# Numerical methods

- Institution: IIT Roorkee
- Department: Mathematics
- Taught by: Prof. Ameeya Kumar Nayak, Prof. Sanjeev Kumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111107105)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111107105)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of non-linear equations, interpolation, numerical differentiation and integration. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences.

Intended audience: UG students of technical universities/colleges.

## Lectures

1. [Introduction to error analysis and linear systems](https://invisiblenetwork.ai/learn/nptel/111107105/333d834a4654) (YouTube)
2. [Gaussian elimination with partial pivoting](https://invisiblenetwork.ai/learn/nptel/111107105/6b4800588db0) (YouTube)
3. [LU decomposition](https://invisiblenetwork.ai/learn/nptel/111107105/a62a47186147) (YouTube)
4. [Jacobi and Gauss Seidel methods](https://invisiblenetwork.ai/learn/nptel/111107105/abeb2aeffd8b) (YouTube)
5. [Iterative methods-II](https://invisiblenetwork.ai/learn/nptel/111107105/971850a49a29) (YouTube)
6. [Introduction to Non-linear equations and Bisection method](https://invisiblenetwork.ai/learn/nptel/111107105/c1216ae18312) (YouTube)
7. [Regula Falsi and Secant methods](https://invisiblenetwork.ai/learn/nptel/111107105/541063c6d691) (YouTube)
8. [Newton-Raphson method](https://invisiblenetwork.ai/learn/nptel/111107105/4e7e0324d94a) (YouTube)
9. [Fixed point iteration method](https://invisiblenetwork.ai/learn/nptel/111107105/b0de00674f3f) (YouTube)
10. [System of Nonlinear equations](https://invisiblenetwork.ai/learn/nptel/111107105/3028c10e778f) (YouTube)
11. [Introduction to Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111107105/82c47466a7c6) (YouTube)
12. [Similarity Transformations and Gershgorin Theorem](https://invisiblenetwork.ai/learn/nptel/111107105/0108f715a7fe) (YouTube)
13. [Jacobi's Method for Computing Eigenvalues](https://invisiblenetwork.ai/learn/nptel/111107105/82f476947f5c) (YouTube)
14. [Power Method](https://invisiblenetwork.ai/learn/nptel/111107105/13ae10843070) (YouTube)
15. [Inverse Power Method](https://invisiblenetwork.ai/learn/nptel/111107105/5b3c9dab684a) (YouTube)
16. [Interpolation Part I (Introduction to Interpolation)](https://invisiblenetwork.ai/learn/nptel/111107105/2056c496099f) (YouTube)
17. [Interpolation part-II ( Some basic operators and their properties)](https://invisiblenetwork.ai/learn/nptel/111107105/ece2c41bbe7d) (YouTube)
18. [Interpolation part-III (Newton’s Forward/ Backward difference and derivation of general error)](https://invisiblenetwork.ai/learn/nptel/111107105/aac337ceefb7) (YouTube)
19. [Interpolation part-IV (Error in approximating a function by a polynomial using Newton’s Forward & Backward difference formula)](https://invisiblenetwork.ai/learn/nptel/111107105/e2fae52cedf8) (YouTube)
20. [Interpolation part-V (Solving problems using Newton's Forward & Backward difference formula)](https://invisiblenetwork.ai/learn/nptel/111107105/c98430b1b07b) (YouTube)
21. [Interpolation part-VI (Central difference formula)](https://invisiblenetwork.ai/learn/nptel/111107105/927219ae9c49) (YouTube)
22. [Interpolation part-VII (Lagrange interpolation formula with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/cd1d90ff0f0c) (YouTube)
23. [Interpolation part-VIII (Divided difference interpolation with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/3aca26193e1c) (YouTube)
24. [Interpolation part-IX (Hermite's interpolation with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/94c1da9e8707) (YouTube)
25. [Numerical differentiation part-I (Introduction to numerical differentiation by interpolation formula)](https://invisiblenetwork.ai/learn/nptel/111107105/0e0eb2827d48) (YouTube)
26. [Numerical differentiation part-II (Numerical differentiation based on Lagrange’s interpolation with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/a94f0de30356) (YouTube)
27. [Numerical differentiation part-III (Numerical differentiation based on Divided difference formula with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/77014047baf3) (YouTube)
28. [Numerical differentiation part-IV (Maxima and minima of a tabulated function and differentiation errors)](https://invisiblenetwork.ai/learn/nptel/111107105/cbf66ad0a979) (YouTube)
29. [Numerical differentiation part-V (Differentiation based on finite difference operators)](https://invisiblenetwork.ai/learn/nptel/111107105/ee7f02419945) (YouTube)
30. [Numerical differentiation part-VI (Method of undetermined coefficients & Derivatives with unequal intervals)](https://invisiblenetwork.ai/learn/nptel/111107105/a20a3806fe98) (YouTube)
31. [Numerical Integration part-I (Methodology of Numerical Integration & Rectangular rule )](https://invisiblenetwork.ai/learn/nptel/111107105/c9fc8ac9a574) (YouTube)
32. [Numerical Integration part-II (Quadrature formula and Trapezoidal rule with associated errors)](https://invisiblenetwork.ai/learn/nptel/111107105/023246ca0eb2) (YouTube)
33. [Numerical Integration part-III (Simpsons 1/3rd rule with associated errors)](https://invisiblenetwork.ai/learn/nptel/111107105/0a5f4b407513) (YouTube)
34. [Numerical Integration part-IV (Composite Simpsons 1/3rd rule & Simpsons 3/8th rule with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/5153ef2a0a2f) (YouTube)
35. [Numerical Integration part-V (Gauss Legendre 2-point and 3-point formula with examples)](https://invisiblenetwork.ai/learn/nptel/111107105/5c34df2fd095) (YouTube)
36. [Introduction to Ordinary Differential equations](https://invisiblenetwork.ai/learn/nptel/111107105/892d4b262ae1) (YouTube)
37. [Numerical methods for ODE-1](https://invisiblenetwork.ai/learn/nptel/111107105/27ca2705b08d) (YouTube)
38. [Numerical Methods-II](https://invisiblenetwork.ai/learn/nptel/111107105/76a9c976e9bd) (YouTube)
39. [R-K Methods for solving ODEs](https://invisiblenetwork.ai/learn/nptel/111107105/62622293aedc) (YouTube)
40. [Multi-step Method for solving ODEs](https://invisiblenetwork.ai/learn/nptel/111107105/85c0296848cf) (YouTube)