NOC:Curves and Surfaces


Lecture 1 - Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation


Lecture 2 - How much a curve is ‘curved’, signed unit normal and signed curvature, rigid motions, constant curvature


Lecture 3 - Curves in R^3, principal normal and binormal, torsion


Lecture 4 - Frenet-Serret formula


Lecture 5 - Simple closed curve and isoperimetric inequality


Lecture 6 - Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.


Lecture 7 - Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism


Lecture 8 - Reparameterization


Lecture 9 - Tangent, Normal


Lecture 10 - Orientable surfaces


Lecture 11 - Examples of Surfaces


Lecture 12 - First Fundamental Form


Lecture 13 - Conformal Mapping


Lecture 14 - Curvature of Surfaces


Lecture 15 - Euler's Theorem


Lecture 16 - Regular Surfaces locally as Quadratic Surfaces


Lecture 17 - Geodesics


Lecture 18 - Existence of Geodesics, Geodesics on Surfaces of revolution


Lecture 19 - Geodesics on surfaces of revolution; Clairaut's Theorem


Lecture 20 - Pseudosphere


Lecture 21 - Classification of Quadratic Surface


Lecture 22 - Surface Area and Equiareal Map