Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics

✍ Scribed by Mikhail Itskov (auth.)

Publisher: Springer International Publishing
Year: 2015
Tongue: English
Leaves: 299
Series: Mathematical Engineering
Edition: 4
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvii
Vectors and Tensors in a Finite-Dimensional Space....Pages 1-36
Vector and Tensor Analysis in Euclidean Space....Pages 37-67
Curves and Surfaces in Three-Dimensional Euclidean Space....Pages 69-96
Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors....Pages 97-119
Fourth-Order Tensors....Pages 121-133
Analysis of Tensor Functions....Pages 135-168
Analytic Tensor Functions....Pages 169-189
Applications to Continuum Mechanics....Pages 191-212
Solutions....Pages 213-280
Back Matter....Pages 281-290

✦ Subjects

Continuum Mechanics and Mechanics of Materials; Differential Geometry; Linear and Multilinear Algebras, Matrix Theory; Mechanics

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