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Full Product Details

Author:   Barrett O'Neill (University of California, Los Angeles, California, U.S.A.)
Publisher:   Elsevier Science Publishing Co Inc
Imprint:   Academic Press Inc
Edition:   2nd edition
Dimensions:   Width: 15.20cm , Height: 3.40cm , Length: 22.90cm
Weight:   0.930kg
ISBN:  

9780120887354

ISBN 10:   0120887355
Pages:   520
Publication Date:   16 May 2006
Audience:   College/higher education ,  Tertiary & Higher Education
Replaced By:   9780443365126
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Chapter 1: Calculus on Euclidean Space: Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings. Chapter 2: Frame Fields: Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations. Chapter 3: Euclidean Geometry: Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves. Chapter 4: Calculus on a Surface: Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds. Chapter 5: Shape Operators: The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution. Chapter 6: Geometry of Surfaces in R3: The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces. Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet. Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.

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Author Information

Barrett O'Neill is currently a Professor in the Department of Mathematics at the University of California, Los Angeles. He has written two other books in advanced mathematics.

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