Polynomial and piecewisepolynomial Interpolation : Divided Difference, Lagrange and Newton Form,Osculatory Interpolation.
Numerical Integration : Some Basic Rules, Gaussian Integration, Composite Rules,Adaptive Quadrature, Romberg integration.

Numerical Differentiation – Vector and Matrix Norms.
Solution of System of Linear Equations : Gauss Elimination Method, Partial Pivoting,Jacobi and GaussSeidel Methods,QR factorization using reflectors.

Eigenvalue Problem : Basic properties,Eigenvalue location,Power Method and its variants.
Initial Value Problems : Single step methods such as Euler’s Method, RungeKutta Methods, Taylor series method,Multistep methods such as AdamsBashforth method,Milne’s method,PredictorCorrector Formula : AdamMoulton method.

Boundary value proble : Finite Difference method.
Solution of nonlinear system of equations

Other Resources

Course Curriculum

Introduction Details 50:24
Polynomial Approximation Details 48:35
Interpolating Polynomials Details 49:37
Properties of Divided Difference Details 50:1
Error in the Interpolating polynomial Details 49:45
Cubic Hermite Interpolation Details 50:16
Piecewise Polynomial Approximation Details 47:58
Cubic Spline Interpolation Details 47:47
Tutorial 1 Details 51:55
Numerical Integration: Basic Rules Details 49:41
Composite Numerical Integration Details 46:42
Gauss 2-point Rule: Construction Details 54:50
Gauss 2-point Rule: Error Details 45:21
Convergence of Gaussian Integration Details 48:49
Tutorial 2 Details 52:53
Numerical Differentiation Details 49:10
Gauss Elimination Details 46:38
L U decomposition Details 46:26
Cholesky decomposition Details 47:18
Gauss Elimination with partial pivoting Details 0:45
Vector and Matrix Norms Details 48:51
Perturbed Linear Systems Details 48:29
ILL-conditioned Linear System Details 48:35
Tutorial 3 Details 45:21
Effect of Small Pivots Details 47:48
Solution of Non-linear Equations Details 48:38
Quadratic Convergence of Newton’s Method Details 47:24
Jacobi Method Details 51:43
Gauss-Seidel Method Details 48:52
Tutorial 4 Details 46:27
Initial Value Problem Details 51:4
Spectral Theorem Details 48:13
Power Method Details 49:48
Inverse Power Method Details 49:59
Q R Decomposition Details 49:53
Q R Method Details 48:43
Multi-step Methods Details 50:40
Predictor-Corrector Formulae Details 47:45
Boundary Value Problems Details 50:35
Eigenvalues and Eigenvectors Details 48:20

This course is delivered by IIT Bombay , as part of NPTEL Free Courses sponsored by Govt of India.

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