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

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Course Curriculum

Introduction and Overview Details 1:33:47
Fundamentals of Vector Spaces Details 46:53
Basic Dimension and Sub-space of a Vector Space Details 48:29
Introduction to Normed Vector Spaces Details 47:34
Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces Details 37:2
Introduction to Inner Product Spaces Details 53:54
Cauchy Schwaz Inequality and Orthogonal Sets Details 43:42
Gram-Schmidt Process and Generation of Orthogonal Sets Details 28:30
Problem Discretization Using Appropriation Theory Details 52:51
Weierstrass Theorem and Polynomial Approximation Details 37:9
Taylor Series Approximation and Newton’s Method Details 47:50
Solving ODE – BVPs Using Firute Difference Method Details 46:32
Solving ODE – BVPs and PDEs Using Finite Difference Method Details 48:22
Finite Difference Method (contd.) and Polynomial Interpolations Details 48:34
Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving Details 34:6
Orthogonal Collocations Method for Solving ODE – BVPs and PDEs Details 1:3:48
Least Square Approximations, Necessary and Sufficient Conditions Details 50:31
Least Square Approximations :Necessary and Sufficient Conditions I Details 55:24
Linear Least Square Estimation and Geometric Interpretation II Details 48:54
Geometric Interpretation of the Least Square Solution (Contd.) and Projection Details 48:14
Projection Theorem in a Hilbert Spaces (Contd.) and Approximation Details 53:18
Discretization of ODE-BVP using Least Square Approximation Details 52:55
Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method I Details 49:11
Model Parameter Estimation using Gauss-Newton Method Details 52:8
Solving Linear Algebraic Equations and Methods of Sparse Linear Systems Details 53:12
Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving Details 48:43
Iterative Methods for Solving Linear Algebraic Equations Details 52:41
Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis I Details 56:18
Iterative Methods for Solving Linear Algebraic Equations II Details 58:1
Iterative Methods for Solving Linear Algebraic Equations: Convergence III Details 46:19
Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis IV Details 46:32
Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method Details 48:13
Conjugate Gradient Method, Matrix Conditioning and Solutions Details 40:17
Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.) Details 54:53
Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations I Details 0:53
Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton’s Method Details 35:2
Solving Nonlinear Algebraic Equations: Optimization Based Methods I Details 48:47
Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis II Details 56:35
Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.) III Details 56:33
Solving Ordinary Differential Equations – Initial Value Problems (ODE-IVPs) IV Details 57:10
Solving Ordinary Differential Equations – Initial Value Problems V Details 59:55
Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods VI Details 55:50
Solving ODE-IVPs : Generalized Formulation of Multi-step Methods VII Details 55:6
Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method VIII Details 52:19
Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis IX Details 51:26
Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) X Details 47:18
Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) XI Details 57:52
Methods for Solving System of Differential Algebraic Equations Details 48:43
Methods for Solving System of Differential Algebraic Equations I Details 56:12

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