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From the back cover: "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 specific. 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 equations 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."
BRIEF CONTENTS
Chapter 0/Set Theory and Topology
Chapter 1/Manifolds
Chapter 2/Tensor Algebra
Chapter 3/Vector Analysis on Manifolds
Appendix to Chapter 3
Chapter 4/Integration Theory
Chapter 5/Riemannian and Semi-riemannian Manifolds
Chapter 6/Physical Application
Bibliography
Index
Note from the publisher: "This Dover edition, first published in 1980, is an unabridged and corrected republication of the work originally published by The Macmillan Company in 1968."
