ENGLISH

Elementary Topics in Differential Geometry

By John A. Thorpe

Book information

Publisher
Springer
Year
1979
ISBN
0387903577, 9780387903576, 3540903577, 9783540903574
LCC
QA641 .T36
Language
english
Format
DJVU
Filesize
9 MB (9443892 bytes)
Series
Undergraduate Texts in Mathematics
Pages
276\265
Time added
2014-10-05 02:30:00

Description

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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