Elementary Topics in Differential Geometry
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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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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $79.95
Copyright year: 1979
Publication date: 10/27/1994
Size: 6.50" wide x 9.75" long x 0.75" tall
|Contents: Graphs and Level Sets|
|The Tangent Space|
|Vector Fields on Surfaces|
|The Gauss Map|
|The Weingarten Map|
|Curvature of Plane Curves|
|Arc Length and Line Integrals|
|Curvature of Surfaces|
|Local Equivalence of Surfaces and Parametrized Surfaces|
|Surface Area and Volume|
|The Exponential Map|
|Surfaces with Boundary|
|The Gauss-Bonnet Theorem|
|Rigid Motions and Congruence|