Arc-length-Tangent and osculating plane-Principal normal and binomial-Curvature and torsion-Seret-Frenet formula
Osculating circle and osculating sphere-Locus of centers of spherical curvature-Tangent surfaces, involutes and evolutes-Spherical indicatrix-Helices
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
Gaussain curvature-The second fundamental form-Principle curvature-Lines of curvature
The Dupinindicatrix-Developable surfaces
Reference Book:
Differential Geometry by M Majumdar, A. Bhattacharyya, Books and Allied Pvt Limited second edition 2010
Text Book:
Differential Geometry A First Course by D.Somasundaram, NarsoPublishing HousePvt.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.
