Elementary Topics in Differential Geometry
Publisher: Springer
Published: Oct 12, 2011
Format: paperback
Number of pages: 270
ISBN-13: 9781461261551
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.
Notes: Source title: Elementary Topics in Differential Geometry (Undergraduate Texts in Mathematics)