Lecture 1: Introduction
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