Elementary Topics in Differential Geometry /
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...
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| Format: | eBook |
| Language: | English |
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New York, NY :
Springer New York,
1979.
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| Series: | Undergraduate texts in mathematics.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (276 pages 100 illustrations) |
| ISBN: | 9781461261537 (electronic bk.) 1461261538 (electronic bk.) |
| ISSN: | 0172-6056 |