# Advanced Calculus for Engineers

- Institution: IIT Kharagpur
- Department: Mathematics
- Taught by: Prof. Jitendra Kumar, Prof. Somesh Kumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105160)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105160)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course is about basic mathematics, which is a fundamental and essential component of all undergraduate studies in sciences and engineering. This course consists of topics in differential, integral, and vector calculus with applications to various engineering problems. This course will cover calculus of two or more variables in detail. Knowledge of ordinary differential equations are part of this course. Students will learn how to perform double and triple integrals. Topic in vector calculus includesline and surface integrals, Green, Gauss and Stokes theorem.

Prerequisites: Higher SecondaryINTENDED AUDIENCE: All branches of science and engineering

## Lectures

1. [Lecture 01 : Rolle’s Theorem](https://invisiblenetwork.ai/learn/nptel/111105160/b5c32be87eb6) (YouTube)
2. [Lecture 02 : Mean Value Theorem](https://invisiblenetwork.ai/learn/nptel/111105160/68e17604f6ea) (YouTube)
3. [Lecture 03 : Taylor’s Formula (Single Variable)](https://invisiblenetwork.ai/learn/nptel/111105160/befe5a868dc7) (YouTube)
4. [Lecture 04 : Indeterminate Forms – Part 01](https://invisiblenetwork.ai/learn/nptel/111105160/73988a4a5a00) (YouTube)
5. [Lecture 05 : Indeterminate Forms – Part 02](https://invisiblenetwork.ai/learn/nptel/111105160/f12ecd841e9d) (YouTube)
6. [Lecture 06 : Introduction to Limit](https://invisiblenetwork.ai/learn/nptel/111105160/2915b4807660) (YouTube)
7. [Lecture 07 : Evaluation of Limit](https://invisiblenetwork.ai/learn/nptel/111105160/0857533dd293) (YouTube)
8. [Lecture 08 : Continuity](https://invisiblenetwork.ai/learn/nptel/111105160/eb8bb860469f) (YouTube)
9. [Lecture 09 : First Order Partial Derivatives](https://invisiblenetwork.ai/learn/nptel/111105160/e4fd94096550) (YouTube)
10. [Lecture 10 : Higher Order Partial Derivatives](https://invisiblenetwork.ai/learn/nptel/111105160/10d4aa12f16a) (YouTube)
11. [Lecture 11 : Differentiability – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/0af8533a4eff) (YouTube)
12. [Lecture 12 : Differentiability – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/e6441cb90815) (YouTube)
13. [Lecture 13 : Differentiability – Part 3](https://invisiblenetwork.ai/learn/nptel/111105160/deebb605a99f) (YouTube)
14. [Lecture 14 : Differentiability – Part 4](https://invisiblenetwork.ai/learn/nptel/111105160/e0b4c1f85ed1) (YouTube)
15. [Lecture 15 : Composite & Homogeneous Functions](https://invisiblenetwork.ai/learn/nptel/111105160/d93480eef79e) (YouTube)
16. [Lecture 16 : Taylor’s Theorem (Multivariable)](https://invisiblenetwork.ai/learn/nptel/111105160/880cf371b009) (YouTube)
17. [Lecture 17 : Maxima & Minima – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/781a5099e4b7) (YouTube)
18. [Lecture 18 : Maxima & Minima – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/b5e8b8a737be) (YouTube)
19. [Lecture 19 : Maxima & Minima – Part 3](https://invisiblenetwork.ai/learn/nptel/111105160/5bf0d526e9ba) (YouTube)
20. [Lecture 20 : Maxima & Minima – Part 4](https://invisiblenetwork.ai/learn/nptel/111105160/632314ac9044) (YouTube)
21. [Lecture 21 : Formation of Differential Equations](https://invisiblenetwork.ai/learn/nptel/111105160/eb55ca3991f5) (YouTube)
22. [Lecture 22 : First Order and First Degree DE](https://invisiblenetwork.ai/learn/nptel/111105160/d9fe70ac9ae5) (YouTube)
23. [Lecture 23 : Exact Differential Equations](https://invisiblenetwork.ai/learn/nptel/111105160/a57cd34f7db7) (YouTube)
24. [Lecture 24 : Integrating Factor](https://invisiblenetwork.ai/learn/nptel/111105160/91bbd91279a8) (YouTube)
25. [Lecture 25 : Linear Differential Equations](https://invisiblenetwork.ai/learn/nptel/111105160/b534455060dc) (YouTube)
26. [Lecture 26 : Introduction to Higher Order DEs](https://invisiblenetwork.ai/learn/nptel/111105160/410e77d3b6de) (YouTube)
