Combines a traditional approach with the symbolic capabilities of Mathematica to explain the classical theory of curves and surfaces. Explains how to define and compute standard geometric functions and explores how to apply techniques from analysis. Contains over 300 exercises and examples to demonstrate concepts. Compatible with Mathematica 3.0.
Curves in the Plane | Studying Curves in the Plane with Mathematica | Famous Plane Curves | Alternate Methods for Plotting Plane Curves | New Curves from Old | Determining a Plane Curve from Its Curvature | Global Properties of Plane Curves | Curves in Space | Tubes and Knots | Construction of Space Curves | Calculus on Euclidean Space | Surfaces in Euclidean Space | Examples of Surfaces | Nonorientable Surfaces | Metrics on Surfaces | Surfaces in 3-Dimensional Space | Surfaces in 3-Dimensional Space via Mathematica | Asymptotic Curves on Surfaces | Ruled Surfaces | Surfaces of Revolution | Surfaces of Constant Gaussian Curvature | Intrinsic Surface Geometry | Differentiable Manifolds | Riemannian Manifolds | Abstract Surfaces | Geodesics on Surfaces | The Gauss-Bonnet Theorem | Principal Curves and Umbilic Points | Triply Orthogonal Systems of Surfaces | Minimal Surfaces I | Minimal Surfaces II | Minimal Surfaces III | Minimal Surfaces IV | Construction of Surfaces | Canal Surfaces and Cyclides of Dupin | Inversions of Curves and Surfaces | Appendices