#### Syllabus

1. Data, its Arrangements and Measures:

Introduction: Data, Data Array; Frequency Distribution Construction and Graphic representation. Mean,

median, mode and standard deviation.

2. Probability and Probability Distributions:

Introduction: Definition probability and Probability Distribution; Conditional probability; Random

variables, Poisson, Normal and Binomial distributions.

3. Sampling and Sampling Distributions:

Introduction: Fundamentals of Sampling, Large samples, small samples; Normal sampling distributions;

Sampling distribution of the means, t-Distribution, F-Distribution, Chi-square Distribution.

4. Errors in Numerical Calculations:

Errors and their analysis, general error formula, errors in a series approximation

5. Solution of Algebraic and Transcendental Equations:

Bisection method, iteration method, Method of false position,, Newton -Raphson method, solution of

systems of non linear equations.

6. Interpolation Method:

Finite difference, forward, backward and central difference, Difference of polynomial, Newton’s

formulae for interpolation, central difference interpolation formulae, Interpolation with unevenly spaced

points, Newton's general interpolation formula, interpolation by iteration.

7. Numerical Differentiation and Integration:

Numerical differentiation, maximum and minimum values of a tabulated function; Numerical Integrationtrapezoidal

rule, Simpson1/3 rule, Simpsons 3/8 rule, Newton-cots integration formulae; Euler-Meclaurin

formula, Gaussian integration(One dimensional only)

8. Solution of Linear Systems of Equations:

Gauss Elimination method (fall and banded symmetric and unsymmetric systems), Gauss Jordon method.

Eigen value problems (Power method only).

9. Numerical solution of ordinary and partial differential equations:

Solution by Taylor's series, Prediction -correction method, Boundary value problems, Prediction corrector

method, Euler's and modified Euler's method, Runge-Kutta method, finite difference methods. Finite

difference approximation to derivatives, Solution to Laplaces equation- Jacobi's method, Gauss -Siedel

method.