Contents:
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

### 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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