# Numerical Analysis

- Institution: IIT Bombay
- Department: Mathematics
- Teacher: Prof. S. Baskar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111101165)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111101165)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Week 1 : Lecture 1 : Introduction](https://invisiblenetwork.ai/learn/nptel/111101165/2794d1e7a147) (Video)
2. [Week 1 : Lecture 2 : Mathematical Preliminaries: Taylor Approximation](https://invisiblenetwork.ai/learn/nptel/111101165/8d4fc9592eca) (Video)
3. [Week 1 : Lecture 3 : Mathematical Preliminaries: Order of Convergence](https://invisiblenetwork.ai/learn/nptel/111101165/4f4455734afe) (Video)
4. [Week 1 : Lecture 4 : Arithmetic Error: Floating-point Approximation](https://invisiblenetwork.ai/learn/nptel/111101165/97bafca9dade) (Video)
5. [Week 1 : Lecture 5 : Arithmetic Error: Significant Digits](https://invisiblenetwork.ai/learn/nptel/111101165/cd2eef1f0d38) (Video)
6. [Week 1 : Lecture 6 : Arithmetic Error: Condition Number and Stable Computation](https://invisiblenetwork.ai/learn/nptel/111101165/d84c5b9d44cd) (Video)
7. [Week 2 : Lecture 7 : Tutorial Session - 1: Problem Solving](https://invisiblenetwork.ai/learn/nptel/111101165/0112108bd068) (Video)
8. [Week 2 : Lecture 8 : Python Coding: Introduction](https://invisiblenetwork.ai/learn/nptel/111101165/9c36c46e1fd3) (Video)
9. [Week 2 : Lecture 9 : Linear Systems: Gaussian Elimination Method](https://invisiblenetwork.ai/learn/nptel/111101165/e2a7031ba741) (Video)
10. [Week 2 : Lecture 10 : Linear Systems: LU-Factorization (Doolittle and Crout)](https://invisiblenetwork.ai/learn/nptel/111101165/3c00f76e73b1) (Video)
11. [Week 2 : Lecture 11 : Linear Systems: LU-Factorization (Cholesky)](https://invisiblenetwork.ai/learn/nptel/111101165/fd1a2cde83c8) (Video)
12. [Week 3 : Lecture 12 : Linear Systems: Operation Count for Direct Methods](https://invisiblenetwork.ai/learn/nptel/111101165/de1460f7645a) (Video)
13. [Week 3 : Lecture 13 : Tutorial Session - 2: Python Coding for Naive Gaussian Elimination Method](https://invisiblenetwork.ai/learn/nptel/111101165/5b9d322bed59) (Video)
14. [Week 3 : Lecture 14 : Tutorial Session - 3: Python Coding for Thomas Algorithm](https://invisiblenetwork.ai/learn/nptel/111101165/27343999acd3) (Video)
15. [Week 3 : Lecture 15 : Matrix Norms: Subordinate Matrix Norms](https://invisiblenetwork.ai/learn/nptel/111101165/7e31babc48d4) (Video)
16. [Week 3 : Lecture 16 : Matrix Norms: Condition Number of a Matrix](https://invisiblenetwork.ai/learn/nptel/111101165/391ea4ffeff6) (Video)
17. [Week 4 : Lecture 17 : Iterative Methods: Jacobi Method](https://invisiblenetwork.ai/learn/nptel/111101165/b6e8b2701547) (Video)
18. [Week 4 : Lecture 18 : Iterative Methods: Convergence of Jacobi Method](https://invisiblenetwork.ai/learn/nptel/111101165/fc4b1abd3d9c) (Video)
19. [Week 4 : Lecture 19 : Iterative Methods: Gauss-Seidel Method](https://invisiblenetwork.ai/learn/nptel/111101165/a62960028ea7) (Video)
20. [Week 4 : Lecture 20 : Iterative Methods: Convergence Analysis of Iterative Methods](https://invisiblenetwork.ai/learn/nptel/111101165/caec74b12163) (Video)
