Errors and significant digits, general error formula, errors in a series approximation
Bisection method, iteration method, Method of false position, Newton -Raphson method, Horner’s Method,
Graeffe’s Root squaring method, methods of iteration: Jacobi’s method, Gauss Siedel Method, Relaxation
Method.
Errors in polynomial interpretation, finite difference, forward, backward and central difference, Difference of a
polynomial, Newton’s formulae for interpolation, central difference interpolation formulae (Gauss Forward, Gauss
Backward), Interpolation with unevenly spaced points (Lagrange’s Interpolation Formulae, Newton’s divided
difference formulae only)
Numerical differentiation-maximum and minimum values of a tabulated function;
Numerical Integration- Newton-cots integration formulae, Trapezoidal rule, Simpson1/3 rule, Simpson’s 3/8 rule;
Gaussian integration (One dimensional only)
Introduction, Inverse of Matrix, Solution of linear systems, Matrix inversion method, Gaussian Elimination
method, Gauss Jordan Method, Partition Method for linear system of equations (Escalator Method), power
method for partition and Eigen value problems
Solution by Picard method, Taylor's series, Euler's method, Runge-Kutta method
Simulation:
Introduction, Continuous and discrete system, System simulation, real time simulation, simulation models, steps
and phases of simulation study, simulation – a management laboratory, advantages & limitations of system
simulation, Monte Carlo simulation, application of Monte Carlo methods: Numerical Integration, value of pi.
Stochastic and random variables, discrete and continuous probability distribution functions, Central tendency,
dispersion, Time flow mechanisms, Verification, Validation and calibration of Simulation Models, design of
simulation experiment, Length of simulation run, Elimination of Initial bias, Variance and its reduction, Analog vs
computer simulation, Simulation languages SIMULA, SIMSCRIPT, GPSS, SIMAN.
Formulation of model for a dynamic system and its simulation (case study).