✦ LIBER ✦

Elementary topics in differential geometry

✍ Scribed by John A. Thorpe

Book ID: 127456742
Publisher: Springer-Verlag
Year: 1979
Tongue: English
Weight: 4 MB
Series: Undergraduate texts in mathematics
Category: Library
City: New York
ISBN-13: 9783540903574

No coin nor oath required. For personal study only.

✦ Synopsis

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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