# Numerical Analysis

- Institution: IIT Madras
- Department: Mathematics
- Teacher: Prof. R. Usha
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106101)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106101)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lesson 1 - Introduction , Motivation](https://invisiblenetwork.ai/learn/nptel/111106101/09ccf6b2fa87) (Video)
2. [Lesson 2 - Part 1 - Mathematical Preliminaries , Polynomial Interpolation – 1](https://invisiblenetwork.ai/learn/nptel/111106101/91309fc58678) (Video)
3. [Lesson 2 - Part 2 - Mathematical Preliminaries , Polynomial Interpolation – 1](https://invisiblenetwork.ai/learn/nptel/111106101/e14f8895033e) (Video)
4. [Lesson 3 - Part 1 - Polynomial Interpolation – 2](https://invisiblenetwork.ai/learn/nptel/111106101/fa5952d3b20e) (Video)
5. [Lesson 3 - Part 2 - Polynomial Interpolation – 2](https://invisiblenetwork.ai/learn/nptel/111106101/70ce38c32acd) (Video)
6. [Lesson 4 - Polynomial Interpolation – 3](https://invisiblenetwork.ai/learn/nptel/111106101/cb6c603e76b2) (Video)
7. [Lagrange Interpolation Polynomial , Error In Interpolation - 1](https://invisiblenetwork.ai/learn/nptel/111106101/b9bb8527797c) (Video)
8. [Lagrange Interpolation Polynomial ; Error In Interpolation - 1](https://invisiblenetwork.ai/learn/nptel/111106101/59bd254c9a3c) (Video)
9. [Error In Interpolation - 2](https://invisiblenetwork.ai/learn/nptel/111106101/b9a93aa8f3f3) (Video)
10. [Error In Interpolation 2](https://invisiblenetwork.ai/learn/nptel/111106101/3e5c3bb530b9) (Video)
11. [Divide Difference Interpolation Polynomial](https://invisiblenetwork.ai/learn/nptel/111106101/81689e222b9b) (Video)
12. [Properties Of Divided Difference , Introduction To Inverse Interpolation](https://invisiblenetwork.ai/learn/nptel/111106101/c9935fbcce38) (Video)
13. [Properties Of Divided Difference Introduction To Inverse Interpolation](https://invisiblenetwork.ai/learn/nptel/111106101/3da32d283f54) (Video)
14. [Inverse Interpolation , Remarks on Polynomial Interpolation](https://invisiblenetwork.ai/learn/nptel/111106101/e7b4f3854fd5) (Video)
15. [Numerical Differentiation - 1 Taylor Series Method](https://invisiblenetwork.ai/learn/nptel/111106101/6c743b4f9999) (Video)
16. [Numerical Differentiation - 2 Method Of Undetermined Coefficients](https://invisiblenetwork.ai/learn/nptel/111106101/2d6a0720d833) (Video)
17. [Numerical Differentiation - 2 Polynomial Interpolation Method](https://invisiblenetwork.ai/learn/nptel/111106101/eb0fa1b8a5f4) (Video)
18. [Numerical Differentiation - 3 Operator Method Numerical Integration - 1](https://invisiblenetwork.ai/learn/nptel/111106101/e740e9771268) (Video)
19. [Numerical Integration - 2 Error in Trapezoidal Rule Simpson's Rule](https://invisiblenetwork.ai/learn/nptel/111106101/3867e5cd2de0) (Video)
20. [Numerical Integration - 3 Error in Simpson's Rule Composite in Trapezoidal Rule , Error](https://invisiblenetwork.ai/learn/nptel/111106101/99d5c7a9e343) (Video)
21. [Numerical Integration - 4 Composite Simpsons Rule , Error Method of Undetermined Coefficients](https://invisiblenetwork.ai/learn/nptel/111106101/5f859d6dc52d) (Video)
22. [Numerical Integration - 5 Gaussian Quadrature (Two-Point Method)](https://invisiblenetwork.ai/learn/nptel/111106101/df907587a97d) (Video)
23. [Numerical Integrature - 5 Gaussian Quadrature (Three-Point Method) Adaptive Quadrature](https://invisiblenetwork.ai/learn/nptel/111106101/5e196640d287) (Video)
24. [Numerical Solution of Ordinary Differential Equation (ODE) - 1](https://invisiblenetwork.ai/learn/nptel/111106101/e03b15ebcd30) (Video)
25. [Numerical Solution Of ODE - 2 Stability , Single-Step Methods - 1 Taylor Series Method](https://invisiblenetwork.ai/learn/nptel/111106101/43b41e796cbb) (Video)
