Les méthodes tensorielles de la physique : calcul tensoriel dans un continuum amorphe / J. WinogradzkiType de document : MonographieCollection : Publications de l'Université de Rouen, 60Langue : français.Pays : France.Éditeur : Paris : Masson, 1979Description : 1 vol. (VIII-219 p.) ; 25 cmISBN : 9782225492693.Bibliographie : Index.Sujet MSC : 53A45, Differential geometry -- Classical differential geometry, Vector and tensor analysis
53A55, Differential geometry -- Classical differential geometry, Differential invariants (local theory), geometric objects
15A72, Linear and multilinear algebra; matrix theory -- Basic linear algebra, Vector and tensor algebra, theory of invariants
15-01, Linear and multilinear algebra; matrix theory, Instructional exposition (textbooks, tutorial papers, etc.)En-ligne : Zentralblatt | MathSciNet
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While this textbook is unlike many other tensor calculus textbooks, it is written from a viewpoint that should be of interest to a wide audience. In particular, it should appeal to applied mathematicians and theoretical physicists. The text consists of nine chapters which are roughly described as follows. Chapters I and II, which serve as an introduction, provide a construction of an n-dimensional continuum parameterized by an arithmetic space. In Chapter III, tensors are introduced as geometric objects possessing certain transformation properties. Thus tensor product spaces are not introduced and they do not appear in this textbook. Chapter IV deals with tensors of ranks 0, 1 and 2, and with the notions of symmetry and skew symmetry, while Chapter V is concerned with such algebraic operations as contraction, addition and multiplication. Chapters VI through VIII describe compound algebraic operations, criteria for tensoriality, and linear algebra. The last chapter, IX, provides a discussion of tensor derivatives.
It should also be noted that this text is the first of a series on tensor methods in physics. (MathSciNet)