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Advanced Numerical Analysis
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Advanced Numerical Analysis
by Prof.Sachin C.Patwardhan

The process of developing a numerical recipe for solving an engineering problem Introduce geometric ideas associated with the development of numerical schemes Familiarize the student with ideas of convergence analysis of numerical methods and other analytical aspects associated with numerical computation...

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FREE
About This Course

The process of developing a numerical recipe for solving an engineering problem Introduce geometric ideas associated with the development of numerical schemes Familiarize the student with ideas of convergence analysis of numerical methods and other analytical aspects associated with numerical computation...

Course Curriculum
1 Sections | 49 Lecture | 41h 42min total length
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Advanced Numerical Analysis

Advanced Numerical Analysis

| 41h 42min total length
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    Lecture 1: Introduction and Overview

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    Lecture -2 Fundamentals of Vector Spaces?

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    Lecture 3 : Basic Dimension and Sub-space of a Vector Space

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    Lecture 4 : Introduction to Normed Vector Spaces

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    Lecture 5 : Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces

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    Lecture 6 : Introduction to Inner Product Spaces?

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    Lecture 7 : Cauchy Schwaz Inequality and Orthogonal Sets

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    Lecture 8 : Gram-Schmidt Process and Generation of Orthogonal Sets?

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    Lecture 9 : Problem Discretization Using Appropriation Theory?

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    Lecture 10 : Weierstrass Theorem and Polynomial Approximation?

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    Lecture 11 : Taylor Series Approximation and Newton's Method?

    47m <?php echo $alt; ?>
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    Lecture 12 : Solving ODE - BVPs Using Firute Difference Method?

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    Lecture 13 :Solving ODE - BVPs and PDEs Using Finite Difference Method?

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    Lecture 14 : Finite Difference Method (contd.) and Polynomial Interpolations

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    Lecture 15 : Polynomial and Function Interpolations

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    Lecture 16 : Orthogonal Collocations Method for Solving ODE - BVPs and PDEs

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    Lecture 17 :Least Square Approximations

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    Lecture 18 : Least Square Approximations?

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    Lecture 19 :Linear Least Square Estimation and Geometric Interpretation of the Least Square Solution

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    Lecture 20 : Geometric Interpretation of the Least Square Solution

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    Lecture 21 : Projection Theorem in a Hilbert Spaces

    53m <?php echo $alt; ?>
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    Lecture 22 :Discretization of ODE-BVP using Least Square Approximation

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    Lecture 23 : Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method

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    Lecture 24 : Model Parameter Estimation using Gauss-Newton Method

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    Lecture 25 : Solving Linear Algebraic Equations and Methods of Sparse Linear Systems

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    Lecture 26 : Methods of Sparse Linear Systems

    48m <?php echo $alt; ?>
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    Lecture 27 : Iterative Methods for Solving Linear Algebraic Equations

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    Lecture 28 : Iterative Methods for Solving Linear Algebraic Equations

    56m <?php echo $alt; ?>
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    Lecture 29 :Iterative Methods for Solving Linear Algebraic Equations

    58m <?php echo $alt; ?>
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    Lecture 30 : Iterative Methods for Solving Linear Algebraic Equations

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    Lecture 31 : Iterative Methods for Solving Linear Algebraic Equations

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    Lecture 32 :Optimization Based Methods for Solving Linear Algebraic Equations

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    Lecture 33 : Conjugate Gradient Method Matrix Conditioning

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    Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations

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    Lecture 35 : Matrix Conditioning and Solving Nonlinear Algebraic Equations

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    Lecture 36 : Solving Nonlinear Algebraic Equations

    35m <?php echo $alt; ?>
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    Lecture 37 : Solving Nonlinear Algebraic Equations

    48m <?php echo $alt; ?>
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    Lecture 38 : Solving Nonlinear Algebraic Equations

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    Lecture 39 : Solving Nonlinear Algebraic Equations Introduction to Convergence analysis

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    Lecture 40 :Solving Ordinary Differential Equations Initial Value Problems

    57m <?php echo $alt; ?>
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    Lecture 41 :Solving Ordinary Differential Equations Initial Value Problems?

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    Lecture 42 :Solving ODE-IVPs Runge Kutta Methods

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    Lecture 43 :Solving ODE-IVPs Generalized Formulation of Multi-step Methods

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    Lecture 44 : Solving ODE-IVPs Multi-step Methods and Orthogonal Collocations Method

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    Lecture 45 : Solving ODE-IVPs Selection of Integration Interval?

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    Lecture 46 : Solving ODE-IVPs Convergence Analysis of Solution Schemes

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    Lecture 47 :Solving ODE-IVPs Convergence Analysis of Solution Schemes

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    Lecture 48 : Methods for Solving System of Differential Algebraic Equations

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    Lecture 49 : Methods for Solving System of Differential Algebraic Equations

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