Course Co-ordinated by IIT Bombay
 Coordinators IIT Bombay

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The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems.

The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer.

 Module No. Topic/s Lectures 1 Polynomial and piecewisepolynomial Interpolation: Divided Difference, Lagrange and Newton Form Osculatory Interpolation 4 2 2 Numerical Integration: Some Basic Rules, Gaussian Integration, Composite Rules Adaptive Quadrature, Romberg integration 4 3 3 Numerical Differentiation 2 4 Vector and Matrix Norms 2 5 Solution of System of Linear Equations: Gauss Elimination Method, Partial Pivoting Jacobi and GaussSeidel Methods QR factorization using reflectors 3 3 2 6 Eigenvalue Problem: Basic properties: Eigenvalue location: Power Method and its variants: 3 3 2 7 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 3 3 2 8 Boundary value problem: Finite Difference method 2 9 Solution of nonlinear system of equations: 3

Basic Course in Calculus / Real Analysis

1. S. D. Conte and Carl de Boor, Elementary Numerical Analysis, An Algorithmic Approach, MacgrawHill International Editions, 1981.

2. K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, paperback, 1989.

D. S. Watkins, Fundamentals of Matrix Computations, John Wiley & Sons, 1991