Advanced Numerical Analysis

Video Lectures

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