Itskov M.Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum Mechanics

3rd edition. — Springer, 2013. — 269 p. — (Tensor algebra - ages).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.Vectors and Tensors in a FiniteDimensional Space.
Vector and Tensor Analysis in Euclidean Space.
Curves and Surfaces in ThreeDimensional Euclidean Space.
Eigenvalue Problem and Spectral Decomposition of SecondOrder Tensors.
Fourth Order Tensors.
Analysis of Tensor Functions.
Analytic Tensor Functions.
Applications to Continuum Mechanics.
Solutions.