INSTRUCTIONS: 1. For Paper Setters: The question paper will consist of five sections A, B, C, D & E. Section E will be compulsory, it will consist of a single question with 10-20 subparts of short answer type, which will cover the entire syllabus. Section A, B, C & D will have two questions from the respective sections of the syllabus. Each section will have a weightage of 20% of the total marks of the semester end examination for the course. 2. For candidates: Candidates are required to attempt five questions in all selecting one question from each of the sections A, B, C & D of the question paper and all the subparts of the questions in Section E. SECTION –A SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS: Bisection method, Method of false position, secant method, Iteration method, Newton-Raphson method and Generalized Newton-Raphson method, Rate of convergence and condition of convergence, solution of simultaneous equations by Iteration method and Newton-Raphson method 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