Price Rs 275/=Book Summary of 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 fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary dicussions 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.
Table of Contents
Chapter 1
Table of Contents
Chapter 1
- Graphs and Level Sets
- Vector Fields
- The Tangent Space
- Surfaces
- Vector Fields on Surfaces; Orientation
- The Gauss Map
- Geodesies
- Parallel Transport
- The Weingarten Map
- Curvature of Plane Curves
- Arc Length and Line Integrals
- Curvature of Surfaces
- Convex Surfaces
- Parameterized Surfaces
- Local Equivalance of Surfaces and Parameterized Surfaces
- Focal Points
- Surface Area and Volume
- Minimal Surfaces
- The Exponential Map
- Surfaces with Boundary
- The Gauess-Boness Theorem
- Regid Motions and Congruence
- Isometrics
- Reimannian Matrics
Details of Book: Elementary Topics in Differential Geometry
| Book: | Elementary Topics in Differential Geometry |
| Author: | Thorpe J. A. |
| ISBN: | 8181281446 |
| ISBN-13: | 9788181281449,978-8181281449 |
| Binding: | Paperback |
| Publishing Date: | 2004 |
| Publisher: | SPRINGER (INDIA) PVT. LTD. |
| Edition: | 01 |
| Language: | English |
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