Elementary Numerical Analysis

Video Lectures

Displaying all 40 video lectures.
I. Polynomials and Piecewise Polynomial Interpolation
Lecture 1
Introduction
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Introduction
Lecture 2
Polynomial Approximation
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Polynomial Approximation
Lecture 3
Interpolating Polynomials
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Interpolating Polynomials
Lecture 4
Properties of Divided Difference
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Properties of Divided Difference
Lecture 5
Error in the Interpolating Polynomial
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Error in the Interpolating Polynomial
Lecture 6
Cubic Hermite Interpolation
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Cubic Hermite Interpolation
Lecture 7
Piecewise Polynomial Approximation
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Piecewise Polynomial Approximation
Lecture 8
Cubic Spline Interpolation
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Cubic Spline Interpolation
Lecture 9
Tutorial 1
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Tutorial 1
II. Numerical Integration
Lecture 10
Numerical Integration: Basic Rules
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Numerical Integration: Basic Rules
Lecture 11
Composite Numerical Integration
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Composite Numerical Integration
Lecture 12
Gauss 2-point Rule: Construction
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Gauss 2-point Rule: Construction
Lecture 13
Gauss 2-point Rule: Error
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Gauss 2-point Rule: Error
Lecture 14
Convergence of Gaussian Integration
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Convergence of Gaussian Integration
Lecture 15
Tutorial 2
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Tutorial 2
III. Numerical Differentiation
Lecture 16
Numerical Differentiation
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Numerical Differentiation
Lecture 17
Gaussian Elimination
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Gaussian Elimination
IV. Vector and Matrix Norms
Lecture 18
LU Decomposition
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LU Decomposition
Lecture 19
Cholesky Decomposition
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Cholesky Decomposition
V. Solution of System of Linear Equations
Lecture 20
Gauss Elimination with Partial Pivoting
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Gauss Elimination with Partial Pivoting
Lecture 21
Vector and Matrix Norms
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Vector and Matrix Norms
Lecture 22
Perturbed Linear Systems
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Perturbed Linear Systems
Lecture 23
ILL-conditioned Linear System
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ILL-conditioned Linear System
Lecture 24
Tutorial 3
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Tutorial 3
Lecture 25
Effect of Small Pivots
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Effect of Small Pivots
VI. Solution of Nonlinear System of Equations
Lecture 26
Solution of Non-linear Equations
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Solution of Non-linear Equations
Lecture 27
Quadratic Convergence of Newton's Method
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Quadratic Convergence of Newton's Method
Lecture 28
Jacobi Method
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Jacobi Method
Lecture 29
Gauss-Seidel Method
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Gauss-Seidel Method
Lecture 30
Tutorial 4
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Tutorial 4
VII. Initial Value Problems
Lecture 31
Initial Value Problem
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Initial Value Problem
Lecture 32
Multi-step Methods
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Multi-step Methods
Lecture 33
Predictor-Corrector Formulae
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Predictor-Corrector Formulae
VIII. Boundary Value Problem
Lecture 34
Boundary Value Problems
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Boundary Value Problems
Lecture 35
Eigenvalues and Eigenvectors
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Eigenvalues and Eigenvectors
Lecture 36
Spectral Theorem
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Spectral Theorem
Lecture 37
Power Method
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Power Method
Lecture 38
Inverse Power Method
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Inverse Power Method
Lecture 39
QR Decomposition
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QR Decomposition
Lecture 40
QR Method
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QR Method