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Auteur : Richard L. Bishop
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"This is a first-rate book and deserves to be widely read." — American Mathematical MonthlyDespite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices. This book is an attempt to broaden this point of view at the stage where the student first encounters the subject. The authors have treated tensor analysis as a continuation of advanced calculus, striking just the right balance between the formal and abstract approaches to the subject.The material proceeds from the general to the special. An introductory chapter establishes notation and explains various topics in set theory and topology. Chapters 1 and 2 develop tensor analysis in its function-theoretical and algebraic aspects, respectively. The next two chapters take up vector analysis on manifolds and integration theory. In the last two chapters (5 and 6) several important special structures are studied, those in Chapter 6 illustrating how the previous material can be adapted to clarify the ideas of classical mechanics. The text as a whole offers numerous examples and problems.A student with a background of advanced calculus and elementary differential equation could readily undertake the study of this book. The more mature the reader is in terms of other mathematical knowledge and experience, the more he will learn from this presentation.

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Tensor analysis on manifolds : Richard L. Bishop : Free ~ Tensor analysis on manifolds by Richard L. Bishop. Publication date 1980 Topics Calculus of tensors., Manifolds (Mathematics) Publisher Dover Publications Collection inlibrary; printdisabled; internetarchivebooks; china Digitizing sponsor Internet Archive Contributor Internet Archive Language English. Access-restricted-item true Addeddate 2012-08-20 17:59:28 Bookplateleaf 0002 Boxid IA1100919 .

Tensor analysis on manifolds : Bishop, Richard L : Free ~ Tensor analysis on manifolds by Bishop, Richard L; Goldberg, Samuel I. Publication date 1980 Topics Calculus of tensors, Manifolds (Mathematics) Publisher New York : Dover Publications Collection inlibrary; printdisabled; internetarchivebooks; china Digitizing sponsor Kahle/Austin Foundation Contributor Internet Archive Language English. Originally published: New York : Macmillan, c1968 .

Tensor Analysis on Manifolds - Dover Books ~ Striking just the right balance between formal and abstract approaches, this text proceeds from generalities to specifics. Topics include function-theoretical and algebraic aspects, manifolds and integration theory, several important structures, and adaptation to classical mechanics. "First-rate. . . deserves to be widely read." — American Mathematical Monthly.</I> 1980 edition.

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A Gentle Introduction to Tensors ~ more. Second, tensor theory, at the most elementary level, requires only linear algebra and some calculus as prerequisites. Proceeding a small step further, tensor theory requires background in multivariate calculus. For a deeper understanding, knowledge of manifolds and some point-set topology is required. Accordingly, we divide the material into three chapters. The first chapter discusses .

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Manifolds, Tensor Analysis, and Applications / SpringerLink ~ The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me­ chanics, electromagnetism, plasma dynamics and control thcory arc given in .

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