Comprehensive Study of Curves in Differential Geometry - Tapa blanda

Mohamed Ali Abou Bakr, Sahar

 
9783659874079: Comprehensive Study of Curves in Differential Geometry
Tapa blanda
ISBN 10: 3659874078 ISBN 13: 9783659874079
Editorial: LAP LAMBERT Academic Publishing, 2016

Sinopsis

The topics of this textbook are curves in differential geometry and they are primarily studied by means of parametrization. Particularly; curvilinear coordinates, plane curves and skew curves like; helices, involutes, evolutes, spherical indicatrix, circles and spheres of curvatures. It also introduces some quadratic surfaces, theory of contacts, curves-surfaces contacts relationships, envelops, the geometry of curves in differential geometry in general. The main properties of these objects, which will be studied, are notions related to the shape;tangents, principle normals, binormals,tangent lines, normal planes, osculating planes, and rectifying planes. The fundamental investigated concepts are curvatures and torsion as the basic intrinsic property of a curve, independent of its isometric embedding in Euclidean space. One of the most important tools used to analyze a curve is the Serret-Frenet frame,a moving frame that provides a coordinate system at each point of the curve that is best adapted to the curve near that point.This text is supplied with sufficient illustrated figures, adequate number of examples, exercises,and problem solving to meet the quality standard.

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Reseña del editor

The topics of this textbook are curves in differential geometry and they are primarily studied by means of parametrization. Particularly; curvilinear coordinates, plane curves and skew curves like; helices, involutes, evolutes, spherical indicatrix, circles and spheres of curvatures. It also introduces some quadratic surfaces, theory of contacts, curves-surfaces contacts relationships, envelops, the geometry of curves in differential geometry in general. The main properties of these objects, which will be studied, are notions related to the shape;tangents, principle normals, binormals,tangent lines, normal planes, osculating planes, and rectifying planes. The fundamental investigated concepts are curvatures and torsion as the basic intrinsic property of a curve, independent of its isometric embedding in Euclidean space. One of the most important tools used to analyze a curve is the Serret-Frenet frame,a moving frame that provides a coordinate system at each point of the curve that is best adapted to the curve near that point.This text is supplied with sufficient illustrated figures, adequate number of examples, exercises,and problem solving to meet the quality standard.

Biografía del autor

Sahar Mohamed Ali is an associate professor of pure mathematics at Ain Shams University, Faculty of Science, Cairo, Egypt, teaches some pure mathematical courses for under graduate and post graduate students, supervising projects, M.Sc and Ph.D thesis, authoring many research papers and books, her major field of study is functional & real Analysis

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Editorial
LAP LAMBERT Academic Publishing
Año de publicación
2016
Idioma
Inglés
ISBN 10 
3659874078
ISBN 13 
9783659874079
Encuadernación
Tapa blanda
Número de páginas
224
Contacto del fabricante
no disponible
Persona responsable
no disponible