# Numerical Techniques and Statistical Methods (2141703)

Syllabus

Sr. Topics Teaching Hours Module Weightage
1
ERROR ANALYSIS:

Round-off errors and truncation errors in numerical computation, error propagation, and numerical instability.

2
4 %
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 Gauss-Jordon method – Iterative methods: Gauss Jacobi and Gauss-Seidel methods – Inverse of matrix by Gauss Jordon method – Eigen value of matrix by power method

5
10 %
3
INTERPOLATION AND APPROXIMATION

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

5
12 %
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
12 %
5
INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERINTIAL EQUATIONS

Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order Runge-Kutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods.

5
12 %
6
INTRODUCTION TO STATISCTICAL PARAMETERS

Significant figures, scientific notations, average- Mean, Mode, Median, geometric mean, harmonic mean, root-mean-square and root-sum-squares average, Logarithmic representation of signal levels, Data classes, Variation – Gaussian curve, standard deviation, variance

2
4 %
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.

6
12 %
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.

6
10 %
9
STATISTICAL INFERENCES, TESTING OF

Introduction, Test of significance for large samples: Difference between small & large samples, Two-tailed 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 t-distribution, testing difference between means of two samples (Independent samples; Dependent samples) Definition of chi-square, degrees of freedom; chi-square distribution, Conditions for applying chi-square test, Uses of chi-square test, Misuse of chi-square test.

8
14 %
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)

4
10 %