Tensor Calculus With Applications

By: Vladislav V Goldberg, Maks A Akivis

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Paperback | 1 October 2003

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380 Pages

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22.6 x 16.1 x 2.2

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This textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering 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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Science Science in General Maths for Scientists Engineering & Technology Technology in General Maths for Engineers Physics Topology

Algebra Booktopia Publisher Services World Scientific Publishing Number Theory Geometry Analytic Geometry

Translator's Introduction
Preface to the Russian Edition
Vector Spaces	p. 1
Multilinear Forms and Tensors	p. 45
Linear Transformations and Second-Order Tensors	p. 77
Reduction of the Matrix of Linear Transformation to the Simplest Form	p. 129
The General Theory of Second-Degree Surfaces	p. 173
Applications of Tensor Calculus to Some Problem of Mechanics and Physics	p. 211
Foundations of Tensor Analysis	p. 259
Selected Answers and Hints	p. 317
Bibliography	p. 345
Index	p. 349
Table of Contents provided by Blackwell. All Rights Reserved.

Tensor Calculus With Applications

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