# Calculus - II

- Institution: IIT Guwahati
- Department: Mathematics
- Teacher: Prof. M. Guru Prem Prasad Prof. Arup Chattopadhyay
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111103764)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111103764)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 1: Coordinates Systems 2-D and 3-D](https://invisiblenetwork.ai/learn/nptel/111103764/0010ead8a6bd) (Video)
2. [Lec 2: Vector Algebra R^n](https://invisiblenetwork.ai/learn/nptel/111103764/7174f6970f5b) (Video)
3. [Lec 3: Euclidean space R^n and some of its properties](https://invisiblenetwork.ai/learn/nptel/111103764/0765a3f04a3f) (Video)
4. [Lec 4: Sequences in R^n](https://invisiblenetwork.ai/learn/nptel/111103764/98dc5e8a47a2) (Video)
5. [Lec 5: Functions of Several Variables and Concept of Limit](https://invisiblenetwork.ai/learn/nptel/111103764/900edac8dddc) (Video)
6. [Lec 6: Properties of Limit, Iterated Limit and Double limit](https://invisiblenetwork.ai/learn/nptel/111103764/e25e45e7e6a9) (Video)
7. [Lec 7: Concept of Continuity and Some of Its Properties](https://invisiblenetwork.ai/learn/nptel/111103764/c106a7fc058d) (Video)
8. [Lec 8: Properties of Continuous Functions](https://invisiblenetwork.ai/learn/nptel/111103764/7732b73c91d5) (Video)
9. [Lec 9: Concept of Differentiability for Vector-valued Functions](https://invisiblenetwork.ai/learn/nptel/111103764/c4db72df439d) (Video)
10. [Lec 10: Properties of Differentiable Functions, Chain Rule](https://invisiblenetwork.ai/learn/nptel/111103764/e22775d70cdd) (Video)
11. [Lec 11: Applications of Differentiability](https://invisiblenetwork.ai/learn/nptel/111103764/9243ded5fe95) (Video)
12. [Lec 12: Concept of Partial Derivates, Examples and Properties](https://invisiblenetwork.ai/learn/nptel/111103764/8143e98a1af8) (Video)
13. [Lec 13: Higher order Partial Derivatives and notion of Directional Derivatives](https://invisiblenetwork.ai/learn/nptel/111103764/f73f8be6519b) (Video)
14. [Lec 14: Concept of Total Derivative and related properties](https://invisiblenetwork.ai/learn/nptel/111103764/c4243cd49cfd) (Video)
15. [Lec 15: Gradient Vector and Necessary condition for Differentiability](https://invisiblenetwork.ai/learn/nptel/111103764/19ea3be03e36) (Video)
16. [Lec 16: Sufficient condition for Differentiability and Chain rule](https://invisiblenetwork.ai/learn/nptel/111103764/3a4ec53b052f) (Video)
17. [Lec 17: Applications: Tangent Plane and Normal Line for a Surface](https://invisiblenetwork.ai/learn/nptel/111103764/15aadf75c1ec) (Video)
18. [Lec 18: Mixed Partial Derivatives and Examples](https://invisiblenetwork.ai/learn/nptel/111103764/75a7a77dcd47) (Video)
19. [Lec 19: Mixed Derivative Theorem and Examples](https://invisiblenetwork.ai/learn/nptel/111103764/e898737fedba) (Video)
20. [Lec 20: Concept of Mean Value Theorem](https://invisiblenetwork.ai/learn/nptel/111103764/cda8ab60b594) (Video)
21. [Lec 21: Notion of Hessian](https://invisiblenetwork.ai/learn/nptel/111103764/ba0bf44e207d) (Video)
22. [Lec 22: Taylor’s theorem and Linear approximation](https://invisiblenetwork.ai/learn/nptel/111103764/e241e1c42103) (Video)
23. [Lec 23: Maxima, Minima and Saddle point](https://invisiblenetwork.ai/learn/nptel/111103764/73e57d7b4a8d) (Video)
24. [Lec 24: Necessary condition for extremum and quadratic forms](https://invisiblenetwork.ai/learn/nptel/111103764/2964d5f162d0) (Video)
25. [Lec 25: Hessian matrix, Method to find the extremum values of f](https://invisiblenetwork.ai/learn/nptel/111103764/09e2196640f4) (Video)
26. [Lec 26: Global extrema, Constrained extrema](https://invisiblenetwork.ai/learn/nptel/111103764/977f6d11bf7e) (Video)
27. [Lec 27: The method of Lagrange multiplies, Exact differentials.](https://invisiblenetwork.ai/learn/nptel/111103764/be5e2692cf65) (Video)
28. [Lec 28: Definition of Double integrals in terms of Upper and Lower sums](https://invisiblenetwork.ai/learn/nptel/111103764/0c2ade7da7ae) (Video)
29. [Lec 29: Definition of Double integrals in terms of Riemaan Sum and Properties](https://invisiblenetwork.ai/learn/nptel/111103764/68fcf9a1c862) (Video)
30. [Lec 30: Iterated integral and Fubini’s theorem](https://invisiblenetwork.ai/learn/nptel/111103764/e083ebb8ad6e) (Video)
31. [Lec 31: Double integral on simple regions and Fubini’s theorem](https://invisiblenetwork.ai/learn/nptel/111103764/8591ccbc4b88) (Video)
