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Course Description

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Course Syllabus
  • Mod-01 Lec-01 Introduction and Overview
  • Mod-01 Lec-02 Fundamentals of Vector Spaces
  • Mod-01 Lec-03 Basic Dimension and Sub-space of a Vector Space
  • Mod-01 Lec-04 Introduction to Normed Vector Spaces
  • Mod-01 Lec-05 Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces
  • Mod-01 Lec-09 Problem Discretization Using Appropriation Theory
  • Mod-01 Lec-10 Weierstrass Theorem and Polynomial Approximation
  • Mod-01 Lec-11 Taylor Series Approximation and Newton's Method
  • Mod-01 Lec-12 Solving ODE - BVPs Using Firute Difference Method
  • Mod-01 Lec-13 Solving ODE - BVPs and PDEs Using Finite Difference Method
  • Mod-01 Lec-14 Finite Difference Method (contd.) and Polynomial Interpolations
  • Mod-01 Lec-15 Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving
  • Mod-01 Lec-26 Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving
  • Mod-01 Lec-27 Iterative Methods for Solving Linear Algebraic Equations
  • Mod-01 Lec-28 Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis
  • Mod-01 Lec-29 Iterative Methods for Solving Linear Algebraic Equations:
  • Mod-01 Lec-30 Iterative Methods for Solving Linear Algebraic Equations: Convergence
  • Mod-01 Lec-25 Solving Linear Algebraic Equations and Methods of Sparse Linear Systems
  • Mod-01 Lec-24 Model Parameter Estimation using Gauss-Newton Method
  • Mod-01 Lec-23 Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method
  • Mod-01 Lec-08 Gram-Schmidt Process and Generation of Orthogonal Sets
  • Mod-01 Lec-47 Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)
  • Mod-01 Lec-38 Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis
  • Mod-01 Lec-22 Discretization of ODE-BVP using Least Square Approximation
  • Mod-01 Lec-07 Cauchy Schwaz Inequality and Orthogonal Sets
  • Mod-01 Lec-46 Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)
  • Mod-01 Lec-37 Solving Nonlinear Algebraic Equations: Optimization Based Methods
  • Mod-01 Lec-21 Projection Theorem in a Hilbert Spaces (Contd.) and Approximation
  • Mod-01 Lec-06 Introduction to Inner Product Spaces
  • Mod-01 Lec-36 Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method
  • Mod-01 Lec-45 Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis
  • Mod-01 Lec-35 Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations
  • Mod-01 Lec-44 Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method
  • Mod-01 Lec-19 Linear Least Square Estimation and Geometric Interpretation
  • Mod-01 Lec-34 Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)
  • Mod-01 Lec-43 Solving ODE-IVPs : Generalized Formulation of Multi-step Methods
  • Mod-01 Lec-18 Least Square Approximations :Necessary and Sufficient Conditions
  • Mod-01 Lec-33 Conjugate Gradient Method, Matrix Conditioning and Solutions
  • Mod-01 Lec-42 Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods
  • Mod-01 Lec-17 Least Square Approximations, Necessary and Sufficient Conditions
  • Mod-01 Lec-16 Orthogonal Collocations Method for Solving ODE - BVPs and PDEs
  • Mod-01 Lec-39 Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.)
  • Mod-01 Lec-40 Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs)
  • Mod-01 Lec-41 Solving Ordinary Differential Equations - Initial Value Problems
  • Mod-01 Lec-48 Methods for Solving System of Differential Algebraic Equations
  • Mod-01 Lec-49 Methods for Solving System of Differential Algebraic Equations
  • Mod-01 Lec-31 Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis
  • Mod-01 Lec-32 Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method
  • Mod-01 Lec-20 Geometric Interpretation of the Least Square Solution (Contd.) and Projection
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