# Advanced Engineering Mathematics

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. H S Mahato
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105167)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105167)
- 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: Introduction on functions of a single variable](https://invisiblenetwork.ai/learn/nptel/111105167/f3ddd3f3a884) (Video)
2. [Lecture 2: Basic definitions](https://invisiblenetwork.ai/learn/nptel/111105167/096d195b3e29) (Video)
3. [Lecture 3: Mean value Theorems](https://invisiblenetwork.ai/learn/nptel/111105167/831309cdc76b) (Video)
4. [Lecture 4: Extremum of function of single variable](https://invisiblenetwork.ai/learn/nptel/111105167/6fbeeb585352) (Video)
5. [Lecture 5: Examples](https://invisiblenetwork.ai/learn/nptel/111105167/6ce8583bbdeb) (Video)
6. [Lecture 6: Introduction on functions of two variable](https://invisiblenetwork.ai/learn/nptel/111105167/21c8d2b5a7e0) (Video)
7. [Lecture 7: Basic definitions](https://invisiblenetwork.ai/learn/nptel/111105167/7032f1e499fc) (Video)
8. [Lecture 8: Partial differentiation](https://invisiblenetwork.ai/learn/nptel/111105167/a753d99012b4) (Video)
9. [Lecture 9: Extremum of function of two variable](https://invisiblenetwork.ai/learn/nptel/111105167/974e8933ac6e) (Video)
10. [Lecture 10: Examples](https://invisiblenetwork.ai/learn/nptel/111105167/d179b345c004) (Video)
11. [Lecture 11: Convergence and divergence test](https://invisiblenetwork.ai/learn/nptel/111105167/9ce915f182bc) (Video)
12. [Lecture 12: Beta function, Gamma function](https://invisiblenetwork.ai/learn/nptel/111105167/ffb35d7d6b2d) (Video)
13. [Lecture 13: Differentiation under integral sign](https://invisiblenetwork.ai/learn/nptel/111105167/f87dfd65bb71) (Video)
14. [Lecture 14: Line integral, integration in R^2 (Double integral)](https://invisiblenetwork.ai/learn/nptel/111105167/e2f97ec686fc) (Video)
15. [Lecture 15: Examples](https://invisiblenetwork.ai/learn/nptel/111105167/9d0ac613c9e4) (Video)
16. [Lecture 16: Double integral](https://invisiblenetwork.ai/learn/nptel/111105167/a3f007cdd43b) (Video)
17. [Lecture 17: Integration in R3](https://invisiblenetwork.ai/learn/nptel/111105167/2856824fe916) (Video)
18. [Lecture 18: Triple integral](https://invisiblenetwork.ai/learn/nptel/111105167/fd4d47550341) (Video)
19. [Lecture 19: Examples](https://invisiblenetwork.ai/learn/nptel/111105167/cf47210af74b) (Video)
20. [Lecture 20: Introduction to Differential equation](https://invisiblenetwork.ai/learn/nptel/111105167/b9333b871a6e) (Video)
21. [Lecture 21: Exact form](https://invisiblenetwork.ai/learn/nptel/111105167/b3c1e42ea864) (Video)
22. [Lecture 22: Second order differential equation](https://invisiblenetwork.ai/learn/nptel/111105167/1d5296c7c8c1) (Video)
23. [Lecture 23: Iterative method (bisection and fixed point)](https://invisiblenetwork.ai/learn/nptel/111105167/16f8c6445092) (Video)
24. [Lecture 24: Newton-Raphson, Jacobi and Gauss-Seidel method](https://invisiblenetwork.ai/learn/nptel/111105167/747123c7ea02) (Video)
25. [Lecture 25: Finite difference method](https://invisiblenetwork.ai/learn/nptel/111105167/4ca12f86afce) (Video)
26. [Lecture 26: Newton’s forward and backward interpolation](https://invisiblenetwork.ai/learn/nptel/111105167/edebff9e8959) (Video)
27. [Lecture 27: Numerical integration](https://invisiblenetwork.ai/learn/nptel/111105167/10dcbcb694f6) (Video)
28. [Lecture 28: Vector space and Subspace](https://invisiblenetwork.ai/learn/nptel/111105167/515e6115f3d0) (Video)
29. [Lecture 29: Basis and dimension](https://invisiblenetwork.ai/learn/nptel/111105167/9f3825b0ef46) (Video)
30. [Lecture 30: Rank of a matrix](https://invisiblenetwork.ai/learn/nptel/111105167/2fe377b70c5c) (Video)
31. [Lecture 31: Gauss-Elimination Method](https://invisiblenetwork.ai/learn/nptel/111105167/71d041508f33) (Video)
32. [Lecture 32: Linear Transformation](https://invisiblenetwork.ai/learn/nptel/111105167/5c2e6c5806f6) (Video)
