IIT Bombay Course , Prof. Sachin C. Patwardhan

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IIT Bombay Course , Prof. Sachin C. Patwardhan

Introduction and Overview - Fundamentals of Vector Spaces - Basic Dimension and Sub-space of a Vector Space - Introduction to Normed Vector Spaces - Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces - Introduction to Inner Product Spaces - Cauchy Schwaz Inequality and Orthogonal Sets - Gram-Schmidt Process and Generation of Orthogonal Sets - Problem Discretization Using Appropriation Theory - Weierstrass Theorem and Polynomial Approximation - Taylor Series Approximation and Newton's Method - Solving ODE - BVPs Using Firute Difference Method - Solving ODE - BVPs and PDEs Using Finite Difference Method - Finite Difference Method (contd.) and Polynomial Interpolations - Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving - Orthogonal Collocations Method for Solving ODE - BVPs and PDEs - Least Square Approximations :Necessary and Sufficient ConditionsLinear Least Square Estimation and Geometric Interpretation - Geometric Interpretation of the Least Square Solution (Contd.) and Projection - Projection Theorem in a Hilbert Spaces (Contd.) and Approximation - Discretization of ODE-BVP using Least Square Approximation - Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method - Model Parameter Estimation using Gauss-Newton Method - Solving Linear Algebraic Equations and Methods of Sparse Linear Systems

Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving - Iterative Methods for Solving Linear Algebraic Equations: Convergence - Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis - Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method - Conjugate Gradient Method, Matrix Conditioning and Solutions - Matrix Conditioning and Solutions and Linear Algebraic Equations and Solving Nonlinear Algebraic Equations - Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method - Solving Nonlinear Algebraic Equations: Optimization Based Methods - Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis - Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) - Solving Ordinary Differential Equations - Initial Value Problems - Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods - Solving ODE-IVPs : Generalized Formulation of Multi-step Methods - Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method - Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis - Solving ODE-IVPs: Convergence Analysis of Solution Schemes - Methods for Solving System of Differential Algebraic Equations

Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving - Iterative Methods for Solving Linear Algebraic Equations: Convergence - Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis - Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method - Conjugate Gradient Method, Matrix Conditioning and Solutions - Matrix Conditioning and Solutions and Linear Algebraic Equations and Solving Nonlinear Algebraic Equations - Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method - Solving Nonlinear Algebraic Equations: Optimization Based Methods - Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis - Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) - Solving Ordinary Differential Equations - Initial Value Problems - Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods - Solving ODE-IVPs : Generalized Formulation of Multi-step Methods - Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method - Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis - Solving ODE-IVPs: Convergence Analysis of Solution Schemes - Methods for Solving System of Differential Algebraic Equations

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Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit httpnptel.ac.in

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The above video lectures are presented by IITBombay, India, under the program NPTEL, there are more than 350+ NPTEL courses Online available.
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- 1.Introduction and Overview
- 2.Fundamentals of Vector Spaces
- 3.Basic Dimension and Sub-space of a Vector Space
- 4.Introduction to Normed Vector Spaces
- 5.Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces
- 6.Introduction to Inner Product Spaces
- 7.Cauchy Schwaz Inequality and Orthogonal Sets
- 8.Gram-Schmidt Process and Generation of Orthogonal Sets
- 9.Problem Discretization Using Appropriation Theory
- 10.Weierstrass Theorem and Polynomial Approximation
- 11.Taylor Series Approximation and Newtons Method
- 12.Solving ODE - BVPs Using Firute Difference Method
- 13.Solving ODE - BVPs and PDEs Using Finite Difference Method
- 14.Finite Difference Method (contd.) and Polynomial Interpolations
- 15.Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving
- 16.Orthogonal Collocations Method for Solving ODE - BVPs and PDEs
- 17.Least Square Approximations, Necessary and Sufficient Conditions
- 18.Least Square Approximations Necessary and Sufficient Conditions I
- 19.Linear Least Square Estimation and Geometric Interpretation II
- 20.Geometric Interpretation of the Least Square Solution (Contd.) and Projection
- 21.Projection Theorem in a Hilbert Spaces (Contd.) and Approximation
- 22.Discretization of ODE-BVP using Least Square Approximation
- 23.Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method I
- 24.Model Parameter Estimation using Gauss-Newton Method
- 25.Solving Linear Algebraic Equations and Methods of Sparse Linear Systems
- 26.Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving
- 27.Iterative Methods for Solving Linear Algebraic Equations
- 28.Iterative Methods for Solving Linear Algebraic Equations Convergence Analysis I
- 29.Iterative Methods for Solving Linear Algebraic Equations II
- 30.Iterative Methods for Solving Linear Algebraic Equations Convergence III
- 31.Iterative Methods for Solving Linear Algebraic Equations Convergence Analysis IV
- 32.Optimization Based Methods for Solving Linear Algebraic Equations Gradient Method
- 33.Conjugate Gradient Method, Matrix Conditioning and Solutions
- 34.Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)
- 35.Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations I
- 36.Solving Nonlinear Algebraic Equations Wegstein Method and Variants of Newtons Method
- 37.Solving Nonlinear Algebraic Equations Optimization Based Methods I
- 38.Solving Nonlinear Algebraic Equations Introduction to Convergence analysis II
- 39.Solving Nonlinear Algebraic Equations Introduction to Convergence analysis (Contd.) III
- 40.Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) IV
- 41.Solving Ordinary Differential Equations - Initial Value Problems V
- 42.Solving ODE-IVPs Runge Kutta Methods (contd.) and Multi-step Methods VI
- 43.Solving ODE-IVPs Generalized Formulation of Multi-step Methods VII
- 44.Solving ODE-IVPs Multi-step Methods (contd.) and Orthogonal Collocations Method VIII
- 45.Solving ODE-IVPs Selection of Integration Interval and Convergence Analysis IX
- 46.Solving ODE-IVPs Convergence Analysis of Solution Schemes (contd.) X
- 47.Solving ODE-IVPs Convergence Analysis of Solution Schemes (contd.) XI
- 48.Methods for Solving System of Differential Algebraic Equations
- 49.Methods for Solving System of Differential Algebraic Equations I

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