Tensor Algebra and Tensor Analysis for Engineers

Beschreibung

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area.

This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area.

This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

Autor*in

Mikhail Itskov

Themen in »Tensor Algebra and Tensor Analysis for Engineers«

Christoffel Symbols Coordinate Transformation Covariant and Contravariant Derivatives Derivative of the Stretch and Rotation Tensor Generalized Rivlin’s Identities Polar Decomposition of the Deformation Gradient Spectral Decomposition of Second-order Tensors Tensor Algebra Tensor-valued Functions Tensors in Finite-dimensional Space matrix theory

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