Elementary Differential Geometry
2nd Edition
Published on 22. May 1997
Book
Hardback
448 pages
978-0-12-526745-8 (ISBN)
Description
Written primarily for readers who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Second Edition provides an introduction to the geometry of curves and surfaces. Although the popular First Edition has been extensively modified, this Second Edition maintains the elementary character of that volume, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis has been placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. For readers with access to the symbolic computation programs, Mathematica or Maple, the book includes approximately 30 optional computer exercises. These are not intended as an essential part of the book, but rather an extension. No computer skill is necessary to take full advantage of this comprehensive text.
More details
Edition
2nd Revised edition
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Edition type
Revised edition
Illustrations
illustrations, bibliography, index
Dimensions
Height: 229 mm
Width: 152 mm
Weight
826 gr
ISBN-13
978-0-12-526745-8 (9780125267458)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Barrett O'Neill
Elementary Differential Geometry, Revised 2nd Edition
Book
05/2006
2nd Edition
Academic Press
€94.50
Shipment within 15-20 days
Previous edition
Barrett O'Neill
Elementary Differential Geometry
Book
10/1997
Academic Press
€29.71
Article exhausted; check for reprint
Person
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.
Content
Part 1 Calculus on Euclidean space: Euclidean space; tangent vectors; directional derivatives; curves in R3; 1-forms; differential forms; mappings. Part 2 Frame fields: dot product; curves; the Frenet formulas; arbitrary speed curves; covariant derivatives; frame fields; connection forms; the structural equations. Part 3 Euclidean geometry: isometries of R3; the tangent map of an isometry; orientation; Euclidean geometry; congruence of curves. Part 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. Part 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. Part 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. Part 7 Riemannian geometry: geometric surfaces; Gaussian curvature; covariant derivative; geodesics; Clairaut parametrizations; the Gauss-Bonnet theorem; applications of Gauss-Bonnet. Part 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.