Advanced Numerical Analysis Video Lectures

Advanced Numerical Analysis
'Advanced Numerical Analysis' Video Lectures by Prof. Sachin C. Patwardhan from IIT Bombay
"Advanced Numerical Analysis" - Video Lectures
1. Lecture 1: Introduction and Overview
2. Lecture -2 Fundamentals of Vector Spaces
3. Lecture 3 : Basic Dimension and Sub-space of a Vector Space
4. Lecture 4 : Introduction to Normed Vector Spaces
5. Lecture 5 : Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces
6. Lecture 6 : Introduction to Inner Product Spaces
7. Lecture 7 : Cauchy Schwaz Inequality and Orthogonal Sets
8. Lecture 8 : Gram-Schmidt Process and Generation of Orthogonal Sets
9. Lecture 9 : Problem Discretization Using Appropriation Theory
10. Lecture 10 : Weierstrass Theorem and Polynomial Approximation
11. Lecture 11 : Taylor Series Approximation and Newton's Method
12. Lecture 12 : Solving ODE - BVPs Using Firute Difference Method
13. Lecture 13 :Solving ODE - BVPs and PDEs Using Finite Difference Method
14. Lecture 14 : Finite Difference Method (contd.) and Polynomial Interpolations
15. Lecture 15 : Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving ODE -BVPs
16. Lecture 16 : Orthogonal Collocations Method for Solving ODE - BVPs and PDEs
17. Lecture 17 :Least Square Approximations, Necessary and Sufficient Conditions for Unconstrained Optimization
18. Lecture 18 : Least Square Approximations :Necessary and Sufficient Conditions for Unconstrained Optimization Least Square Approximations ( contd..)
19. Lecture 19 :Linear Least Square Estimation and Geometric Interpretation of the Least Square Solution
20. Lecture 20 : Geometric Interpretation of the Least Square Solution (Contd.) and Projection Theorem in a Hilbert Spaces
21. Lecture 21 : Projection Theorem in a Hilbert Spaces (Contd.) and Approximation Using Orthogonal Basis
22. Lecture 22 :Discretization of ODE-BVP using Least Square Approximation
23. Lecture 23 : Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method
24. Lecture 24 : Model Parameter Estimation using Gauss-Newton Method
25. Lecture 25 : Solving Linear Algebraic Equations and Methods of Sparse Linear Systems
26. Lecture 26 : Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving Linear Algebraic Equations
27. Lecture 27 : Iterative Methods for Solving Linear Algebraic Equations
28. Lecture 28 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Eigenvalues
29. Lecture 29 :Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms
30. Lecture 30 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms (Contd.)
31. Lecture 31 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis (Contd.)
32. Lecture 32 :Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method
33. Lecture 33 : Conjugate Gradient Method, Matrix Conditioning and Solutions of Linear Algebraic Equations
34. Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)
35. Lecture 35 : Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations
36. Lecture 36 : Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method
37. Lecture 37 : Solving Nonlinear Algebraic Equations: Optimization Based Methods
38. Lecture 38 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis of Iterative Solution Techniques
39. Lecture 39 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.) and Solving ODE-IVPs
40. Lecture 40 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Basic Concepts
41. Lecture 41 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Runge Kutta Methods
42. Lecture 42 :Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods
43. Lecture 43 :Solving ODE-IVPs : Generalized Formulation of Multi-step Methods
44. Lecture 44 : Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method
45. Lecture 45 : Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis of Solution Schemes
46. Lecture 46 : Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)
47. Lecture 47 :Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) and Solving ODE-BVP using Single Shooting Method
48. Lecture 48 : Methods for Solving System of Differential Algebraic Equations
49. Lecture 49 : Methods for Solving System of Differential Algebraic Equations (contd.) and Concluding Remarks
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