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Elementary Differential Geometry

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ISBN-10: 1852331526

ISBN-13: 9781852331528

Edition: 2001

Authors: Andrew Pressley

List price: $44.95
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Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques. It is a subject that contains some of the most beautiful and profound results in mathematics, yet many of them are accessible to higher level undergraduates.Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum. Nothing more than first courses in linear algebra and multivariate…    
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Book details

List price: $44.95
Copyright year: 2001
Publisher: Springer
Publication date: 9/18/2002
Binding: Paperback
Pages: 332
Size: 7.00" wide x 9.25" long x 1.00" tall
Weight: 1.232
Language: English

Andrew Pressley is Professor of Mathematics at King�s College London, UK.

Curves in the Plane and in Space
What is a Curve?
Level Curves vs. Parametrized Curves
How Much Does a Curve Curve?
Plane Curves
Space Curves
Global Properties of Curves
Simple Closed Curves
The Isopcrimetric Inequality
The Four Vertex Theorem
Surfaces in Three Dimensions
What is a Surface?
Smooth Surfaces
Tangents, Normals and Orientability
Examples of Surfaces
Quadric Surfaces
Triply Orthogonal Systems
Applications of the Inverse Function Theorem
The First Fundamental Form
Lengths of Curves on Surfaces
Lsometries of Surfaces
Conformal Mappings of Surfaces
Surface Area
Equiareal Maps and a Theorem of Archimedes
Curvature of Surfaces
The Second Fundamental Form
The Curvature of Curves on a Surface
The Normal and Principal Curvatures
Geometric Interpretation of Pincipal Curvatures
Gaussian Curvature and the Gauss Map
The Gaussian and Mean Curvatures
The Pseudosphere
Flat Surfaces
Surfaces of Constant Mean Curvature
Gaussian Curvature of Compact Surfaces
The Gauss map
Deinition and Basic Properties
Geodesic Equations
Geodesies on Surfaces of Revolution
Geodesies as Shortest Paths
Geodesic Coordinates
Minimal Surfaces
Plateau's Problem
Examples of Minimal Surfaces
Gauss map of a Minimal Surface
Minimal Surfaces and Holomorphic Functions
Gauss's Theorema Egregiuxn
Gauss's Remarkable Theorem
Isomctries of Surfaces
The Codazzi-Mainardi Equations
Compact Surfaces of Constant Gaussian Curvature
The Gauss-Bonnet Theorem
Gauss-Bonnet for Simple Closed Curves
Gauss-Bonnet for Curvilinear Polygons
Gauss-Bonnet for Compact Surfaces
Singularities of Vector Fields
Critical Points