Elementary Differential Geometry, Revised 2nd Edition

Elementary Differential Geometry, Revised 2nd Edition

4.14 (28 ratings by Goodreads)
By (author) 

List price: US$89.95

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

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.
show more

Product details

  • Hardback | 448 pages
  • 158 x 230 x 28mm | 879.96g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 2nd edition
  • illustrations, bibliography, index
  • 0125267452
  • 9780125267458

Table of contents

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.
show more

About Barrett O'Neill

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.
show more

Rating details

28 ratings
4.14 out of 5 stars
5 43% (12)
4 39% (11)
3 11% (3)
2 4% (1)
1 4% (1)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X