Cartesian Tensors: An Introduction
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of tensors in orthogonal curvilinear coordinates. Numerous examples illustrate the general theory and indicate certain extensions and applications. 1960 ed.
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angle angular velocity tensor antisymmetric tensor axis basis bilinear body forces CALCULUS Cartesian tensors CATALOG OF DOVER chapter Classic Clifford algebra coefficients complex numbers components curl curvilinear coordinates defined definition DIFFERENTIAL EQUATIONS direction cosines divergence DOVER BOOKS eigenvalues eigenvectors elementary Exercises fluid formulae FOURIER SERIES functions of direction fundamental geometry Hence integral INTRODUCTION isotropic parameter isotropic tensors isotropic vector linear function momentum multilinear functions notation number system numbers numerical multiple orthogonal curvilinear coordinates orthogonal transformations particle plane polar coordinates polynomial problems rate of strain real number rectilinear reflexion relation Riemannian right handed base rotation satisfy the equation scalar second rank tensor set of numbers Show simplest specified spherical mean spinor strain tensor stress tensor symmetric tensor tensor analysis tensor of rank tensor theory text covers theorem theory of tensors three dimensions tion TOPOLOGY transformation law transformation matrix unit vector vector PQ zero