# Calculus of Several Real Variables

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Joydeep Dutta
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104125)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104125)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, study multiple integrals and their applications and end with the stokes Theorem and Gauss divergence theorem.

INTENDED AUDIENCE: Any Interested Learners

PREREQUISITES: Calculus of One Real Variable

## Lectures

1. [Vectors in plane and space](https://invisiblenetwork.ai/learn/nptel/111104125/758ded7c1898) (YouTube)
2. [Inner product and distance](https://invisiblenetwork.ai/learn/nptel/111104125/763ebe6b0cb4) (YouTube)
3. [Application to real world problems](https://invisiblenetwork.ai/learn/nptel/111104125/286441043349) (YouTube)
4. [Matrices and determinants](https://invisiblenetwork.ai/learn/nptel/111104125/8eb7af823cdf) (YouTube)
5. [Cross product of two vectors](https://invisiblenetwork.ai/learn/nptel/111104125/77b8f626217c) (YouTube)
6. [Higher dimensional Euclidean space](https://invisiblenetwork.ai/learn/nptel/111104125/399a11b12b3f) (YouTube)
7. [Functions of more than one real-variable](https://invisiblenetwork.ai/learn/nptel/111104125/79449cec5ac1) (YouTube)
8. [Partial derivatives and Continuity](https://invisiblenetwork.ai/learn/nptel/111104125/422a1d975276) (YouTube)
9. [Vector-valued maps and Jacobian matrix](https://invisiblenetwork.ai/learn/nptel/111104125/908c8c3f5866) (YouTube)
10. [Chain rule for partial derivatives](https://invisiblenetwork.ai/learn/nptel/111104125/132282bdb294) (YouTube)
11. [The Gradient Vector and Directional Derivative](https://invisiblenetwork.ai/learn/nptel/111104125/ac17d1f25ec3) (YouTube)
12. [The Implicit Function Theorem](https://invisiblenetwork.ai/learn/nptel/111104125/97b6efc10426) (YouTube)
13. [Higher Order Partial Derivatives](https://invisiblenetwork.ai/learn/nptel/111104125/2a9d461876bb) (YouTube)
14. [Taylor's Theorem in Higher Dimension](https://invisiblenetwork.ai/learn/nptel/111104125/90a59e014691) (YouTube)
15. [Maxima and Minima for Several Variables](https://invisiblenetwork.ai/learn/nptel/111104125/2af8065ffede) (YouTube)
16. [Second Derivative Test for Maximum and Minimum](https://invisiblenetwork.ai/learn/nptel/111104125/c3c6baabbce6) (YouTube)
17. [Constrained Optimization and The Lagrange Multiplier Rule](https://invisiblenetwork.ai/learn/nptel/111104125/2b8c2c9c36a9) (YouTube)
18. [Vector Valued Function and Classical Mechanics](https://invisiblenetwork.ai/learn/nptel/111104125/0c5fcfcce065) (YouTube)
19. [Arc Length](https://invisiblenetwork.ai/learn/nptel/111104125/363af54be12b) (YouTube)
20. [Vector Fields](https://invisiblenetwork.ai/learn/nptel/111104125/b50b18b26aa6) (YouTube)
21. [Multiple Integral I](https://invisiblenetwork.ai/learn/nptel/111104125/6fe8b4beb698) (YouTube)
22. [Multiple Integral II](https://invisiblenetwork.ai/learn/nptel/111104125/f1f07960bc3d) (YouTube)
23. [Multiple Integral III](https://invisiblenetwork.ai/learn/nptel/111104125/e3c114219ef9) (YouTube)
24. [Multiple Integral IV](https://invisiblenetwork.ai/learn/nptel/111104125/b33724d6db32) (YouTube)
25. [Cylindrical and Spherical Coordinates](https://invisiblenetwork.ai/learn/nptel/111104125/575d75835f3c) (YouTube)
26. [Multiple Integrals and Mechanics](https://invisiblenetwork.ai/learn/nptel/111104125/4b41ae16d112) (YouTube)
27. [Line Integral-I](https://invisiblenetwork.ai/learn/nptel/111104125/ccb379b307c3) (YouTube)
28. [Line Integral-II](https://invisiblenetwork.ai/learn/nptel/111104125/c79bcebd9d5d) (YouTube)
29. [Parametrized Surfaces](https://invisiblenetwork.ai/learn/nptel/111104125/bc2cb78453c0) (YouTube)
30. [Area of a surface Integral](https://invisiblenetwork.ai/learn/nptel/111104125/c7cf5c455ee0) (YouTube)
31. [Area of parametrized surface](https://invisiblenetwork.ai/learn/nptel/111104125/d013e05a73e0) (YouTube)
32. [Surface Integrals](https://invisiblenetwork.ai/learn/nptel/111104125/e582e80ac20f) (YouTube)
33. [Green's Theorem](https://invisiblenetwork.ai/learn/nptel/111104125/b358945d9fcc) (YouTube)
34. [Stoke's Theorem](https://invisiblenetwork.ai/learn/nptel/111104125/2db1dde6c61c) (YouTube)
35. [Examples of Stoke's Theorem](https://invisiblenetwork.ai/learn/nptel/111104125/4ef989f175e2) (YouTube)
36. [Gauss Divergence Theorem](https://invisiblenetwork.ai/learn/nptel/111104125/158f335beb16) (YouTube)
37. [Facts about vector fields](https://invisiblenetwork.ai/learn/nptel/111104125/72145df9d52d) (YouTube)