Overview
- Notation simplicity and rigor
- Dealing with tensors as vectors (column matrices)
- New concepts as rotation of tensors, transposer tensor, eigentensors, permutation tensor, etc.
- A computer package in Mathematica (available via Internet)
- Inside and end of chapter exercises
- Introducing metrics in tensor spaces
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (14 chapters)
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Tensors over Linear Spaces with Inner Product
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Classic Tensors in Geometry and Mechanics
Keywords
About this book
Reviews
From the reviews:
"The book bridges a gap between the classical theory of tensors and the possibility of solving tensor problems with a computer. … For the first time, tensor contraction is formulated in terms of matrix operations. … 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." (Bulletin Bibliographique, 51:1-2, 2005)
"In this textbook, the authors present a new and, to some extent, unconventional approach to tensors … . This volume gives a thorough treatment of the topic of sensors. … the exposition of the book is a very transparent one and a pleasure to read. … Primary addressees of the book are (graduate) students in applied mathematics, mathematical physics, and engineering sciences as well. Moreover, the book can be recommended without reservations to instructors … ." (A. R. Kräuter, Internationale Mathematische Nachrichten, Issue 203, 2006)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: From Vectors to Tensors
Authors: Juan Ramón Ruíz-Tolosa, Enrique Castillo
Series Title: Universitext
DOI: https://doi.org/10.1007/b138560
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Softcover ISBN: 978-3-540-22887-5Published: 29 November 2004
eBook ISBN: 978-3-540-27066-9Published: 08 December 2005
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVI, 670
Topics: Theory of Computation, Algebra, Physics, general, Linear and Multilinear Algebras, Matrix Theory, Theoretical, Mathematical and Computational Physics, Mathematical and Computational Engineering
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