# Advanced Numerical Analysis

- Institution: IIT Bombay
- Department: Chemical Engineering
- Teacher: Prof. Sachin C. Patwardhan
- Level: Undergraduate
- Language: English
- Subjects: Chemistry, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/103101111)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/103101111)
- 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 and Overview](https://invisiblenetwork.ai/learn/nptel/103101111/470fb5a5a174) (Video)
2. [Lecture -2 Fundamentals of Vector Spaces](https://invisiblenetwork.ai/learn/nptel/103101111/453c13167bd7) (Video)
3. [Lecture 3 : Basic Dimension and Sub-space of a Vector Space](https://invisiblenetwork.ai/learn/nptel/103101111/424d28f31636) (Video)
4. [Lecture 4 : Introduction to Normed Vector Spaces](https://invisiblenetwork.ai/learn/nptel/103101111/ba5bb09672dd) (Video)
5. [Lecture 5 : Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces](https://invisiblenetwork.ai/learn/nptel/103101111/20bf6ae0a3bf) (Video)
6. [Lecture 6 : Introduction to Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/103101111/6a4b5627b42d) (Video)
7. [Lecture 7 : Cauchy Schwaz Inequality and Orthogonal Sets](https://invisiblenetwork.ai/learn/nptel/103101111/0df014ce3ac8) (Video)
8. [Lecture 8 : Gram-Schmidt Process and Generation of Orthogonal Sets](https://invisiblenetwork.ai/learn/nptel/103101111/94926027e398) (Video)
9. [Lecture 9 : Problem Discretization Using Appropriation Theory](https://invisiblenetwork.ai/learn/nptel/103101111/7163d860afa1) (Video)
10. [Lecture 10 : Weierstrass Theorem and Polynomial Approximation](https://invisiblenetwork.ai/learn/nptel/103101111/af489180ed10) (Video)
11. [Lecture 11 : Taylor Series Approximation and Newton's Method](https://invisiblenetwork.ai/learn/nptel/103101111/03128194de7f) (Video)
12. [Lecture 12 : Solving ODE - BVPs Using Firute Difference Method](https://invisiblenetwork.ai/learn/nptel/103101111/5f620f2af26d) (Video)
13. [Lecture 13 :Solving ODE - BVPs and PDEs Using Finite Difference Method](https://invisiblenetwork.ai/learn/nptel/103101111/04087d6eab07) (Video)
14. [Lecture 14 : Finite Difference Method (contd.) and Polynomial Interpolations](https://invisiblenetwork.ai/learn/nptel/103101111/dcedb065395b) (Video)
15. [Lecture 15 : Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving ODE -BVPs](https://invisiblenetwork.ai/learn/nptel/103101111/60a012b42235) (Video)
16. [Lecture 16 : Orthogonal Collocations Method for Solving ODE - BVPs and PDEs](https://invisiblenetwork.ai/learn/nptel/103101111/ecad3ce32686) (Video)
17. [Lecture 17 :Least Square Approximations, Necessary and Sufficient Conditions for Unconstrained Optimization](https://invisiblenetwork.ai/learn/nptel/103101111/0a202cfc1b95) (Video)
18. [Lecture 18 : Least Square Approximations :Necessary and Sufficient Conditions for Unconstrained Optimization Least Square Approximations ( contd..)](https://invisiblenetwork.ai/learn/nptel/103101111/0e26daafb1fd) (Video)
19. [Lecture 19 :Linear Least Square Estimation and Geometric Interpretation of the Least Square Solution](https://invisiblenetwork.ai/learn/nptel/103101111/c631a2f822b0) (Video)
20. [Lecture 20 : Geometric Interpretation of the Least Square Solution (Contd.) and Projection Theorem in a Hilbert Spaces](https://invisiblenetwork.ai/learn/nptel/103101111/a6bc20d570e0) (Video)
21. [Lecture 21 : Projection Theorem in a Hilbert Spaces (Contd.) and Approximation Using Orthogonal Basis](https://invisiblenetwork.ai/learn/nptel/103101111/98b74a26df90) (Video)
22. [Lecture 22 :Discretization of ODE-BVP using Least Square Approximation](https://invisiblenetwork.ai/learn/nptel/103101111/b342733e9cf1) (Video)
23. [Lecture 23 : Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method](https://invisiblenetwork.ai/learn/nptel/103101111/661aa2261421) (Video)
24. [Lecture 24 : Model Parameter Estimation using Gauss-Newton Method](https://invisiblenetwork.ai/learn/nptel/103101111/385ce248a9a2) (Video)
