Junior/Senior level courses, introductory courses for graduate students, individual study by mathematicians and by those in applied areas such as physics. The Gauss-Bonnet Theorem. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. Covariant Derivative. Chapter 7:

## Differential Geometry Curves Surfaces Manifolds

Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 7nd Edition, provides an introduction to the geometry of curves and surfaces.

### Manifolds and Differential Geometry Graduate Studies in

Clairaut Parametrizations. Applications of Gauss-Bonnet. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.