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

Description

This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, 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. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. 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 textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided. Front Matter ....Pages i-xix Vectors and Tensors in a Finite-Dimensional Space (Mikhail Itskov)....Pages 1-36 Vector and Tensor Analysis in Euclidean Space (Mikhail Itskov)....Pages 37-72 Curves and Surfaces in Three-Dimensional Euclidean Space (Mikhail Itskov)....Pages 73-97 Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors (Mikhail Itskov)....Pages 99-121 Fourth-Order Tensors (Mikhail Itskov)....Pages 123-135 Analysis of Tensor Functions (Mikhail Itskov)....Pages 137-171 Analytic Tensor Functions (Mikhail Itskov)....Pages 173-193 Applications to Continuum Mechanics (Mikhail Itskov)....Pages 195-215 Solutions (Mikhail Itskov)....Pages 217-290 Back Matter ....Pages 291-300