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

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.