Differential geometry of curves and surfaces. (2010)

• Record Type: Book
• Further Information: Note: Thomas Banchoff, Stephen Lovett.
• Authors: Banchoff, Thomas; Lovett, Stephen (Stephen T.)
• Contents: Preface Acknowledgements Plane Curves: Local Properties Parameterizations 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 The Gauss Map The Second Fundamental Form Normal and Principal Curvatures Gaussian and Mean Curvature Ruled Surfaces and Minimal Surfaces The Fundamental Equations of Surfaces Tensor Notation Gauss’s Equations and the Christoffel Symbols Codazzi Equations and the Theorema Egregium The Fundamental Theorem of Surface Theory Curves on Surfaces Curvatures and Torsion Geodesics Geodesic Coordinates Gauss-Bonnet Theorem and Applications Intrinsic Geometry Bibliography
• Publisher Details: Natick, Massachusetts : CRC Press
• Publication Date: 2010
• Copyright Date: 2010
• Extent: 1 online resource (345 pages), illustrations
• Subjects: 516.36; Geometry, Differential; Geometry, Differential; Electronic books
• Languages: English
• ISBNs: 9781439894057; 1439894051
• Related ISBNs: 9781568814568
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• 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.