NPTEL : Advanced Numerical Analysis (Chemical Engineering)

Co-ordinators : Prof. Sachin C. Patwardhan


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