Differential Geometry

Heinrich W. Guggenheimer

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Paperback

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English

Dover
01 June 1977

Mathematics & Sciences; Differential & Riemannian geometry

Series: Dover Books on Mathema 1.4tics

Summary
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This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a general theory of connections. The author presents a full development of the Erlangen Program in the foundations of geometry as used by Elie Cartan as a basis of modern differential geometry; the book can serve as an introduction to the methods of E. Cartan. The theory is applied to give a complete development of affine differential geometry in two and three dimensions. Although the text deals only with local problems (except for global problems that can be treated by methods of advanced calculus), the definitions have been formulated so as to be applicable to modern global differential geometry. The algebraic development of tensors is equally accessible to physicists and to pure mathematicians. The wealth of specific resutls and the replacement of most tensor calculations by linear algebra makes the book attractive to users of mathematics in other disciplines.

By: Heinrich W. Guggenheimer
Imprint: Dover
Country of Publication: United States
Dimensions: Height: 210mm, Width: 142mm, Spine: 20mm
Weight: 422g
ISBN: 9780486634333
ISBN 10: 0486634337
Series: Dover Books on Mathema 1.4tics
Publication Date: 01 June 1977
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Unspecified

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Differential Geometry

Heinrich W. Guggenheimer

$38.95

Paperback

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