Elementary Numerical Analysis

IIT Bombay Course , Prof. Rekha P. Kulkarni

Lecture 1: Introduction

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Lecture Details :

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

Course Description :

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

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