32. [Lec 32: Change of Variables in a Double Integral and Applications](https://invisiblenetwork.ai/learn/nptel/111103764/b5648b122035) (Video)
33. [Lec 33: Definition of Triple integrals as Riemann Integral and Examples](https://invisiblenetwork.ai/learn/nptel/111103764/2c23ffb5534d) (Video)
34. [Lec 34: Triple integral on simple regions and Fubini’s theorem](https://invisiblenetwork.ai/learn/nptel/111103764/b13773ff2603) (Video)
35. [Lec 35: More on Triple integral on simple regions and Fubini’s theorem](https://invisiblenetwork.ai/learn/nptel/111103764/f299ff6a57b6) (Video)
36. [Lec 36: Change of Variables in Triple Integral and Examples](https://invisiblenetwork.ai/learn/nptel/111103764/90587692a1b7) (Video)
37. [Lec 37: Definition of Vector Fields and visualization of them by arrows](https://invisiblenetwork.ai/learn/nptel/111103764/fd10e5e3fbcb) (Video)
38. [Lec 38: Integral curves of Vector Fields, conservative and non-conservative vector fields, Gradient](https://invisiblenetwork.ai/learn/nptel/111103764/bef83a7c3a73) (Video)
39. [Lec 39: Necessary and sufficient conditions for a conservative/gradient vector field.](https://invisiblenetwork.ai/learn/nptel/111103764/4d8cfdf8b06c) (Video)
40. [Lec 40: Concept of Divergence and Curl](https://invisiblenetwork.ai/learn/nptel/111103764/9602c40d1a65) (Video)
41. [Lec 41: Curl, rotational vector field, Divergence of curl, Laplace operator](https://invisiblenetwork.ai/learn/nptel/111103764/797fe4013373) (Video)
42. [Lec 42: Recall of Curves, Smooth Curves, Piecewise Smooth Curves](https://invisiblenetwork.ai/learn/nptel/111103764/b235b226a251) (Video)
43. [Lec 43: Definition of Scalar Line Integral, Some examples and properties](https://invisiblenetwork.ai/learn/nptel/111103764/398e48749f49) (Video)
44. [Lec 44: Orientation of smooth curve and definition of Vector Line Integral](https://invisiblenetwork.ai/learn/nptel/111103764/ba73652ea066) (Video)
45. [Lec 45: Definition of Vector Line Integral, Examples , Properties and Applications](https://invisiblenetwork.ai/learn/nptel/111103764/060cf23892ba) (Video)
46. [Lec 46: Definition of surfaces, smooth surfaces, and parametrization of surfaces](https://invisiblenetwork.ai/learn/nptel/111103764/be42c95b1de7) (Video)
47. [Lec 47: Definition of scalar surface integral and some examples](https://invisiblenetwork.ai/learn/nptel/111103764/19b68fde2e55) (Video)
48. [Lec 48: Oriented surfaces and the definition of vector surface integral](https://invisiblenetwork.ai/learn/nptel/111103764/4ae0172c79fc) (Video)
49. [Lec 49: Vector surface integral and some examples](https://invisiblenetwork.ai/learn/nptel/111103764/9a4fe6bc7b6a) (Video)
50. [Lec 50: Recall the definition of curves, orientation of curves, Jordan curve theorem.](https://invisiblenetwork.ai/learn/nptel/111103764/b170ebfc713d) (Video)
51. [Lec 51: Statement, and proof of Green's theorem ona simply connected region](https://invisiblenetwork.ai/learn/nptel/111103764/36a354f0b378) (Video)
52. [Lec 52: Application of Green's theorem and Green's theorem for multiply connected regions.](https://invisiblenetwork.ai/learn/nptel/111103764/b8c88ebe4717) (Video)
53. [Lec 53: Application of Green's theorem for multiply connected regions and Examples.](https://invisiblenetwork.ai/learn/nptel/111103764/c76efa1d20eb) (Video)
54. [Lec 54: Recall the definition of surfaces, smooth surfaces, and orientation of surfaces](https://invisiblenetwork.ai/learn/nptel/111103764/ac89307895f3) (Video)
55. [Lec 55: Oriented surfaces, Stokes theorem on smooth surfaces with examples](https://invisiblenetwork.ai/learn/nptel/111103764/74e2bca18cdf) (Video)
56. [Lec 56: Stokes theorem on smooth surfaces with finitely many holes, Gauss Divergence theorem and examples](https://invisiblenetwork.ai/learn/nptel/111103764/39a1cd7844f6) (Video)
57. [Lec 57: Gauss Divergence theorem, Application of Divergence theorem and examples](https://invisiblenetwork.ai/learn/nptel/111103764/c1c5e5e91c69) (Video)
58. [Live Session 21-08-2025](https://invisiblenetwork.ai/learn/nptel/111103764/0010ead8a6bd-2) (Video)
59. [Live Session 22-09-2025](https://invisiblenetwork.ai/learn/nptel/111103764/7174f6970f5b-2) (Video)
60. [Live Session 10-10-2025](https://invisiblenetwork.ai/learn/nptel/111103764/0765a3f04a3f-2) (Video)