Vector and Tensor Analysis with Applications

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Author: A. I. Borisenko,I. E. Tarapov

Publisher: Courier Corporation

ISBN: 0486131904

Category: Mathematics

Page: 288

View: 4831

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.

Applications of Tensor Analysis

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Author: A J McConnell

Publisher: N.A

ISBN: 9781614276890

Category: Mathematics

Page: 332

View: 9398

2014 Reprint of 1957 Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. Formerly entitled "Applications of the Absolute Differential Calculus," this work applies tensorial methods to subjects within the realm of advanced college mathematics. In four major divisions, it explains the fundamental ideas and notation of tensor theory; covers the geometrical treatment of tensor algebra; introduces the theory of the differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics.

Applications of Tensor Analysis

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Author: A. J. McConnell

Publisher: Courier Corporation

ISBN: 0486603733

Category: Mathematics

Page: 318

View: 1694

Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.

Tensor and Vector Analysis

With Applications to Differential Geometry

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Author: C. E. Springer

Publisher: Courier Corporation

ISBN: 048632091X

Category: Mathematics

Page: 256

View: 4084

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.

Introduction to Vector and Tensor Analysis

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Author: Robert C. Wrede

Publisher: Courier Corporation

ISBN: 0486137112

Category: Mathematics

Page: 418

View: 3359

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.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

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Author: Pavel Grinfeld

Publisher: Springer Science & Business Media

ISBN: 1461478677

Category: Mathematics

Page: 302

View: 2632

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.

Tensor Calculus

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Author: J. L. Synge,A. Schild

Publisher: Courier Corporation

ISBN: 048614139X

Category: Mathematics

Page: 336

View: 1829

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.

Elements of Tensor Calculus

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Author: A. Lichnerowicz

Publisher: Courier Dover Publications

ISBN: 0486805174

Category: Mathematics

Page: 176

View: 9619

Part I: rigorous presentation of tensor calculus as a develoment of vector analysis. Part II: important applications of tensor calculus. Concluding section: field equations of general relativity theory. 1962 edition.

The Absolute Differential Calculus

Calculus of Tensors

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Author: Tullio Levi-Civita

Publisher: Dover Publications

ISBN: 9780486446370

Category: Mathematics

Page: 452

View: 9199

A chief requirement in the study of relativity is knowledge of the absolute differential calculus, the subject that Einstein found necessary for developing his ideas mathematically. Tullio Levi-Civita was one of the founders of this field of mathematics, and he presents a clear, detailed exposition of the subject in this classic book. The first section of the three-part treatment examines functional determinants and matrices; systems of total differential equations; linear partial differential equations in complete systems; and algebraic foundations of the absolute differential calculus, concluding with a geometrical introduction to the theory of differential quadratic forms. Part two, a study of the fundamental quadratic form and the absolute differential calculus, focuses on covariant differentiation, invariants and differential parameters, and locally geodesic coordinates; Riemann's symbols and properties relating to curvature, Ricci's and Einstein's symbols, and geodesic deviation; relations between two different metrics referred to the same parameters, manifolds of constant curvature; and differential quadratic forms of class zero and class one; and some applications of intrinsic geometry. The third and final section explores physical applications, including the evolution of mechanics and geometrical optics and their relation to a four-dimensional world according to Einstein; and gravitational equations and general relativity.

Tensors

The Mathematics of Relativity Theory and Continuum Mechanics

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Author: Anadi Jiban Das

Publisher: Springer Science & Business Media

ISBN: 0387694692

Category: Science

Page: 290

View: 9697

Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.

Vectors, Tensors and the Basic Equations of Fluid Mechanics

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Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 048613489X

Category: Mathematics

Page: 320

View: 6789

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

Manifolds, Tensor Analysis, and Applications

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Author: Ralph Abraham,Jerrold E. Marsden,Tudor Ratiu

Publisher: Springer Science & Business Media

ISBN: 1461210291

Category: Mathematics

Page: 656

View: 1337

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.

A Brief on Tensor Analysis

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Author: James G. Simmonds

Publisher: Springer Science & Business Media

ISBN: 1441985220

Category: Mathematics

Page: 114

View: 5557

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.

Applications of the Theory of Matrices

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Author: F. R. Gantmacher,J.L. Brenner

Publisher: Courier Corporation

ISBN: 0486445542

Category: Mathematics

Page: 317

View: 7656

The breadth of matrix theory's applications is reflected by this volume, which features material of interest to applied mathematicians as well as to control engineers studying stability of a servo-mechanism and numerical analysts evaluating the roots of a polynomial. Starting with a survey of complex symmetric, antisymmetric, and orthogonal matrices, the text advances to explorations of singular bundles of matrices and matrices with nonnegative elements. Applied mathematicians will take particular note of the full and readable chapter on applications of matrix theory to the study of systems of linear differential equations, and the text concludes with an exposition on the Routh-Hurwitz problem plus several helpful appendixes. 1959 edition.

Tensors, Differential Forms, and Variational Principles

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Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 7370

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Tensor Analysis for Physicists

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Author: Jan Arnoldus Schouten

Publisher: Courier Corporation

ISBN: 0486655822

Category: Science

Page: 277

View: 3023

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.

Tensor Calculus with Applications

translated from Russian by Vladislav V Goldberg

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Author: Maks A Akivis

Publisher: World Scientific Publishing Company

ISBN: 981310225X

Category: Science

Page: 380

View: 1830

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.

Tensor Calculus

A Concise Course

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Author: Barry Spain

Publisher: Courier Corporation

ISBN: 0486428311

Category: Mathematics

Page: 125

View: 4392

A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity. Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition.

An Introduction to Linear Algebra and Tensors

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Author: M. A. Akivis,V. V. Goldberg

Publisher: Courier Corporation

ISBN: 0486148785

Category: Mathematics

Page: 192

View: 4454

Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.

Matrix and Tensor Calculus

With Applications to Mechanics, Elasticity and Aeronautics

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Author: Aristotle D. Michal

Publisher: N.A

ISBN: 9780486462462

Category: Mathematics

Page: 132

View: 2481

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.