Les méthodes tensorielles de la physique : calcul tensoriel dans un continuum amorphe / J. Winogradzki

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)

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