Advances:

SOLUTION OF SIMULTANEOUS ALGEBRAIC EQUATIONS: Partial and Complete Pivoting, Gauss Elimination method, Gauss Jordan method, Jacobi‟s method, Gauss-Seidal method, Relaxation method and LU-decomposition method. SECTION-B FINITE DIFFERENCE AND INTERPOLATION: Errors and approximation analysis, Interpolation, Various difference operators and relation between them, Newton‟s forward and backward interpolation formulae, Central difference Interpolation formula, Gauss‟s forward and backward interpolation formulae, Stirling formula, Bessel formula, Lagrange‟s interpolation formula of unequal intervals, Newton‟s divided difference formulae. SECTION-C NUMERICAL DIFFERENTIATION AND INTEGRATION: Numerical differentiation: Derivatives using Newton forward, backward and central difference formulas, Derivatives using Gauss forward and backward formulas, Derivatives using Bessel formula, Derivatives using Newton divided difference formulas, Maxima and minima of tabulated functions. NUMERICAL INTEGRATION: Newton-Cotes Quadrature formula, Trapezoidal rule, Simpson‟s 1/3rd and 3/8th rules, Boole‟s and Weddle‟s rules, Errors and accuracy of these formulae (Trapezoidal rule, Simpson‟s 1/3rd rule) Romberg‟s integration. SECTION-D NUMERICAL SOLUTIONS OF ORDINARY EQUATIONS: Picard method, Taylor‟s series method, Euler‟s method, Runge‟s method, Runge-Kutta method, Predictor- Corrector Methods: Milne‟s method and Adams-Bashforth method. 58

NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL: Finite difference approximations of partial derivatives, solution of Laplace equation (Standard five-point formula and Diagonal five-point formula), Solution of Poisson equation. TEXT BOOKS: 1. Numerical methods for Scientific & Engg. Computations: M. K. Jain, S. R. K. Iyengar & R. K. Jain; Wiley Eastern Ltd. 2. Introductory Methods of Numerical A