Elementary Numerical Analysis

Video Lectures

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