# Multivariable Calculus

- Institution: IIT Roorkee
- Department: Mathematics
- Teacher: Prof. S. K. Gupta Prof. Sanjeev Kumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111107108)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111107108)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Functions of several variables](https://invisiblenetwork.ai/learn/nptel/111107108/d792441b38f1) (Video)
2. [Limits for multivariable functions-I](https://invisiblenetwork.ai/learn/nptel/111107108/b5f2d10ea0e9) (Video)
3. [Limits for multivariable functions-II](https://invisiblenetwork.ai/learn/nptel/111107108/3c271ac5c22b) (Video)
4. [Continuity of multivariable functions](https://invisiblenetwork.ai/learn/nptel/111107108/7be61b1d6873) (Video)
5. [Partial Derivatives-I](https://invisiblenetwork.ai/learn/nptel/111107108/aad8e1f2e12c) (Video)
6. [Partial Derivatives-II](https://invisiblenetwork.ai/learn/nptel/111107108/5c21590ce41b) (Video)
7. [Differentiability-I](https://invisiblenetwork.ai/learn/nptel/111107108/08dc356a8f5d) (Video)
8. [Differentiability-II](https://invisiblenetwork.ai/learn/nptel/111107108/2bc8de7a5c51) (Video)
9. [Chain rule-I](https://invisiblenetwork.ai/learn/nptel/111107108/adbdb8ec6df1) (Video)
10. [Chain rule-II](https://invisiblenetwork.ai/learn/nptel/111107108/df4349db0862) (Video)
11. [Change of variables](https://invisiblenetwork.ai/learn/nptel/111107108/0211aa2f1ebf) (Video)
12. [Euler's theorem for homogeneous functions](https://invisiblenetwork.ai/learn/nptel/111107108/2cab29cff39e) (Video)
13. [Tangent planes and Normal lines](https://invisiblenetwork.ai/learn/nptel/111107108/0e2fbc47491b) (Video)
14. [Extreme values-I](https://invisiblenetwork.ai/learn/nptel/111107108/f607077062b5) (Video)
15. [Extreme values-II](https://invisiblenetwork.ai/learn/nptel/111107108/6ec88a7f22a5) (Video)
16. [Lagrange multipliers](https://invisiblenetwork.ai/learn/nptel/111107108/7addf4c3c99c) (Video)
17. [Taylor's theorem](https://invisiblenetwork.ai/learn/nptel/111107108/3e97a0fe6ee2) (Video)
18. [Error approximation](https://invisiblenetwork.ai/learn/nptel/111107108/e5349d6e3d31) (Video)
19. [Polar-curves](https://invisiblenetwork.ai/learn/nptel/111107108/f57dc9bf0082) (Video)
20. [Multiple Integrals](https://invisiblenetwork.ai/learn/nptel/111107108/4bbfdff0d8df) (Video)
21. [Change Of Order Of Integration](https://invisiblenetwork.ai/learn/nptel/111107108/c28a1ce8ab79) (Video)
22. [Change of Variables in Multiple Integral](https://invisiblenetwork.ai/learn/nptel/111107108/ce4062b972f2) (Video)
23. [Introduction to Gamma Function](https://invisiblenetwork.ai/learn/nptel/111107108/594b73b31f8a) (Video)
24. [Introduction to Beta Function](https://invisiblenetwork.ai/learn/nptel/111107108/e562210758fe) (Video)
25. [Properties of Beta and Gamma Functions-I](https://invisiblenetwork.ai/learn/nptel/111107108/a46d034fe269) (Video)
26. [Properties of Beta and Gamma Functions-II](https://invisiblenetwork.ai/learn/nptel/111107108/8825dd305777) (Video)
27. [Dirichlet's Integral](https://invisiblenetwork.ai/learn/nptel/111107108/155a072f0d99) (Video)
28. [Applications of Multiple Integrals](https://invisiblenetwork.ai/learn/nptel/111107108/4779c975588d) (Video)
29. [Vector Differentiation](https://invisiblenetwork.ai/learn/nptel/111107108/c934f849f64c) (Video)
30. [Gradient of a Scalar Field and Directional Derivative](https://invisiblenetwork.ai/learn/nptel/111107108/124ee61649a1) (Video)
31. [Normal Vector and Potential field](https://invisiblenetwork.ai/learn/nptel/111107108/c24a04963a6e) (Video)
32. [Gradient(Identities), Divergence and Curl(Identities)](https://invisiblenetwork.ai/learn/nptel/111107108/dfe288ed774d) (Video)
33. [Some Identities on Divergence and Curl](https://invisiblenetwork.ai/learn/nptel/111107108/b3175ac9871a) (Video)
34. [Line Integral (I)](https://invisiblenetwork.ai/learn/nptel/111107108/f855d6f453b1) (Video)
35. [Applications of Line Integrals](https://invisiblenetwork.ai/learn/nptel/111107108/562d1fdf01f2) (Video)
36. [Green's Theorem](https://invisiblenetwork.ai/learn/nptel/111107108/8868f17be409) (Video)
37. [Surface Area](https://invisiblenetwork.ai/learn/nptel/111107108/e040b3634e29) (Video)
38. [Surface Integral](https://invisiblenetwork.ai/learn/nptel/111107108/3aa6cc156a6c) (Video)
39. [Divergence Theorem of Gauss](https://invisiblenetwork.ai/learn/nptel/111107108/ee5f2b34e2b6) (Video)
40. [Stoke's Theorem](https://invisiblenetwork.ai/learn/nptel/111107108/5a29a8b5ca36) (Video)