Tensor Calculus with Applications

Author: Maks A Akivis
Publisher: World Scientific Publishing Company
ISBN: 9789813102255
Release Date: 2003-09-29
Genre: Science

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics. While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering. With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis. All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.

Matrix and Tensor Calculus

Author: Aristotle D. Michal
Publisher:
ISBN: 0486462463
Release Date: 2008-07
Genre: Mathematics

This volume offers a working knowledge of the fundamentals of matrix and tensor calculus. Relevant to several fields, particularly aeronautical engineering, the text skillfully combines mathematical statements with practical applications. 1947 edition.

Vector and Tensor Analysis with Applications

Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 9780486131900
Release Date: 2012-08-28
Genre: Mathematics

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.

Tensor Analysis with Applications in Mechanics

Author: L. P. Lebedev
Publisher: World Scientific
ISBN: 9789814313995
Release Date: 2010
Genre: Mathematics

The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book.

Manifolds Tensor Analysis and Applications

Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 9781461210290
Release Date: 2012-12-06
Genre: Mathematics

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.

Applications of Tensor Analysis

Author: A. J. McConnell
Publisher: Courier Corporation
ISBN: 9780486145020
Release Date: 2014-06-10
Genre: Mathematics

DIVTensor theory, applications to dynamics, electricity, elasticity, hydrodynamics, etc. Level is advanced undergraduate. Over 500 solved problems. /div

Spinor and non Euclidean tensor calculus with applications

Author: Iulian Beju
Publisher: Taylor & Francis
ISBN: UOM:39015015624193
Release Date: 1983-01-01
Genre: Mathematics

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Tensor Calculus and Applications

Author: Bhaben Chandra Kalita
Publisher: CRC Press
ISBN: 0367138069
Release Date: 2019
Genre: Calculus of tensors

Theoretically, the subject of "Tensor calculus" is critical for students to under understand for the complex nature of uses of subscripts and superscripts. Besides the lack of knowledge about the fields of application, this poses rather more difficulty to learn the concepts. The elegant nature of description of the theory with specific style of changing the suffixes and prefixes and reasons to recover meaningful results of the subsequent fields will inspire the readers for the book. Special techniques are adopted in the book to remove confusion from the minds (as inferred from practical experience) of students/readers for pure knowledge. For absolute understanding of the subject clear indication on where to change the suffix in terms and to what, are given with directions (hints) in respective terms. Moreover, this book distinguishes different classes of tensors; pictorial representations are furnished as well. Without identification of non-isotropic media where application of tensors is inevitable, researchers /readers cannot use it in true sense. For this purpose, the Chapter 7 is included for step-by-step evolution of the branch. To amplify the uses of tensors in gravitationally distorted space-time of General Theory of Relativity and in non-isotropic media like viscous fluids and physical bodies with elasticity including Structural Geology, Chapter 7 is developed to infuse real interest in to the minds of readers. Features Provides a clear indication and understanding of the subject on how to change suffixes Describes the original evolution of symbols necessary for tensors Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems Presents the correlation between critical concepts

Tensor Analysis and Its Applications

Author: Quddus Khan
Publisher: Partridge Publishing
ISBN: 9781482850680
Release Date: 2015-08-27
Genre: Mathematics

This book is intended to serve as a textbook for undergraduate and postgraduate students of mathematics. It will be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and other higher education tests. The text starts with the basic concepts and results, which shall refer throughout this book and is followed by the study of the tensor algebra and its calculus, consisting the notion of tensor, its operations, and its different types; Christoffels symbols and its properties, the concept of covariant differentiation of tensors and its properties, tensor form of gradient, divergence, laplacian and curl, divergence of a tensor, intrinsic derivatives, and parallel displacement of vectors, Riemanns symbols and its properties, and application of tensor in different areas.

Tensor Calculus

Author: J. L. Synge
Publisher: Courier Corporation
ISBN: 9780486141398
Release Date: 2012-04-26
Genre: Mathematics

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.

Tensor analysis

Author: Ivan Stephen Sokolnikoff
Publisher:
ISBN: WISC:89080438419
Release Date: 1951
Genre: Calculus of tensors


Applications of Tensor Analysis in Continuum Mechanics

Author: Victor A. Eremeyev
Publisher: World Scientific Publishing Company
ISBN: 9813238968
Release Date: 2018-07-10
Genre: Technology & Engineering

A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas. The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.

Tensor Algebra and Tensor Analysis for Engineers

Author: Mikhail Itskov
Publisher: Springer
ISBN: 9783319163420
Release Date: 2015-03-25
Genre: Technology & Engineering

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Tensor and Vector Analysis

Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 9780486320915
Release Date: 2013-09-26
Genre: Mathematics

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.