Dot Product. Curves. The Frenet Formulas. Arbitrar ySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. Th e Structural Equations.
Chapter 3: Euclidean
Geometry:
Isometries of R3. The Tangent Map of an Isometr y. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces i n R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Fo rms. Topological Properties. Manifolds.
Chap ter 5: Shape Operators:
The Shape Operator of M R3. Normal
Curvature. Gaussian Curvature. Computational Techniques. The Implicit C ase. Special Curves in a Surface. Surfaces of Revolution.
By:
Barrett O'Neill (University of California Los Angeles California U.S.A.) Imprint: Academic Press Inc Country of Publication: United States Edition: 2nd Revised edition Dimensions:
Height: 229mm,
Width: 151mm,
Spine: 34mm
Weight: 930g ISBN:9780120887354 ISBN 10: 0120887355 Pages: 520 Publication Date:27 March 2006 Audience:
College/higher education
,
Primary
Format:Paperback Publisher's Status: Active
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.