# vector and tensor analysis with applications dover books on mathematics

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## Vector And Tensor Analysis With Applications

**Author :**A. I. Borisenko

**ISBN :**9780486131900

**Genre :**Mathematics

**File Size :**84. 29 MB

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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.

## Vector And Tensor Analysis

**Author :**George E. Hay

**ISBN :**9780486601090

**Genre :**Mathematics

**File Size :**24. 4 MB

**Format :**PDF, ePub

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"Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.

## Applications Of Tensor Analysis

**Author :**A. J. McConnell

**ISBN :**9780486603735

**Genre :**Mathematics

**File Size :**51. 74 MB

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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

**Author :**C. E. Springer

**ISBN :**9780486320915

**Genre :**Mathematics

**File Size :**31. 12 MB

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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.

## Elements Of Tensor Calculus

**Author :**A. Lichnerowicz

**ISBN :**9780486805177

**Genre :**Mathematics

**File Size :**45. 76 MB

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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.

## Tensor Calculus

**Author :**J. L. Synge

**ISBN :**9780486141398

**Genre :**Mathematics

**File Size :**50. 39 MB

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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 For Physicists

**Author :**Jan Arnoldus Schouten

**ISBN :**9780486655826

**Genre :**Science

**File Size :**62. 90 MB

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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.

## Introduction To Tensor Analysis And The Calculus Of Moving Surfaces

**Author :**Pavel Grinfeld

**ISBN :**9781461478676

**Genre :**Mathematics

**File Size :**38. 49 MB

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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

**Author :**Barry Spain

**ISBN :**9780486428314

**Genre :**Mathematics

**File Size :**48. 78 MB

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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.

## Introduction To Vector And Tensor Analysis

**Author :**Robert C. Wrede

**ISBN :**9780486137117

**Genre :**Mathematics

**File Size :**53. 62 MB

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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.