27. [Lecture 27 : Complementary Function](https://invisiblenetwork.ai/learn/nptel/111105160/4dcb692f3394) (YouTube)
28. [Lecture 28 : Particular Integral](https://invisiblenetwork.ai/learn/nptel/111105160/a09aa9c5ac0f) (YouTube)
29. [Lecture 29 : Cauchy-Euler Equations](https://invisiblenetwork.ai/learn/nptel/111105160/59b285d95082) (YouTube)
30. [Lecture 30 : Method of Variation of Parameters](https://invisiblenetwork.ai/learn/nptel/111105160/9b782b6b48ca) (YouTube)
31. [Lecture 31 : Improper Integral – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/69ad801c330f) (YouTube)
32. [Lecture 32 : Improper Integral – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/938ffc5a2dfe) (YouTube)
33. [Lecture 33 : Improper Integral – Part 3](https://invisiblenetwork.ai/learn/nptel/111105160/c4aaaa16fd26) (YouTube)
34. [Lecture 34 : Improper Integral – Part 4](https://invisiblenetwork.ai/learn/nptel/111105160/6214a9d4bb10) (YouTube)
35. [Lecture 35 : Beta & Gamma Function – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/784955c840b8) (YouTube)
36. [Lecture 36 : Beta & Gamma Function – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/129327380ba5) (YouTube)
37. [Lecture 37 : Differentiation under the Integral Sign](https://invisiblenetwork.ai/learn/nptel/111105160/eafcbf363a20) (YouTube)
38. [Lecture 38 : Double Integrals – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/37bc5027ad2e) (YouTube)
39. [Lecture 39 : Double Integrals – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/3ac7f9c03527) (YouTube)
40. [Lecture 40 : Double Integrals – Part 3](https://invisiblenetwork.ai/learn/nptel/111105160/a6a6f084a0cd) (YouTube)
41. [Lecture 41 : Double Integrals – Part 4](https://invisiblenetwork.ai/learn/nptel/111105160/eef864d10334) (YouTube)
42. [Lecture 42 : Double Integrals – Part 5](https://invisiblenetwork.ai/learn/nptel/111105160/886427c2d7be) (YouTube)
43. [Lecture 43 : Double Integrals – Part 6](https://invisiblenetwork.ai/learn/nptel/111105160/205794b64e75) (YouTube)
44. [Lecture 44 : Triple Integrals – Part 1](https://invisiblenetwork.ai/learn/nptel/111105160/b0d828a6bc17) (YouTube)
45. [Lecture 45 : Triple Integrals – Part 2](https://invisiblenetwork.ai/learn/nptel/111105160/252902a38363) (YouTube)
46. [Lecture 46 : Vector Functions](https://invisiblenetwork.ai/learn/nptel/111105160/a9e4afbd2e40) (YouTube)
47. [Lecture 47 : Vector and Scalar Fields](https://invisiblenetwork.ai/learn/nptel/111105160/8c9e0cf3f921) (YouTube)
48. [Lecture 48 : Divergence and Curl of a Vector Field](https://invisiblenetwork.ai/learn/nptel/111105160/65066fd14fdf) (YouTube)
49. [Lecture 49 : Line Integrals](https://invisiblenetwork.ai/learn/nptel/111105160/0511b6f1da85) (YouTube)
50. [Lecture 50 : Conservative Vector Fields](https://invisiblenetwork.ai/learn/nptel/111105160/becbfbd300df) (YouTube)
51. [Lecture 51 : Green’s Theorem](https://invisiblenetwork.ai/learn/nptel/111105160/39953a668865) (YouTube)
52. [Lecture 52 : Surface Integral (Part - 1)](https://invisiblenetwork.ai/learn/nptel/111105160/3ad5c9f09348) (YouTube)
53. [Lecture 53 : Surface Integrals (Part - 2)](https://invisiblenetwork.ai/learn/nptel/111105160/a2a751d2bf01) (YouTube)
54. [Lecture 54 : Stokes’ Theorem](https://invisiblenetwork.ai/learn/nptel/111105160/407969abdc8d) (YouTube)
55. [Lecture 55 : Divergence Theorem](https://invisiblenetwork.ai/learn/nptel/111105160/2f7f85c7347d) (YouTube)
56. [Lecture 56 : Application of Derivatives](https://invisiblenetwork.ai/learn/nptel/111105160/0fc895b416f4) (YouTube)
57. [Lecture 57 : Application of Derivatives-Continued](https://invisiblenetwork.ai/learn/nptel/111105160/6a350e101b59) (YouTube)
58. [Lecture 58 : Properties of Gradient, Divergence and Curl](https://invisiblenetwork.ai/learn/nptel/111105160/44878eb93017) (YouTube)
59. [Lecture 59 : Properties of Gradient, Divergence and Curl-Continued](https://invisiblenetwork.ai/learn/nptel/111105160/f9f375da061b) (YouTube)
60. [Lecture 60 : Curl and Integrals](https://invisiblenetwork.ai/learn/nptel/111105160/b09beddbd143) (YouTube)