21. [Week 4 : Lecture 21 : Iterative Methods: Successive Over Relaxation Method](https://invisiblenetwork.ai/learn/nptel/111101165/94d9e665f318) (Video)
22. [Week 5 : Lecture 22 : Tutorial Session - 4: Python implementation of Jacobi Method](https://invisiblenetwork.ai/learn/nptel/111101165/17866c63f4fb) (Video)
23. [Week 5 : Lecture 23 : Eigenvalues and Eigenvectors: Power Method (Construction)](https://invisiblenetwork.ai/learn/nptel/111101165/368d8bb4576a) (Video)
24. [Week 5 : Lecture 24 : Eigenvalues and Eigenvectors: Power Method (Convergence Theorem)](https://invisiblenetwork.ai/learn/nptel/111101165/d73af111239e) (Video)
25. [Week 5 : Lecture 25 : Eigenvalues and Eigenvectors: Gerschgorin's Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111101165/c309e029541d) (Video)
26. [Week 5 : Lecture 26 : Eigenvalues and Eigenvectors: Power Method (Inverse and Shifted Methods)](https://invisiblenetwork.ai/learn/nptel/111101165/e1fa7d5beb35) (Video)
27. [Week 6 : Lecture 27 : Nonlinear Equations: Overview](https://invisiblenetwork.ai/learn/nptel/111101165/79c536616ba5) (Video)
28. [Week 6 : Lecture 28 : Nonlinear Equations: Bisection Method](https://invisiblenetwork.ai/learn/nptel/111101165/591c9394b77a) (Video)
29. [Week 6 : Lecture 29 : Tutorial Session - 5: Implementation of Bisection Method](https://invisiblenetwork.ai/learn/nptel/111101165/85e4bdab025b) (Video)
30. [Week 6 : Lecture 30 : Nonlinear Equations: Regula-falsi and Secant Methods](https://invisiblenetwork.ai/learn/nptel/111101165/6af154f14486) (Video)
31. [Week 6 : Lecture 31 : Nonlinear Equations: Convergence Theorem of Secant Method](https://invisiblenetwork.ai/learn/nptel/111101165/bf456ed08c09) (Video)
32. [Week 7 : Lecture 32 : Nonlinear Equations: Newton-Raphson's method](https://invisiblenetwork.ai/learn/nptel/111101165/f542c10fa9cf) (Video)
33. [Week 7 : Lecture 33 : Nonlinear Equations: Newton-Raphson's method (Convergence Theorem)](https://invisiblenetwork.ai/learn/nptel/111101165/811f2df14e65) (Video)
34. [Week 7 : Lecture 34 : Nonlinear Equations: Fixed-point Iteration Methods](https://invisiblenetwork.ai/learn/nptel/111101165/7f2375d422cf) (Video)
35. [Lecture 35:Nonlinear Equations: Fixed-point Iteration Methods (Convergence)&Modified Newton's Method](https://invisiblenetwork.ai/learn/nptel/111101165/ed2a14f93b8f) (Video)
36. [Week 7 : Lecture 36 : Nonlinear Equations: System of Nonlinear Equations](https://invisiblenetwork.ai/learn/nptel/111101165/52e99bcff352) (Video)
37. [Week 8 : Lecture 37 : Nonlinear Equations: Implementation of Newton-Raphson's Method as Python Code](https://invisiblenetwork.ai/learn/nptel/111101165/7aa9b63cbc34) (Video)
38. [Week 8 : Lecture 38 : Polynomial Interpolation: Existence and Uniqueness](https://invisiblenetwork.ai/learn/nptel/111101165/93cf162a9a99) (Video)
39. [Week 8 : Lecture 39 : Polynomial Interpolation: Lagrange and Newton Forms](https://invisiblenetwork.ai/learn/nptel/111101165/de5af4df1cdb) (Video)
40. [Week 8 : Lecture 40 : Polynomial Interpolation: Newton’s Divided Difference Formula](https://invisiblenetwork.ai/learn/nptel/111101165/138b33b57da8) (Video)
41. [Week 8 : Lecture 41 : Polynomial Interpolation: Mathematical Error in Interpolating Polynomial](https://invisiblenetwork.ai/learn/nptel/111101165/c14b09b42e9d) (Video)
