# Geometry of Curves and Surfaces

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Abhijit Pal
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104765)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104765)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : Parametrized Curves and Differentiable Curves](https://invisiblenetwork.ai/learn/nptel/111104765/272e94c6e994) (YouTube)
2. [Lecture 2 : Length of a Curve](https://invisiblenetwork.ai/learn/nptel/111104765/4ad7dd2959f6) (YouTube)
3. [Lecture 3 : Regular Curve, Arc-length, Re-parametrization of a Curve](https://invisiblenetwork.ai/learn/nptel/111104765/039f73eface4) (YouTube)
4. [Lecture 4 : Unit Speed Re-parametrization, Curvature of a Curve](https://invisiblenetwork.ai/learn/nptel/111104765/50aa50ee18c3) (YouTube)
5. [Lecture 5 : Curvature of a regular curve & Curvature formulas](https://invisiblenetwork.ai/learn/nptel/111104765/358d6fb1c0ef) (YouTube)
6. [Lecture 6 : Level curves, Implicit function theorem](https://invisiblenetwork.ai/learn/nptel/111104765/06772bad1b07) (YouTube)
7. [Lecture 7 : Orientation of a curve, Signed curvature, Tangent & Normal vectors](https://invisiblenetwork.ai/learn/nptel/111104765/9973a1326e13) (YouTube)
8. [Lecture 8 : Turning Angle](https://invisiblenetwork.ai/learn/nptel/111104765/29f3cb66c4dd) (YouTube)
9. [Lecture 9 : Curve determined by curvature, Total Curvature](https://invisiblenetwork.ai/learn/nptel/111104765/7319d95edcf6) (YouTube)
10. [Lecture 10 : Hopf's Rotation Index Theorem](https://invisiblenetwork.ai/learn/nptel/111104765/34600c405013) (YouTube)
11. [Lecture 11 : Four Vertex Theorem](https://invisiblenetwork.ai/learn/nptel/111104765/2bd73785b5c0) (YouTube)
12. [Lecture 12 : Isoperimetric Inequality](https://invisiblenetwork.ai/learn/nptel/111104765/741ef159376e) (YouTube)
13. [Lecture 13 : Space Curves & Principal Vectors](https://invisiblenetwork.ai/learn/nptel/111104765/e05f78c5953e) (YouTube)
14. [Lecture 14 : Frenet-Serret Equations](https://invisiblenetwork.ai/learn/nptel/111104765/2bedd9706ae7) (YouTube)
15. [Lecture 15 : Curve determined by curvature and torsion](https://invisiblenetwork.ai/learn/nptel/111104765/2160674e01fe) (YouTube)
16. [Lecture 16 :Several variable calculus](https://invisiblenetwork.ai/learn/nptel/111104765/7dd260246d16) (YouTube)
17. [Lecture 17 : Regular surfaces in real three dimensional space](https://invisiblenetwork.ai/learn/nptel/111104765/e157d10595ef) (YouTube)
18. [Lecture 18 : Examples of regular surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/32006114d15a) (YouTube)
19. [Lecture 19 : Regular Value, Critical Value of a differentiable map](https://invisiblenetwork.ai/learn/nptel/111104765/95585920c318) (YouTube)
20. [Lecture 20 : Regular surface locally graph of a differentiable function](https://invisiblenetwork.ai/learn/nptel/111104765/d80b836342a1) (YouTube)
21. [Lecture 21 : Change of parametrizations in regular surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/5cfd39ff83f9) (YouTube)
22. [Lecture 22 : Differentiable function on surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/05968f94bcb2) (YouTube)
23. [Lecture 23 : Surface of Revolution, Torus, Higher genus surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/b44358d8f99f) (YouTube)
24. [Lecture 24 : Tangent Plane and Tangent Vectors](https://invisiblenetwork.ai/learn/nptel/111104765/512eb7465caf) (YouTube)
25. [Lecture 25 : Examples of Tangent Planes](https://invisiblenetwork.ai/learn/nptel/111104765/830110943eab) (YouTube)
26. [Lecture 26 : Differential Map between Tangent Spaces](https://invisiblenetwork.ai/learn/nptel/111104765/4c73e367b0cf) (YouTube)
27. [Lecture 27 : Orientation of Surfaces and Normal Vector Field](https://invisiblenetwork.ai/learn/nptel/111104765/882b5b23a64c) (YouTube)
28. [Lecture 28 : First Fundamental Form on Surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/b6987c283967) (YouTube)
29. [Lecture 29 : Change of Parametrization in First Fundamental Form and Area](https://invisiblenetwork.ai/learn/nptel/111104765/ca065f236eb7) (YouTube)
30. [Lecture 30 : Area of Some Surfaces and Gradient on Surfaces](https://invisiblenetwork.ai/learn/nptel/111104765/523a84f9fc26) (YouTube)
31. [Lecture 31 : Isometries, local isometries, conformal maps](https://invisiblenetwork.ai/learn/nptel/111104765/bbbe65c14933) (YouTube)
32. [Lecture 32 : Gauss Map and its Fundamental Properties](https://invisiblenetwork.ai/learn/nptel/111104765/f5f45d7cb848) (YouTube)
33. [Lecture 33 : Self Adjoint Operator](https://invisiblenetwork.ai/learn/nptel/111104765/cb38554ca3be) (YouTube)
34. [Lecture 34 : Second Fundamental Form and normal Curvature](https://invisiblenetwork.ai/learn/nptel/111104765/c4ec0601ec3b) (YouTube)
35. [Lecture 35 : Examples for second fundamental form](https://invisiblenetwork.ai/learn/nptel/111104765/a20dab5cb21a) (YouTube)
36. [Lecture 36 : Principal curvatures and Principal Directions](https://invisiblenetwork.ai/learn/nptel/111104765/6563eccce3b8) (YouTube)
37. [Lecture 37 : Examples for principal curvatures and principal directions](https://invisiblenetwork.ai/learn/nptel/111104765/434d54cbcd3c) (YouTube)
38. [Lecture 38 : Gaussian Curvature and Mean Curvature](https://invisiblenetwork.ai/learn/nptel/111104765/c0047bfe4b16) (YouTube)
39. [Lecture 39 : Christoffel Symbols and The Gauss's Remarkable Theorem](https://invisiblenetwork.ai/learn/nptel/111104765/b100d07b5739) (YouTube)
40. [Lecture 40 : Invariance of Gaussian Curvature and Examples of Christoffel Symbols](https://invisiblenetwork.ai/learn/nptel/111104765/2dfe7e1e908b) (YouTube)
41. [Lecture 41 : Vector Field and Covariant Derivative](https://invisiblenetwork.ai/learn/nptel/111104765/d22e109b3f55) (YouTube)
42. [Lecture 42 : Vector Field along a curve, parallel vector field and geodesics](https://invisiblenetwork.ai/learn/nptel/111104765/af27d0dd80eb) (YouTube)
43. [Lecture 43 : Geodesics and its equations](https://invisiblenetwork.ai/learn/nptel/111104765/ba270d9593a0) (YouTube)
44. [Lecture 44 : Simplicial Complex, Triangulation and Euler Characteristics](https://invisiblenetwork.ai/learn/nptel/111104765/5b3247b798e7) (YouTube)
45. [Lecture 45 : Gauss Bonnet Theorem](https://invisiblenetwork.ai/learn/nptel/111104765/3afd515bbef5) (YouTube)