1

ERROR ANALYSIS:
Roundoff errors and truncation errors in numerical computation, error propagation, and numerical instability.



2

SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Linear interpolation (method of false position) – Newton’s method  Statement of fixed point theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian elimination and GaussJordon method – Iterative methods: Gauss Jacobi and GaussSeidel methods – Inverse of matrix by Gauss Jordon method – Eigen value of matrix by power method



3

INTERPOLATION AND APPROXIMATION
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward difference formulas.



4

NUMERICAL DIFFERENTION AND INTEGRATION
Derivatives from difference tables – Divided differences and finite differences – numerical integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpson’s rules



5

INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERINTIAL EQUATIONS
Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order RungeKutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods.



6

INTRODUCTION TO STATISCTICAL PARAMETERS
Significant figures, scientific notations, average Mean, Mode, Median, geometric mean, harmonic mean, rootmeansquare and rootsumsquares average, Logarithmic representation of signal levels, Data classes, Variation – Gaussian curve, standard deviation, variance



7

PROBABILITY AND PROBABILITY DISTRIBUTIONS
Introduction to probability; Random Experiments, Sample Space, Events and their probabilities; Some basic results of probability, Conditional probability, Random variables: Probability distributions; Expected value & variance of a probability distribution; Discrete probability distributions: Binomial, Poisson. Continuous probability distributions: Exponential, Normal.



8

SAMPLING, SAMPLING DISTRIBUTION & INTERVAL ESTIMATION
Simple random sampling, point estimation, introduction to sampling distributions, sampling distributions of
, Sampling distribution of sample proportion
, Properties of point estimation, Other sampling methods, Interval estimation: Population mean: σ known, σ unknown, Determining the sample size. Sampling distribution of variance.



9

STATISTICAL INFERENCES, TESTING OF
Introduction, Test of significance for large samples: Difference between small & large samples, Twotailed test for difference between the means of two samples, Standard error of the difference between two standard deviations, Test of significance for small samples: The assumption of normality, Students’distribution; properties and application of tdistribution, testing difference between means of two samples (Independent samples; Dependent samples) Definition of chisquare, degrees of freedom; chisquare distribution, Conditions for applying chisquare test, Uses of chisquare test, Misuse of chisquare test.



10

NETWORK ANALYSIS
Network definition, Minimal spanning tree problem, Shortest route problem, Maximum flow problem concepts and solution algorithm as applied to problems. Project planning and control by CPM network, Probability assessment in PERT network.
PROJECT MANAGEMENT AND SCHEDULING
Project management (CPM & PERT)
Network concepts, components, rules for network construction, critical path method (CPM) and Project
evaluation and review Techniques (PERT)


