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Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics) by John A. Thorpe (Repost)

Posted on 2011-08-17




Name:Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics) by John A. Thorpe (Repost)
ASIN/ISBN:0387903577
Publisher:Springer (April 16, 1979)
Pages:276
Publisher: Springer (April 16, 1979)
ISBN: 0387903577
Pages: 276
File Size: 8.35 MB
Other Info: DJVU
   Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics) by John A. Thorpe (Repost)

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This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.

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