Elementary Numerical Analysis


Lecture 1 - Introduction


Lecture 2 - Polynomial Approximation


Lecture 3 - Interpolating Polynomials


Lecture 4 - Properties of Divided Difference


Lecture 5 - Error in the Interpolating polynomial


Lecture 6 - Cubic Hermite Interpolation


Lecture 7 - Piecewise Polynomial Approximation


Lecture 8 - Cubic Spline Interpolation


Lecture 9 - Tutorial 1


Lecture 10 - Numerical Integration: Basic Rules


Lecture 11 - Composite Numerical Integration


Lecture 12 - Gauss 2-point Rule: Construction


Lecture 13 - Gauss 2-point Rule: Error


Lecture 14 - Convergence of Gaussian Integration


Lecture 15 - Tutorial 2


Lecture 16 - Numerical Differentiation


Lecture 17 - Gauss Elimination


Lecture 18 - L U decomposition


Lecture 19 - Cholesky decomposition


Lecture 20 - Gauss Elimination with partial pivoting


Lecture 21 - Vector and Matrix Norms


Lecture 22 - Perturbed Linear Systems


Lecture 23 - Ill-conditioned Linear System


Lecture 24 - Tutorial 3


Lecture 25 - Effect of Small Pivots


Lecture 26 - Solution of Non-linear Equations


Lecture 27 - Quadratic Convergence of Newton's Method


Lecture 28 - Jacobi Method


Lecture 29 - Gauss-Seidel Method


Lecture 30 - Tutorial 4


Lecture 31 - Initial Value Problem


Lecture 32 - Multi-step Methods


Lecture 33 - Predictor-Corrector Formulae


Lecture 34 - Boundary Value Problems


Lecture 35 - Eigenvalues and Eigenvectors


Lecture 36 - Spectral Theorem


Lecture 37 - Power Method


Lecture 38 - Inverse Power Method


Lecture 39 - Q R Decomposition


Lecture 40 - Q R Method