Elementary Topics in Differential Geometrytxt,chm,pdf,epub,mobi下载
作者:
Thorpe, John A.
出版社: Spring 出版年: 1979 页数: 253 定价: USD 90.34 装帧: Hardcover 丛书: Undergraduate Texts in Mathematics ISBN: 9780387903576
内容简介
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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...
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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很独特的视角