Curves and Surfaces WZ6NGD09CR

Expressions

Language	en
Date	2016-07-11

Contents

part 1: Module 1 Curves in R2 and R3
session 1: Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation
session 2: How much a curve is ‘curved’, signed unit normal and signed curvature, rigid motions, constant curvature
session 3: Curves in R^3, principal normal and binormal, torsion
session 4: Frenet-Serret formula
session 5: Simple closed curve and isoperimetric inequality
part 2: Module II Surfaces-1: Smooth surfaces
session 6: Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.
session 7: Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism
session 8: Reparameterization
session 9: Tangent, Normal
session 10: Orientable surfaces
part 3: Module III Surfaces-2: First Fundamental Form
session 11: Examples of Surfaces
session 12: First Fundamental Form
session 13: Conformal Mapping
session 14: Curvature of Surfaces
session 15: Euler's Theorem
part 4: Module IV Surfaces- 3: Curvature and Geodesics
session 16: Regular Surfaces locally as Quadratic Surfaces
session 17: Geodesics
session 18: Existence of Geodesics, Geodesics on Surfaces of revolution
session 19: Geodesics on surfaces of revolution; Clairaut's Theorem
session 20: Pseudosphere
session 21: Classification of Quadratic Surface
session 22: Surface Area and Equiareal Map