From Vectors to Tensors

This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

Auteur

Enrique Castillo is Professor of Applied Mathematics at the University of Cantabria in Santander (Spain). He is a Mathematician and a Civil engineer and Member of the Spanish Royal Academy of Engineering. He has taught at several other universities in the Europe and America. The author/coauthor of eleven other books in English and fourteen in Spanish, and more than 300 papers in journals and Congresses. More information can be found at his Web site: http://personales.unican.es/castie//.

Juan R. Ruiz-Tolosa is an Industrial and Civil Engineer and has been Professor of Algebra, Tensors, Topology, Differential Geometry and Calculus at the Civil Engineering School, University of Cantabria for 30 years. His field of research includes Number Theory, Euclidean Geometry, Elliptic Integrals, Algebraic Roots of Equations, etc.

Contenu

Basic Tensor Algebra.- Tensor Spaces.- to Tensors.- Homogeneous Tensors.- Change-of-basis in Tensor Spaces.- Homogeneous Tensor Algebra: Tensor Homomorphisms.- Special Tensors.- Symmetric Homogeneous Tensors: Tensor Algebras.- Anti-symmetric Homogeneous Tensors, Tensor and Inner Product Algebras.- Pseudotensors; Modular, Relative or Weighted Tensors.- Exterior Algebras.- Exterior Algebras: Totally Anti-symmetric Homogeneous Tensor Algebras.- Mixed Exterior Algebras.- Tensors over Linear Spaces with Inner Product.- Euclidean Homogeneous Tensors.- Modular Tensors over En (IR) Euclidean Spaces.- Euclidean Exterior Algebra.- Classic Tensors in Geometry and Mechanics.- Affine Tensors.