By J. A. Schouten
This exceptional learn through a famed mathematical pupil and previous professor of arithmetic on the collage of Amsterdam integrates a concise exposition of the mathematical foundation of tensor research with admirably selected actual examples of the theory.
The first 5 chapters incisively set out the mathematical conception underlying using tensors. The tensor algebra in EN and RN is constructed in Chapters I and II. bankruptcy II introduces a sub-group of the affine staff, then offers with the identity of amounts in EN. The tensor research in XN is constructed in bankruptcy IV. In chapters VI via IX, Professor Schouten provides purposes of the idea which are either intrinsically attention-grabbing and sturdy examples of the use and benefits of the calculus. bankruptcy VI, in detail attached with bankruptcy III, exhibits that the size of actual amounts depend on the alternative of the underlying workforce, and that tensor calculus is the easiest software for facing the houses of anisotropic media. In bankruptcy VII, sleek tensor calculus is utilized to a few previous and a few sleek difficulties of elasticity and piezo-electricity. bankruptcy VIII provides examples pertaining to anholonomic structures and the homogeneous therapy of the equations of Lagrange and Hamilton. bankruptcy IX bargains first with relativistic kinematics and dynamics, then deals an exposition of contemporary therapy of relativistic hydrodynamics. bankruptcy X introduces Dirac’s matrix calculus. particularly invaluable gains of the ebook are the routines on the finish of every bankruptcy, and a precis of the mathematical thought inside the first 5 chapters — excellent for readers whose fundamental curiosity is in physics instead of mathematics.
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