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