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