Tensor Algebra and Tensor Analysis for Engineers - Itskov, Mikhail

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Résumé :
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....

Sommaire:
Prof. Itskov studied Automobile Engineering at the Moscow State Automobile and Road Technical University, Russia. In 1990 he received his doctoral degree in mechanics, and in 2002 he obtained his habilitation degree in mechanics from the University of Bayreuth, Germany. Since 2004 he has been full professor for continuum mechanics at the RWTH Aachen University, Germany. His research interests comprise tensor analysis, non-linear continuum mechanics, in particular the application to anisotropic materials, as well as the mechanics of elastomers and soft tissues in a broad sense....

From the reviews: Most books on continuum mechanics begin with a more or less lengthy introduction into this mere mathematical topic. ... With the present introduction to tensors, Itskov has filled this gap. ... It is written in a clear and modern style ... . contains a lot of interesting representations, which will be appreciated by researchers in the field. ... All in all, the book can be clearly recommended both for students and researchers in the field of continuum mechanics. (Technische Mechanik, Vol. 28 (3), 2008)