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Subject:
Mathematics
Topic:
Numerical Analysis
Views:
43,138
Educator
Name:
Indian Institute of Technology, Bombay (IIT Bombay)
Type:
University
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Elementary Numerical Analysis
Video Lectures
Displaying all 40 video lectures.
I. Polynomials and Piecewise Polynomial Interpolation
Lecture 1
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Introduction
Lecture 2
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Polynomial Approximation
Lecture 3
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Interpolating Polynomials
Lecture 4
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Properties of Divided Difference
Lecture 5
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Error in the Interpolating Polynomial
Lecture 6
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Cubic Hermite Interpolation
Lecture 7
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Piecewise Polynomial Approximation
Lecture 8
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Cubic Spline Interpolation
Lecture 9
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Tutorial 1
II. Numerical Integration
Lecture 10
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Numerical Integration: Basic Rules
Lecture 11
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Composite Numerical Integration
Lecture 12
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Gauss 2-point Rule: Construction
Lecture 13
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Gauss 2-point Rule: Error
Lecture 14
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Convergence of Gaussian Integration
Lecture 15
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Tutorial 2
III. Numerical Differentiation
Lecture 16
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Numerical Differentiation
Lecture 17
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Gaussian Elimination
IV. Vector and Matrix Norms
Lecture 18
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LU Decomposition
Lecture 19
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Cholesky Decomposition
V. Solution of System of Linear Equations
Lecture 20
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Gauss Elimination with Partial Pivoting
Lecture 21
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Vector and Matrix Norms
Lecture 22
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Perturbed Linear Systems
Lecture 23
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ILL-conditioned Linear System
Lecture 24
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Tutorial 3
Lecture 25
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Effect of Small Pivots
VI. Solution of Nonlinear System of Equations
Lecture 26
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Solution of Non-linear Equations
Lecture 27
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Quadratic Convergence of Newton's Method
Lecture 28
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Jacobi Method
Lecture 29
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Gauss-Seidel Method
Lecture 30
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Tutorial 4
VII. Initial Value Problems
Lecture 31
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Initial Value Problem
Lecture 32
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Multi-step Methods
Lecture 33
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Predictor-Corrector Formulae
VIII. Boundary Value Problem
Lecture 34
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Boundary Value Problems
Lecture 35
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Eigenvalues and Eigenvectors
Lecture 36
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Spectral Theorem
Lecture 37
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Power Method
Lecture 38
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Inverse Power Method
Lecture 39
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QR Decomposition
Lecture 40
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QR Method
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Subject: Mathematics
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Elementary Numerical Analysis