Syllabus of Madhya Pradesh Bhoj Open University MSc(CS) - MCS07 Numerical Methods and Statistical Analysis

Madhya Pradesh Bhoj (Open) University
M.Sc. CS (Previous Year)
Syllabus for the Session 2004-05

Unit – I

Introduction: Limitation of Number Representation, Arithmetic rules for Floating Point Numbers, Errors in Numbers, