Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Sudipta Dutta
NPTEL Co-ordinating Institute : IIT Kanpur
NPTEL Lecture Count : 22
NPTEL Course Size : 1.1 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
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