42. [Week 9 : Lecture 42 : Polynomial Interpolation: Arithmetic Error in Interpolating Polynomials](https://invisiblenetwork.ai/learn/nptel/111101165/a92716b2115a) (Video)
43. [Week 9 : Lecture 43 : Polynomial Interpolation: Implementation of Lagrange Form as Python Code](https://invisiblenetwork.ai/learn/nptel/111101165/e2848bd93bda) (Video)
44. [Week 9 : Lecture 44: Polynomial Interpolation: Runge Phenomenon & Piecewise Polynomial Interpolation](https://invisiblenetwork.ai/learn/nptel/111101165/b6d4c1754974) (Video)
45. [Week 9 : Lecture 45 : Polynomial Interpolation: Hermite Interpolation](https://invisiblenetwork.ai/learn/nptel/111101165/8eaeb534c6e1) (Video)
46. [Week 9 : Lecture 46 : Polynomial Interpolation: Cubic Spline Interpolation](https://invisiblenetwork.ai/learn/nptel/111101165/341c30ad9ab0) (Video)
47. [Week 10 : Lecture 47 : Polynomial Interpolation: Tutorial Session](https://invisiblenetwork.ai/learn/nptel/111101165/e74690a88ab2) (Video)
48. [Week 10 : Lecture 48 : Numerical Integration: Rectangle Rule](https://invisiblenetwork.ai/learn/nptel/111101165/f9d4f60a5f74) (Video)
49. [Week 10 : Lecture 49 : Numerical Integration: Trapezoidal Rule](https://invisiblenetwork.ai/learn/nptel/111101165/de5d9ee191cb) (Video)
50. [Lecture 50 : Numerical Integration: Simpson's Rule](https://invisiblenetwork.ai/learn/nptel/111101165/ecaa2b7f97a0) (Video)
51. [Week 10 : Lecture 51 : Numerical Integration: Gaussian Quadrature Rule](https://invisiblenetwork.ai/learn/nptel/111101165/4b68e39b6e57) (Video)
52. [Week 11 : Lecture 52 : Numerical Integration: Tutorial Session](https://invisiblenetwork.ai/learn/nptel/111101165/ca95897543c2) (Video)
53. [Week 11 : Lecture 53 : Numerical Differentiation: Primitive Finite Difference Formulae](https://invisiblenetwork.ai/learn/nptel/111101165/a34827994994) (Video)
54. [Lecture 54 : Numerical Differentiation: Method of Undetermined Coefficients and Arithmetic Error](https://invisiblenetwork.ai/learn/nptel/111101165/2758fbd4dafb) (Video)
55. [Week 11 : Lecture 55 : Numerical ODEs: Euler Methods](https://invisiblenetwork.ai/learn/nptel/111101165/a53570ad4409) (Video)
56. [Week 11 : Lecture 56 : Numerical ODEs: Euler Methods (Error Analysis)](https://invisiblenetwork.ai/learn/nptel/111101165/8252b424d303) (Video)
57. [Week 12 : Lecture 57 : Numerical ODEs: Runge-Kutta Methods](https://invisiblenetwork.ai/learn/nptel/111101165/2b97b9f7d91d) (Video)
58. [Week 12 : Lecture 58 : Numerical ODEs: Modified Euler's Methods](https://invisiblenetwork.ai/learn/nptel/111101165/b0c2c30772e0) (Video)
59. [Week 12 : Lecture 59 : Numerical ODEs: Multistep Methods](https://invisiblenetwork.ai/learn/nptel/111101165/5441dd4c7300) (Video)
60. [Week 12 : Lecture 60 : Numerical ODEs: Stability Analysis](https://invisiblenetwork.ai/learn/nptel/111101165/3d4b488e7ce1) (Video)
61. [Week 12 : Lecture 61 : Numerical ODEs: Two-point Boundary Value Problems](https://invisiblenetwork.ai/learn/nptel/111101165/31576e5c4c9a) (Video)
62. [Live Session 21-02-2024](https://invisiblenetwork.ai/learn/nptel/111101165/2794d1e7a147-2) (Video)
63. [Live Session 06-03-2025](https://invisiblenetwork.ai/learn/nptel/111101165/8d4fc9592eca-2) (Video)