33. [Lecture 33: Examples](https://invisiblenetwork.ai/learn/nptel/111105167/63f2bd74e209) (Video)
34. [Lecture 34: Matrix Representation](https://invisiblenetwork.ai/learn/nptel/111105167/3a43814f2b34) (Video)
35. [Lec 35: Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111105167/a68b18aba59a) (Video)
36. [Lecture 36: Cayley-Hamilton Theorem](https://invisiblenetwork.ai/learn/nptel/111105167/9430a9036960) (Video)
37. [Lecture 37: Diagonalisation of a Matrix](https://invisiblenetwork.ai/learn/nptel/111105167/cd37bdbca283) (Video)
38. [Lecture 38: Examples and applications](https://invisiblenetwork.ai/learn/nptel/111105167/d9e664342ae2) (Video)
39. [Lecture 39: Types of matrices](https://invisiblenetwork.ai/learn/nptel/111105167/bf8a26698831) (Video)
40. [Lecture 40: Equivalent Matrices and Elementary Matrices](https://invisiblenetwork.ai/learn/nptel/111105167/39ac8c092df3) (Video)
41. [Lecture 41: Introduction to the vector function](https://invisiblenetwork.ai/learn/nptel/111105167/2b46a614a744) (Video)
42. [Lecture 42: Differentiation and integration of the vector function](https://invisiblenetwork.ai/learn/nptel/111105167/363f790e7f06) (Video)
43. [Lecture 43: Partial differentiation of vector function](https://invisiblenetwork.ai/learn/nptel/111105167/f26d1be75ea0) (Video)
44. [Lecture 44: Directional derivative of a vector function](https://invisiblenetwork.ai/learn/nptel/111105167/dd2e19c475e3) (Video)
45. [Lecture 45: Examples on directional derivative, tangent plane and normal](https://invisiblenetwork.ai/learn/nptel/111105167/17f8f24b7db4) (Video)
46. [Lecture 46: Divergence and curl of a vector function](https://invisiblenetwork.ai/learn/nptel/111105167/0ea1fdb66ec3) (Video)
47. [Lecture 47: Application to mechanics of vector calculus](https://invisiblenetwork.ai/learn/nptel/111105167/fe5b2b9049da) (Video)
48. [Lecture 48: Serret-Frenet formula and more applications to mechanics](https://invisiblenetwork.ai/learn/nptel/111105167/6bb2094477a7) (Video)
49. [Lecture 49: Examples on finding unit vectors, curvature and torsion](https://invisiblenetwork.ai/learn/nptel/111105167/e3738b85a19e) (Video)
50. [Lecture 50: Application of vector calculus to the particle dynamics](https://invisiblenetwork.ai/learn/nptel/111105167/5f6bd6248437) (Video)
51. [Lecture 51: Line integral of vector function](https://invisiblenetwork.ai/learn/nptel/111105167/2e81964d7fb0) (Video)
52. [Lecture 52: Surface integral of vector function](https://invisiblenetwork.ai/learn/nptel/111105167/bb4fe07d3e6a) (Video)
53. [Lecture 53: Volume integral of vector function and Gauss Divergence Theorem](https://invisiblenetwork.ai/learn/nptel/111105167/3f40a32b72b7) (Video)
54. [Lecture 54: Green's theorem and Stoke's theorem](https://invisiblenetwork.ai/learn/nptel/111105167/54082a8f0fe7) (Video)
55. [Lecture 55: Verification and application of Divergencen theorem, Green's theorem and Stoke's theorem](https://invisiblenetwork.ai/learn/nptel/111105167/7ccdb9038367) (Video)
56. [Lecture 56: Basic properties of a complex valued function](https://invisiblenetwork.ai/learn/nptel/111105167/093154129533) (Video)
57. [Lecture 57: Analytic Complex valued function](https://invisiblenetwork.ai/learn/nptel/111105167/bc24e1ffdcea) (Video)
58. [Lecture 58: Complex Integration and theorems](https://invisiblenetwork.ai/learn/nptel/111105167/c35230b4e7d4) (Video)
59. [Lecture 59: Application of Cauchy's integral formula](https://invisiblenetwork.ai/learn/nptel/111105167/563789ddb605) (Video)
60. [Lecture 60: Regular and Singular point of a complex valued function](https://invisiblenetwork.ai/learn/nptel/111105167/6856f6d78956) (Video)
61. [Live Session 15-02-2024](https://invisiblenetwork.ai/learn/nptel/111105167/f3ddd3f3a884-2) (Video)
62. [Live Session 19-04-2024](https://invisiblenetwork.ai/learn/nptel/111105167/096d195b3e29-2) (Video)
63. [Live Session 11-02-2025](https://invisiblenetwork.ai/learn/nptel/111105167/831309cdc76b-2) (Video)