Introduction-Representation of space curves-Arc-length-Tangent and osculating plane-Principal normal and binomial-Curvature and torsion-Seret-Frenet formula.
Contact between curves and surfaces-Osculating circle and osculating sphere-Locus of centers of spherical curvature-Tangent surfaces, involutes and evolutes-Spherical indicatrix-Helices.
Surfaces: Definition of surfaces-Nature of points on a surface-Representation of a surface-Metric on a surface-The first fundamental form. Geodesics and their differential equations-Theorems-Examples
Geodesics curvature-Gaussain curvature-The second fundamental form-Principle curvature-Lines of curvature.
The Dupin indicatrix-Developable surfaces.
Reference Book:
1. Differential Geometry – M Majumdar, A. Bhattacharyya, Books and Allied Pvt Limited second edition 2010.
Text Book:
1. Differential Geometry A First Course, D.Somasundaram, Narso Publishing House Pvt.Ltd, 2012. UNIT I: Chapter 1: Sections: 1.1-1.2, 1.4-1.7 UNIT II: Chapter 1: Sections: 1.10-1.13, 1.15, 1.18 UNIT III: Chapter 2: Sections: 2.1-2.4, 2.9 Chapter 3: Sections: 3.1, 3.2 UNIT IV: Chapter 3: Sections: 3.10, 3.12 Chapter 4: Sections: 4.2, 4.4, 4.5 UNIT V: Chapter 4: Sections: 4.6, 4.7
