Differential geometry of curves and surfaces. (2015)
- Record Type:
- Book
- Title:
- Differential geometry of curves and surfaces. (2015)
- Main Title:
- Differential geometry of curves and surfaces
- Further Information:
- Note: Thomas F. Banchoff, Stephen T. Lovett.
- Authors:
- Banchoff, Thomas
Lovett, Stephen (Stephen T.) - Contents:
- Plane Curves: Local Properties; Parametrizations; Position, Velocity, and Acceleration; Curvature; Osculating Circles, Evolutes, and Involutes; Natural Equations Plane Curves: Global Properties; Basic Properties; Rotation Index; Isoperimetric Inequality; Curvature, Convexity, and the Four-Vertex Theorem Curves in Space: Local Properties; Definitions, Examples, and Differentiation; Curvature, Torsion, and the Frenet Frame; Osculating Plane and Osculating Sphere; Natural Equations Curves in Space: Global Properties ; Basic Properties; Indicatrices and Total Curvature; Knots and Links Regular Surfaces; Parametrized Surfaces; Tangent Planes and Regular Surfaces; Change of Coordinates; The Tangent Space and the Normal Vector; Orientable Surfaces The First and Second Fundamental Forms ; The First Fundamental Form; Map Projections (Optional); The Gauss Map; The Second Fundamental Form; Normal and Principal Curvatures; Gaussian and Mean Curvature; Developable Surfaces and Minimal Surfaces The Fundamental Equations of Surfaces ; Gauss’s Equations and the Christoffel Symbols; Codazzi Equations and the Theorema Egregium; The Fundamental Theorem of Surface Theory The Gauss–Bonnet Theorem and Geometry of Geodesics ; Curvatures and Torsion; Gauss–Bonnet Theorem, Local Form; Gauss–Bonnet Theorem, Global Form; Geodesics; Geodesic Coordinates; Applications to Plane, Spherical and Elliptic Geometry; Hyperbolic Geometry Curves and Surfaces in n -Dimensional Euclidean Space; Curves in nPlane Curves: Local Properties; Parametrizations; Position, Velocity, and Acceleration; Curvature; Osculating Circles, Evolutes, and Involutes; Natural Equations Plane Curves: Global Properties; Basic Properties; Rotation Index; Isoperimetric Inequality; Curvature, Convexity, and the Four-Vertex Theorem Curves in Space: Local Properties; Definitions, Examples, and Differentiation; Curvature, Torsion, and the Frenet Frame; Osculating Plane and Osculating Sphere; Natural Equations Curves in Space: Global Properties ; Basic Properties; Indicatrices and Total Curvature; Knots and Links Regular Surfaces; Parametrized Surfaces; Tangent Planes and Regular Surfaces; Change of Coordinates; The Tangent Space and the Normal Vector; Orientable Surfaces The First and Second Fundamental Forms ; The First Fundamental Form; Map Projections (Optional); The Gauss Map; The Second Fundamental Form; Normal and Principal Curvatures; Gaussian and Mean Curvature; Developable Surfaces and Minimal Surfaces The Fundamental Equations of Surfaces ; Gauss’s Equations and the Christoffel Symbols; Codazzi Equations and the Theorema Egregium; The Fundamental Theorem of Surface Theory The Gauss–Bonnet Theorem and Geometry of Geodesics ; Curvatures and Torsion; Gauss–Bonnet Theorem, Local Form; Gauss–Bonnet Theorem, Global Form; Geodesics; Geodesic Coordinates; Applications to Plane, Spherical and Elliptic Geometry; Hyperbolic Geometry Curves and Surfaces in n -Dimensional Euclidean Space; Curves in n -Dimensional Euclidean Space; Surfaces in Rn Appendix: Tensor Notation … (more)
- Edition:
- Second edition
- Publisher Details:
- Boca Raton : Chapman & Hall/CRC
- Publication Date:
- 2015
- Extent:
- 1 online resource, illustrations (black and white)
- Subjects:
- 516.36
Geometry, Differential
Curves on surfaces
Surfaces - Languages:
- English
- ISBNs:
- 9781482247473
9781482247374
9781482247459 - Related ISBNs:
- 9781482247343
- Notes:
- Note: Description based on CIP data; item not viewed.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.137334
- Ingest File:
- 02_134.xml