Kay D.С. Schaum's outline of theory and problems of tensor calculus

McGraw-Hill, 1988. – 238 pp. – (Schaum's Outline series). – ISBN: 0-07-033484-6This Outline is designed for use by both undergraduates and graduates who find they need to master the basic methods and concepts of tensors. The material is written from both an elementary and applied point of view, in order to provide a lucid introduction to the subject. The material is of fundamental importance to theoretical physics (e.g., field and electromagnetic theory) and to certain areas of engineering (e.g., aerodynamics and fluid mechanics). Whenever a change of coordinates emerges as a satisfactory way to solve a problem, the subject of tensors is an immediate requisite. Indeed, many techniques in partial differential equations are tensor transformations in disguise. While physicists readily recognize the importance and utility of tensors, many mathematicians do not. It is hoped that the solved problems of this book will allow all readers to find out what tensors have to offer them.
Since there are two avenues to tensors and since there is general disagreement over which is the better approach for beginners, any author has a major decision to make. After many hours in the classroom it is the author's opinion that the tensor component approach (replete with subscripts and superscripts) is the correct one to use for beginners, even though it may require some painful initial adjustments. Although the more sophisticated, noncomponent approach is necessary for modern applications of the subject, it is believed that a student will appreciate and have an immensely deeper understanding of this sophisticated approach to tensors after a mastery of the component approach. In fact, noncomponent advocates frequently surrender to the introduction of components after all; some proofs and important tensor results just do not lend themselves to a completely component-free treatment.