25. [Lecture 25 : Solving Linear Algebraic Equations and Methods of Sparse Linear Systems](https://invisiblenetwork.ai/learn/nptel/103101111/0731528067f9) (Video)
26. [Lecture 26 : Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving Linear Algebraic Equations](https://invisiblenetwork.ai/learn/nptel/103101111/a25cad2a8071) (Video)
27. [Lecture 27 : Iterative Methods for Solving Linear Algebraic Equations](https://invisiblenetwork.ai/learn/nptel/103101111/87a3c07e511e) (Video)
28. [Lecture 28 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Eigenvalues](https://invisiblenetwork.ai/learn/nptel/103101111/faa8c095a9f6) (Video)
29. [Lecture 29 :Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms](https://invisiblenetwork.ai/learn/nptel/103101111/80cc00c9449f) (Video)
30. [Lecture 30 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms (Contd.)](https://invisiblenetwork.ai/learn/nptel/103101111/3ebd47617c5b) (Video)
31. [Lecture 31 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis (Contd.)](https://invisiblenetwork.ai/learn/nptel/103101111/f19fb71e3f89) (Video)
32. [Lecture 32 :Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method](https://invisiblenetwork.ai/learn/nptel/103101111/d3c5c56cc7b3) (Video)
33. [Lecture 33 : Conjugate Gradient Method, Matrix Conditioning and Solutions of Linear Algebraic Equations](https://invisiblenetwork.ai/learn/nptel/103101111/ed4c13ec2a27) (Video)
34. [Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)](https://invisiblenetwork.ai/learn/nptel/103101111/37c18ea19390) (Video)
35. [Lecture 35 : Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations](https://invisiblenetwork.ai/learn/nptel/103101111/999bb98276e1) (Video)
36. [Lecture 36 : Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method](https://invisiblenetwork.ai/learn/nptel/103101111/d51c4de5e066) (Video)
37. [Lecture 37 : Solving Nonlinear Algebraic Equations: Optimization Based Methods](https://invisiblenetwork.ai/learn/nptel/103101111/6fc93549d1cb) (Video)
38. [Lecture 38 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis of Iterative Solution Techniques](https://invisiblenetwork.ai/learn/nptel/103101111/ddd60f47b65f) (Video)
39. [Lecture 39 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.) and Solving ODE-IVPs](https://invisiblenetwork.ai/learn/nptel/103101111/e561df72387e) (Video)
40. [Lecture 40 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Basic Concepts](https://invisiblenetwork.ai/learn/nptel/103101111/a06df28697e6) (Video)
41. [Lecture 41 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Runge Kutta Methods](https://invisiblenetwork.ai/learn/nptel/103101111/d458b230eb49) (Video)
42. [Lecture 42 :Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods](https://invisiblenetwork.ai/learn/nptel/103101111/029b79663052) (Video)
43. [Lecture 43 :Solving ODE-IVPs : Generalized Formulation of Multi-step Methods](https://invisiblenetwork.ai/learn/nptel/103101111/44a785f4e3d1) (Video)
44. [Lecture 44 : Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method](https://invisiblenetwork.ai/learn/nptel/103101111/b624ec539e58) (Video)
45. [Lecture 45 : Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis of Solution Schemes](https://invisiblenetwork.ai/learn/nptel/103101111/afe27bbfac0f) (Video)
46. [Lecture 46 : Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)](https://invisiblenetwork.ai/learn/nptel/103101111/6cfd2d137286) (Video)
47. [Lecture 47 :Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) and Solving ODE-BVP using Single Shooting Method](https://invisiblenetwork.ai/learn/nptel/103101111/a58937373aa3) (Video)
48. [Lecture 48 : Methods for Solving System of Differential Algebraic Equations](https://invisiblenetwork.ai/learn/nptel/103101111/866e619c8703) (Video)
49. [Lecture 49 : Methods for Solving System of Differential Algebraic Equations (contd.) and Concluding Remarks](https://invisiblenetwork.ai/learn/nptel/103101111/9c036b815ef7) (Video)