# Curves and Surfaces

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Sudipta Dutta
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104095)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104095)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Level curves and locus, definition of parametric curves, tangent, arc length, arc length parametrisation](https://invisiblenetwork.ai/learn/nptel/111104095/7c50abacac5a) (Video)
2. [How much a curve is ‘curved’, signed unit normal and signed curvature, rigid motions, constant curvature](https://invisiblenetwork.ai/learn/nptel/111104095/857be293d570) (Video)
3. [Curves in R^3, principal normal and binormal, torsion](https://invisiblenetwork.ai/learn/nptel/111104095/d88a153e0f2c) (Video)
4. [Frenet-Serret formula](https://invisiblenetwork.ai/learn/nptel/111104095/63a3e32c3ecc) (Video)
5. [Simple closed curve and isoperimetric inequality](https://invisiblenetwork.ai/learn/nptel/111104095/d93e871debb6) (Video)
6. [Surfaces and parametric surfaces, examples, regular surface and non-example of regular surface, transition maps.](https://invisiblenetwork.ai/learn/nptel/111104095/be3aff45d144) (Video)
7. [Transition maps of smooth surfaces, smooth function between surfaces, diffeomorphism](https://invisiblenetwork.ai/learn/nptel/111104095/221bedf6ad10) (Video)
8. [Reparameterization](https://invisiblenetwork.ai/learn/nptel/111104095/f9ab8513f4b6) (Video)
9. [Tangent, Normal](https://invisiblenetwork.ai/learn/nptel/111104095/33a924daf112) (Video)
10. [Orientable surfaces](https://invisiblenetwork.ai/learn/nptel/111104095/245850816dbe) (Video)
11. [Examples of Surfaces](https://invisiblenetwork.ai/learn/nptel/111104095/bca648068c19) (Video)
12. [First Fundamental Form](https://invisiblenetwork.ai/learn/nptel/111104095/18d7f5493b3b) (Video)
13. [Conformal Mapping](https://invisiblenetwork.ai/learn/nptel/111104095/80581d7d9430) (Video)
14. [Curvature of Surfaces](https://invisiblenetwork.ai/learn/nptel/111104095/f2bb832dfef9) (Video)
15. [Euler's Theorem](https://invisiblenetwork.ai/learn/nptel/111104095/5648969f68fa) (Video)
16. [Regular Surfaces locally as Quadratic Surfaces](https://invisiblenetwork.ai/learn/nptel/111104095/f3762d720132) (Video)
17. [Geodesics](https://invisiblenetwork.ai/learn/nptel/111104095/17f611059ab0) (Video)
18. [Existence of Geodesics, Geodesics on Surfaces of revolution](https://invisiblenetwork.ai/learn/nptel/111104095/99da4ae0152d) (Video)
19. [Geodesics on surfaces of revolution; Clairaut's Theorem](https://invisiblenetwork.ai/learn/nptel/111104095/4e6a5c662801) (Video)
20. [Pseudosphere](https://invisiblenetwork.ai/learn/nptel/111104095/d4d54a7b5fe4) (Video)
21. [Classification of Quadratic Surface](https://invisiblenetwork.ai/learn/nptel/111104095/327893e02ebc) (Video)
22. [Surface Area and Equiareal Map](https://invisiblenetwork.ai/learn/nptel/111104095/969424aa753b) (Video)