NMSE (B-TECH Automobile Engineering 5th)

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).