Modern Differential Geometry of Curves and Surfaces with Mathematica (Textbooks in Mathematics) （4 Revised）

Abbena, Elsa/ Gray, Alfred/ Salamon, Simon

Chapman & Hall（2017/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 850 p.
• 言語 ENG
• 商品コード 9781466599116
• DDC分類 516

Full Description

Reflecting the latest version of Mathematica (R), this text provides an introduction to differential geometry by covering curves and surfaces in detail. Popular with students and professionals in mathematics, physics, and computer science, the book shows readers how to reproduce a large number of illustrations using Mathematica. This edition covers the latest mathematical research and moves the Mathematica notebooks to the authors' website, making the book even easier to use.

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.