Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition

Alfred Gray, Elsa Abbena, and Simon Salamon, 2006, Chapman & Hall/CRC, 1016 pp., hardcover

ISBN: 1584884487

With over 300 illustrations, 300 miniprograms, and many examples, this textbook explains the classical theory of curves and surfaces, how to define and compute standard geometric functions, and how to apply techniques from analysis. It highlights important theorems and alleviates the drudgery of computations such as the curvature and torsion of a curve in space.

Contents
Curves in the Plane | Famous Plane Curves | Alternative Ways of Plotting Curves | New Curves from Old | Determining a Plane Curve from Its Curvature | Global Properties of Plane Curves | Curves in Space | Construction of Space Curves | Calculus on Euclidean Space | Surfaces in Euclidean Space | Nonorientable Surfaces | Metrics on Surfaces | Shape and Curvature | Ruled Surfaces | Surfaces of Revolution and Constant Curvature | A Selection of Minimal Surfaces | Intrinsic Surface Geometry | Asymptotic Curves and Geodesics on Surfaces | Principal Curves and Umbilic Points | Canal Surfaces and Cyclides of Dupin | The Theory of Surfaces of Constant Negative Curvature | Minimal Surfaces via Complex Variables | Rotation and Animation Using Quaternions | Differentiable Manifolds | Riemannian Manifolds | Abstract Surfaces and Their Geodesics | The Gauss-Bonnet Theorem

This book is available in the Wolfram Research bookstore.