26. [Numerical Solution Of ODE - 3 Examples of Taylor Series Method Euler's Method](https://invisiblenetwork.ai/learn/nptel/111106101/4dd979594499) (Video)
27. [Numerical Solution Of ODE-4 Runge-Kutta Methods](https://invisiblenetwork.ai/learn/nptel/111106101/db9fedb0a47b) (Video)
28. [Numerical Solution Of ODE-5 Example For RK-Method Of Order 2 Modified Euler's Method](https://invisiblenetwork.ai/learn/nptel/111106101/bd2182e7ea40) (Video)
29. [Numerical Solution Of Ordinary DifferentialEquations- 6 Predictor-Corrector Methods (Adam-Moulton)](https://invisiblenetwork.ai/learn/nptel/111106101/c4cfa60a2630) (Video)
30. [Numerical Solution Of Ordinary DifferentialEquations- 7](https://invisiblenetwork.ai/learn/nptel/111106101/e4c2f7fb8a9d) (Video)
31. [Numerical Solution Of Differential Equations - 8](https://invisiblenetwork.ai/learn/nptel/111106101/fefb1ce9f633) (Video)
32. [Numerical Solution of Ordinary Differential Equations - 9](https://invisiblenetwork.ai/learn/nptel/111106101/65c2b8868709) (Video)
33. [Numerical Solution of Ordinary Differential Equations - 10](https://invisiblenetwork.ai/learn/nptel/111106101/6a4c5a48f8a7) (Video)
34. [Numerical Solution of Ordinary Differential Equations - 11](https://invisiblenetwork.ai/learn/nptel/111106101/1627e38b63ff) (Video)
35. [Root Finding Methods - 1 The Bisection Method - 1](https://invisiblenetwork.ai/learn/nptel/111106101/b0f112730849) (Video)
36. [Root Finding Methods - 2 The Bisection Method - 2](https://invisiblenetwork.ai/learn/nptel/111106101/2a9fce650fdd) (Video)
37. [Root Finding Methods - 3 Newton-Raphson Method - 1](https://invisiblenetwork.ai/learn/nptel/111106101/f1c25db99628) (Video)
38. [Root Finding Methods - 4 Newton-Raphson Method - 2](https://invisiblenetwork.ai/learn/nptel/111106101/c767a8522fcb) (Video)
39. [Root Finding Methods - 5 Secant Method, Method Of false Position](https://invisiblenetwork.ai/learn/nptel/111106101/3994230ada1e) (Video)
40. [Root Finding Methods - 6 Fixed Point Methods - 1](https://invisiblenetwork.ai/learn/nptel/111106101/a95319a2c5cc) (Video)
41. [Root Finding Methods - 7 Fixed Point Methods - 2](https://invisiblenetwork.ai/learn/nptel/111106101/a0f600340da7) (Video)
42. [Root Finding Methods - 8 Fixed Point Iteration Methods - 3](https://invisiblenetwork.ai/learn/nptel/111106101/0e909e16deed) (Video)
43. [Root Finding Methods - 9 Practice Problems](https://invisiblenetwork.ai/learn/nptel/111106101/e0182cb92c86) (Video)
44. [Solution Of Linear Systems Of Equations - 1](https://invisiblenetwork.ai/learn/nptel/111106101/5fccab83acbc) (Video)
45. [Solution Of Linear Systems Of Equations - 2](https://invisiblenetwork.ai/learn/nptel/111106101/13eadc44ad11) (Video)
46. [Solution Of Linear Systems Of Equations - 3](https://invisiblenetwork.ai/learn/nptel/111106101/2a2abd3919f8) (Video)
47. [Solution Of Linear Systems Of Equations - 4](https://invisiblenetwork.ai/learn/nptel/111106101/053ad20055b3) (Video)
48. [Solution Of Linear Systems Of Equations - 5](https://invisiblenetwork.ai/learn/nptel/111106101/3fafbe0dc050) (Video)
49. [Solution Of Linear Systems Of Equations - 6](https://invisiblenetwork.ai/learn/nptel/111106101/27056c7157f0) (Video)
50. [Solution Of Linear Systems Of Equations - 7](https://invisiblenetwork.ai/learn/nptel/111106101/cf8f7c4e474e) (Video)
51. [Solutions Of Linear Systems Of Equations - 8 Iterative Method - 1](https://invisiblenetwork.ai/learn/nptel/111106101/3cf4de8c20fb) (Video)
52. [Solutions Of Linear Systems Of Equations - 8 Iterative Method - 2](https://invisiblenetwork.ai/learn/nptel/111106101/8f89c6bf941f) (Video)
53. [Matrix Eigenvalue Problems - 2 Power Method - 2](https://invisiblenetwork.ai/learn/nptel/111106101/a274cb08aed9) (Video)
54. [Practice Problems](https://invisiblenetwork.ai/learn/nptel/111106101/a91a4878e583) (Video)