# Integral and Vector Calculus

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Hari Shankar Mahato
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105122)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105122)
- 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 : Partition, Riemann intergrability and One example](https://invisiblenetwork.ai/learn/nptel/111105122/6baee0bbdbbe) (Video)
2. [Lecture 2 : Partition, Riemann intergrability and One example (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/8c098415eb23) (Video)
3. [Lecture 3 : Condition of integrability](https://invisiblenetwork.ai/learn/nptel/111105122/00095b9e75d5) (Video)
4. [Lecture 4 : Theorems on Riemann integrations](https://invisiblenetwork.ai/learn/nptel/111105122/603fc3b6cb1f) (Video)
5. [Lecture 5 : Examples](https://invisiblenetwork.ai/learn/nptel/111105122/ed78a4e6d1ba) (Video)
6. [Lecture 06: Examples (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/d81c7c542ce4) (Video)
7. [Lecture 07: Reduction formula](https://invisiblenetwork.ai/learn/nptel/111105122/3012dd22b9d6) (Video)
8. [Lecture 08: Reduction formula (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/07f01ee21a60) (Video)
9. [Lecture 09: Improper Integral](https://invisiblenetwork.ai/learn/nptel/111105122/dd50fe7c6ab1) (Video)
10. [Lecture 10: Improper Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/0daef223f935) (Video)
11. [Lecture 11 : Improper Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/4c6cd40cf5b1) (Video)
12. [Lecture 12 : Improper Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/62ccabc0f2d8) (Video)
13. [Lecture 13 : Introduction to Beta and Gamma Function](https://invisiblenetwork.ai/learn/nptel/111105122/04bc404805e8) (Video)
14. [Lecture 14 : Beta and Gamma Function](https://invisiblenetwork.ai/learn/nptel/111105122/2041706cd91a) (Video)
15. [Lecture 15 :Differentiation under Integral Sign](https://invisiblenetwork.ai/learn/nptel/111105122/dc03658bca7e) (Video)
16. [Lecture 16 : Differentiation under Integral Sign (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/8a92a6abcfd4) (Video)
17. [Lecture 17 : Double Integral](https://invisiblenetwork.ai/learn/nptel/111105122/783cb91e5d32) (Video)
18. [Lecture 18 : Double Integral over a Region E](https://invisiblenetwork.ai/learn/nptel/111105122/9c0c3ab13fc9) (Video)
19. [Lecture 19 : Examples of Integral over a Region E](https://invisiblenetwork.ai/learn/nptel/111105122/6cf6c41612c5) (Video)
20. [Lecture 20 : Change of variables in a Double Integral](https://invisiblenetwork.ai/learn/nptel/111105122/e74af89131d1) (Video)
21. [Lecture 21: Change of order of Integration](https://invisiblenetwork.ai/learn/nptel/111105122/c84ad06b4068) (Video)
22. [Lecture 22: Triple Integral](https://invisiblenetwork.ai/learn/nptel/111105122/be6710af1bad) (Video)
23. [Lecture 23: Triple Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/9308c7fd9b63) (Video)
24. [Lecture 24: Area of Plane Region](https://invisiblenetwork.ai/learn/nptel/111105122/eb6867251591) (Video)
25. [Lecture 25: Area of Plane Region (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/d1df0a1cf4dd) (Video)
26. [Lecture 26 :Rectification](https://invisiblenetwork.ai/learn/nptel/111105122/694dd5208bc1) (Video)
27. [Lecture 27 : Rectification (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/5e4b4271f61d) (Video)
28. [Lecture 28 : Surface Integral](https://invisiblenetwork.ai/learn/nptel/111105122/59bc4e5e0307) (Video)
29. [Lecture 29 : Surface Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/ba6b82a9023b) (Video)
30. [Lecture 30 : Surface Integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/571cff2a443b) (Video)
31. [Lecture 31: Volume Integral, Gauss Divergence Theorem](https://invisiblenetwork.ai/learn/nptel/111105122/413bfbb806cf) (Video)
32. [Lecture 32: Vector Calculus](https://invisiblenetwork.ai/learn/nptel/111105122/8f4aa484da16) (Video)
33. [Lecture 33: Limit, Continuity, Differentiability](https://invisiblenetwork.ai/learn/nptel/111105122/d68da7bcc4f8) (Video)
