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. 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 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, sincesuch tensors are important in applications to physics and engineering. 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 (he problems, as well as hints and solutions to selected problems at the end of the book.40, 000 copies of the book sold out very quickly, and in 1972 aquot;Naukaaquot; published the second edition of the book. 35, 000 copies of the second edition also sold out quickly. In the book, the foundations of tensor calculus and elements of tensor analysis are developed, and numerous ... There are answers provided to most of the problems, and hints and solutions to selected problems appear at the end of the ... Note that the authors consider chapters 5-7 as an essential part of the book .

Title | : | Tensor Calculus with Applications |

Author | : | Maks Aĭzikovich Akivis, Vladislav Viktorovich Golʹdberg |

Publisher | : | World Scientific - 2003-01-01 |

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