Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics 3rd by Itskov 9783319163413 3319163426

ISBN 10: 3319163426

ISBN 13: 9783319163413

Author: Itskov

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.

1. Vectors and Tensors in a Finite-Dimensional Space

2. Vector and Tensor Analysis in Euclidean Space

3. Curves and Surfaces in Three-Dimensional Euclidean Space

4. Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors

5. Fourth-Order Tensors

6. Analysis of Tensor Functions

7. Analytic Tensor Functions

8. Applications to Continuum Mechanics

9. Solutions