From Vectors to Tensors

Juan Ramón Ruíz-Tolosa, Enrique Castillo - Collection Universitext

670 pages, parution le 27/01/2005

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Résumé

This textbook deals with tensors that are treated as vectors, and its orientation is practical. In addition to dealing with the classical topics of standard books on tensors, it introduces new tensor concepts, such as the rotation of tensors, the transposer tensor, the eigentensors, the permutation tensor structure. The book bridges a gap between the classical theory of tensors and the possibility of solving tensor problems with a computer. In fact, the computational algebra required is formulated in matrix form to facilitate its implementation on computers. For the first time, tensor contraction is formulated in terms of matrix operations. A computer package complementing the book and written in Mathematica, is available at:
http://personales.unican.es/castie/tensors.

Addressed primarily to students of engineering, applied mathematics and mathematical physics, this unconventional approach to tensors is original for its orientation, its novel concepts, the choice of notation and the stretching-condensing techniques applied to most of the transformations used.

L'auteur - Juan Ramón Ruíz-Tolosa

JUAN RAMON RUIZ-TOLOSA is an industrial and civil engineer and has, as Professor at the Civil Engineering School of the University of Cantabria, taught algebra, tensors, topology, differential geometry and calculus for 30 years. His field of research includes number theory, Euclidean geometry, elliptic integrals, algebraic roots of equations.

L'auteur - Enrique Castillo

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. He is author of 25 books in English and in Spanish.

Sommaire

Basic Tensor Algebra
- Tensor Spaces
- Introduction 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

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Juan Ramón Ruíz-Tolosa, Enrique Castillo
Collection	Universitext
Parution	27/01/2005
Nb. de pages	670
Format	15,5 x 23,5
Couverture	Broché
Poids	1012g
Intérieur	Noir et Blanc
EAN13	9783540228875