Modern differential geometry of curves and surfaces with Mathematica
Alfred Gray.
2nd ed.
Boca Raton : CRC Press, ©1998.
xxiv, 1053 págs. : ilustraciones ; 26 cm.
ISBN: 0849371643
Compatible con Mathematica 3.0.
Incluye referencias bibliográficas (p. 1005-1020) e índices.
Reseña: MathSciNet, 2000i:53001
Contenido
- 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 surves
- 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
- Minimal surfaces and complex variables
- Minimal surfaces via the Weierstrass representation
- Minimal surfaces via Björling's formula
- Construction of surfaces
- Canal surfaces and cyclides of Dupin
- Inversions of curves and surfaces
- Appendices.
