin Singh Koranga |
Publisher | : CRC Press |
Total Pages | : 127 |
Release | : 2022-09-01 |
Genre | : Mathematics |
ISBN | : 1000795918 |
Download An Introduction to Tensor Analysis Book in PDF, ePub and Kindle
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 | : Robert C. Wrede |
Publisher | : Courier Corporation |
Total Pages | : 418 |
Release | : 2013-01-30 |
Genre | : Mathematics |
ISBN | : 0486137112 |
Download Introduction to Vector and Tensor Analysis Book in PDF, ePub and Kindle
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 | : Louis Brand |
Publisher | : |
Total Pages | : 472 |
Release | : 1947 |
Genre | : Calculus of tensors |
ISBN | : |
Download Vector and Tensor Analysis Book in PDF, ePub and Kindle
Author | : Yuriy I. Dimitrienko |
Publisher | : Springer Science & Business Media |
Total Pages | : 680 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 9401732213 |
Download Tensor Analysis and Nonlinear Tensor Functions Book in PDF, ePub and Kindle
Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.