This is a revised printing of one of the classic mathematics texts published in the last 25 years. This revised edition includes updated references and indexes and error corrections and will continue to serve as the standard text for students and professionals in the field.Differential manifolds are the underlying objects of study in much of advanced calculus and analysis. Topics such as line and surface integrals, divergence and curl of vector fields, and Stoke's and Green's theorems find their most natural setting in manifold theory. Riemannian plane geometry can be visualized as the geometry on the surface of a sphere in which "lines" are taken to be great circle arcs.
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The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.
Line and surface integrals
Divergence and curl of vector fields
Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance in many areas of mathematics and its applications. Although basically and extension of advanced, or multivariable calculus, the leap from Euclidean space to manifolds can often be difficult. It takes time and patience, and it is easy to become mirred in abstraction and generalization.
In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties. The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power. There are more than 400 exercises for the reader.
This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.
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Book Description Academic Press Inc. Hardcover. Book Condition: New. 0121160505 New Condition. Bookseller Inventory # NEW4.0039945
Book Description Academic Press Inc, 1975. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service!. Bookseller Inventory # ABE_book_new_0121160505
Book Description Elsevier Science & Technology, 1975. Paperback. Book Condition: New. Bookseller Inventory # DADAX0121160505
Book Description Academic Press Inc, 1975. Hardcover. Book Condition: New. book. Bookseller Inventory # 0121160505
Book Description Academic Press Inc, 1975. Hardcover. Book Condition: New. Bookseller Inventory # P110121160505