34. [Lecture 34: Successive Differentiation](https://invisiblenetwork.ai/learn/nptel/111105122/b8a2f07451bc) (Video)
35. [Lecture 35: Integration of Vector Function](https://invisiblenetwork.ai/learn/nptel/111105122/96d2fbac2d45) (Video)
36. [Lecture 36: Gradient of a Function](https://invisiblenetwork.ai/learn/nptel/111105122/00d1188691c0) (Video)
37. [Lecture 37: Divergence & Curl](https://invisiblenetwork.ai/learn/nptel/111105122/0aeac01409e2) (Video)
38. [Lecture 38: Divergence & Curl Examples](https://invisiblenetwork.ai/learn/nptel/111105122/8f8e6bd93578) (Video)
39. [Lecture 39: Divergence & Curl important Identities](https://invisiblenetwork.ai/learn/nptel/111105122/16f3ed2f7589) (Video)
40. [Lecture 40: Level Surface Relevant Theorems](https://invisiblenetwork.ai/learn/nptel/111105122/6b3f04603075) (Video)
41. [Lecture 41: Directional Derivative (Concept & Few Results)](https://invisiblenetwork.ai/learn/nptel/111105122/6ea0e5c58941) (Video)
42. [Lecture 42: Directional Derivative (Concept & Few Results) (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/22c6d788bbb1) (Video)
43. [Lecture 43: Directional Derivatives, Level Surfaces](https://invisiblenetwork.ai/learn/nptel/111105122/1102b3691ef1) (Video)
44. [Lecture 44: Application to Mechanics](https://invisiblenetwork.ai/learn/nptel/111105122/aa2cc9ab0cd1) (Video)
45. [Lecture 45: Equation of Tangent, Unit Tangent Vector](https://invisiblenetwork.ai/learn/nptel/111105122/67864e18ebbf) (Video)
46. [Lecture 46: Unit Normal, Unit binormal, Equation of Normal Plane](https://invisiblenetwork.ai/learn/nptel/111105122/f353df1267df) (Video)
47. [Lecture 47: Introduction and Derivation of Serret-Frenet Formula, few results](https://invisiblenetwork.ai/learn/nptel/111105122/6c884778059e) (Video)
48. [Lecture 48: Example on binormal, normal tangent, Serret-Frenet Formula](https://invisiblenetwork.ai/learn/nptel/111105122/ba0f5e34efc0) (Video)
49. [Lecture 49: Osculating Plane, Rectifying plane, Normal plane](https://invisiblenetwork.ai/learn/nptel/111105122/703e7b2d0daa) (Video)
50. [Lecture 50: Application to Mechanics, Velocity, speed , acceleration](https://invisiblenetwork.ai/learn/nptel/111105122/e9ecc184e227) (Video)
51. [Lecture 51: Angular Momentum, Newton's Law](https://invisiblenetwork.ai/learn/nptel/111105122/692397962a1a) (Video)
52. [Lecture 52: Example on derivation of equation of motion of particle](https://invisiblenetwork.ai/learn/nptel/111105122/8c0e5ab7ff98) (Video)
53. [Lecture 53: Line Integral](https://invisiblenetwork.ai/learn/nptel/111105122/b0e4e675d819) (Video)
54. [Lecture 54: Surface integral](https://invisiblenetwork.ai/learn/nptel/111105122/e0eada5e7351) (Video)
55. [Lecture 55: Surface integral (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105122/f7a89acffaea) (Video)
56. [Lecture 56: Green's Theorem & Example](https://invisiblenetwork.ai/learn/nptel/111105122/83797efae046) (Video)
57. [Lecture 57: Volume integral, Gauss theorem](https://invisiblenetwork.ai/learn/nptel/111105122/c9172654d4ee) (Video)
58. [Lecture 58: Gauss divergence theorem](https://invisiblenetwork.ai/learn/nptel/111105122/72fb34a8c7ea) (Video)
59. [Lecture 59: Stoke's Theorem](https://invisiblenetwork.ai/learn/nptel/111105122/9a61f5626910) (Video)
60. [Lecture 60: Overview of Course](https://invisiblenetwork.ai/learn/nptel/111105122/8f4799aad861) (Video)
61. [Live Session 07-04-2021](https://invisiblenetwork.ai/learn/nptel/111105122/6baee0bbdbbe-2) (Video)
62. [Live Session 21-04-2021](https://invisiblenetwork.ai/learn/nptel/111105122/8c098415eb23-2) (Video)
63. [Live Session 20-02-2020](https://invisiblenetwork.ai/learn/nptel/111105122/00095b9e75d5-2) (Video)
64. [Live Session 16-03-2020](https://invisiblenetwork.ai/learn/nptel/111105122/603fc3b6cb1f-2) (Video)
65. [Live Session 03-03-2022](https://invisiblenetwork.ai/learn/nptel/111105122/ed78a4e6d1ba-2) (Video)
66. [Live Session 01-04-2022](https://invisiblenetwork.ai/learn/nptel/111105122/d81c7c542ce4-2) (Video)
67. [Live Session 18-04-2022](https://invisiblenetwork.ai/learn/nptel/111105122/3012dd22b9d6-2) (Video)