Advanced Numerical Analysis

Video Lectures

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