There is a gap between engineering courses in tensor algebra, and the treatment of linear transformations within classical linear algebra. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as absolutely necessary. The many exercises provided include solutions, enabling autonomous study. The last chapters address modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore interest PhD-students and scientists working in this area.

In recent decades, the absolute notation for tensors has become widely accepted and is now state-of-the-art for publications in solid and structural mechanics. This is opposed to a majority of books on tensor calculus referring to index notation. The latter one complicates the understanding of the matter especially for readers with initial knowledge. This is a modern textbook on tensor calculus for engineers in line with contemporary scientific publications.

Zusammenfassung
This second edition is completed by a number of additional examples and exercises. In response of comments and questions of students using this book, solutions of many exercises have been improved for a better understanding. Some changes and enhancements are concerned with the treatment of sk- symmetric and rotation tensors in the ?rst chapter. Besides, the text and formulae have thoroughly been reexamined and improved where necessary. Aachen, January 2009 Mikhail Itskov Preface to the First Edition Like many other textbooks the present one is based on a lecture course given by the author for master students of the RWTH Aachen University. In spite of a somewhat di?cult matter those students were able to endure and, as far as I know, are still ?ne. I wish the same for the reader of the book. Although the present book can be referred to as a textbook one ?nds only little plain text inside. I tried to explain the matter in a brief way, nevert- lessgoinginto detailwherenecessary.Ialsoavoidedtediousintroductions and lengthy remarks about the signi?cance of one topic or another. A reader - terested in tensor algebra and tensor analysis but preferring, however, words instead of equations can close this book immediately after having read the preface.

Inhalt

Vectors and Tensors in a Finite-Dimensional Space.- Vector and Tensor Analysis in Euclidean Space.- Curves and Surfaces in Three-Dimensional Euclidean Space.- Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors.- Fourth-Order Tensors.- Analysis of Tensor Functions.- Analytic Tensor Functions.- Applications to Continuum Mechanics.