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Modern Differential Geometry of Curves and Surfaces
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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 | Curves in Space | Tubes and Knots | 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 | Principal Curves and Umbilic Points | Minimal Surfaces | Construction of Surfaces | Differentiable Manifolds | Riemannian Manifolds | Abstract Surfaces | Geodesics on Surfaces | Appendices
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Contains many Mathematica programs for doing the geometry of curves in R2 and R3, and surfaces in R3. Examples include the computation of curvature, geodesics, minimal surfaces, and surfaces of constant curvature. Fully illustrated. A separate diskette containing all programs and notebooks is also available from the publisher. Winner of the Distinguished Mathematics Software Development Award, EDUCOM '93.
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