Tensor Algebra and Tensor Analysis for Engineers [electronic resource] : With Applications to Continuum Mechanics / by Mikhail Itskov.Material type: TextLanguage: English Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XII, 244 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540360476Subject(s): Engineering | Matrix theory | Mathematical physics | Mechanics | Materials | Engineering | Numerical and Computational Methods in Engineering | Continuum Mechanics and Mechanics of Materials | Mathematical Methods in Physics | Linear and Multilinear Algebras, Matrix Theory | MechanicsAdditional physical formats: Printed edition:: No titleDDC classification: 006.3 LOC classification: Q342Online resources: Click here to access online
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.
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 is addressed primarily to engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling an autonomous 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 might therefore be of high interest for PhD-students and scientists working in this area.