Lecture 5 of 22Module 1 Curves in R2 and R3
Simple closed curve and isoperimetric inequality
Prof. Sudipta Dutta · IIT Kanpur
Credits and licence
- From
- Curves and Surfaces, IIT Kanpur (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation
- How much a curve is ‘curved’, signed unit normal and signed curvature, rigid motions, constant curvature
- Curves in R^3, principal normal and binormal, torsion
- Frenet-Serret formula
- Simple closed curve and isoperimetric inequality
- Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.
- Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism
- Reparameterization
- Tangent, Normal
- Orientable surfaces
- Examples of Surfaces
- First Fundamental Form
- Conformal Mapping
- Curvature of Surfaces
- Euler's Theorem
- Regular Surfaces locally as Quadratic Surfaces
- Geodesics
- Existence of Geodesics, Geodesics on Surfaces of revolution
- Geodesics on surfaces of revolution; Clairaut's Theorem
- Pseudosphere
- Classification of Quadratic Surface
- Surface Area and Equiareal Map