# Advanced Engineering Mathematics

- Institution: IIT Kharagpur
- Department: Mathematics
- Taught by: Prof. J. Kumar, Prof. P.D. Srivastava, Dr. P. Panigrahi, Prof. Somesh Kumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105035)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105035)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Review Groups, Fields and Matrices](https://invisiblenetwork.ai/learn/nptel/111105035/f1ce0d588e38) (Video)
2. [Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors](https://invisiblenetwork.ai/learn/nptel/111105035/2713b99ec0c1) (Video)
3. [Basis, Dimension, Rank and Matrix Inverse](https://invisiblenetwork.ai/learn/nptel/111105035/8bf326cff4d3) (Video)
4. [Linear Transformation, Isomorphism and Matrix Representation](https://invisiblenetwork.ai/learn/nptel/111105035/993c850661da) (Video)
5. [System of Linear Equations, Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111105035/6fef0aea7343) (Video)
6. [Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices](https://invisiblenetwork.ai/learn/nptel/111105035/beb8a799678a) (Video)
7. [Jordan Canonical Form, Cayley Hamilton Theorem](https://invisiblenetwork.ai/learn/nptel/111105035/9077ad859cbb) (Video)
8. [Inner Product Spaces, Cauchy-Schwarz Inequality](https://invisiblenetwork.ai/learn/nptel/111105035/ce4300f41880) (Video)
9. [Orthogonality, Gram-Schmidt Orthogonalization Process](https://invisiblenetwork.ai/learn/nptel/111105035/3171e4cb506c) (Video)
10. [Spectrum of special matrices,positive/negative definite matrices](https://invisiblenetwork.ai/learn/nptel/111105035/0586d98d7742) (Video)
11. [Concept of Domain, Limit, Continuity and Differentiability](https://invisiblenetwork.ai/learn/nptel/111105035/242a5f8bbe34) (Video)
12. [Analytic Functions, C-R Equations](https://invisiblenetwork.ai/learn/nptel/111105035/01b16e98867e) (Video)
13. [Harmonic Functions](https://invisiblenetwork.ai/learn/nptel/111105035/52247feb58ab) (Video)
14. [Line Integral in the Complex](https://invisiblenetwork.ai/learn/nptel/111105035/64f1fecd2723) (Video)
15. [Cauchy Integral Theorem](https://invisiblenetwork.ai/learn/nptel/111105035/d11440dd24f0) (Video)
16. [Cauchy Integral Theorem (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105035/eb7cfba50047) (Video)
17. [Cauchy Integral Formula](https://invisiblenetwork.ai/learn/nptel/111105035/c50eef2deae7) (Video)
18. [Power and Taylor's Series of Complex Numbers](https://invisiblenetwork.ai/learn/nptel/111105035/abcbc91938bd) (Video)
19. [Power and Taylor's Series of Complex Numbers (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105035/88c0c194cadb) (Video)
20. [Taylor's, Laurent Series of f(z) and Singularities](https://invisiblenetwork.ai/learn/nptel/111105035/3647da93e8fd) (Video)
21. [Classification of Singularities, Residue and Residue Theorem](https://invisiblenetwork.ai/learn/nptel/111105035/b4aecb38ee2e) (Video)
22. [Laplace Transform and its Existence](https://invisiblenetwork.ai/learn/nptel/111105035/f9a4c150e1db) (Video)
23. [Properties of Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105035/6eb140b35a3b) (Video)
24. [Evaluation of Laplace and Inverse Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105035/4464434a94b8) (Video)
25. [Applications of Laplace Transform to Integral Equations and ODEs](https://invisiblenetwork.ai/learn/nptel/111105035/b29befd0f4e3) (Video)
26. [Applications of Laplace Transform to PDEs](https://invisiblenetwork.ai/learn/nptel/111105035/d6f3795fd827) (Video)
27. [Fourier Series](https://invisiblenetwork.ai/learn/nptel/111105035/46696f6bafac) (Video)
28. [Fourier Series (Contd.)](https://invisiblenetwork.ai/learn/nptel/111105035/ee87e6c992c1) (Video)
29. [Fourier Integral Representation of a Function](https://invisiblenetwork.ai/learn/nptel/111105035/70ed66dbad7a) (Video)
30. [Introduction to Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105035/faf3c2579360) (Video)
31. [Applications of Fourier Transform to PDEs](https://invisiblenetwork.ai/learn/nptel/111105035/74a99015177e) (Video)
32. [Laws of Probability - I](https://invisiblenetwork.ai/learn/nptel/111105035/3f7e763b8fbf) (Video)
33. [Laws of Probability - II](https://invisiblenetwork.ai/learn/nptel/111105035/9e9521f351ee) (Video)
34. [Problems in Probability](https://invisiblenetwork.ai/learn/nptel/111105035/de6ffeda351f) (Video)
35. [Random Variables](https://invisiblenetwork.ai/learn/nptel/111105035/f1a4234d3f23) (Video)
36. [Special Discrete Distributions](https://invisiblenetwork.ai/learn/nptel/111105035/25bf353bffc3) (Video)
37. [Special Continuous Distributions](https://invisiblenetwork.ai/learn/nptel/111105035/9f3b41096f99) (Video)
38. [Joint Distributions and Sampling Distributions](https://invisiblenetwork.ai/learn/nptel/111105035/46c33a8c2881) (Video)
39. [Point Estimation](https://invisiblenetwork.ai/learn/nptel/111105035/e3d041ea8bc3) (Video)
40. [Interval Estimation](https://invisiblenetwork.ai/learn/nptel/111105035/386cbd50f21e) (Video)
41. [Basic Concepts of Testing of Hypothesis](https://invisiblenetwork.ai/learn/nptel/111105035/bf6e7072bcc0) (Video)
42. [Tests for Normal Populations](https://invisiblenetwork.ai/learn/nptel/111105035/c7e4a333e59e) (Video)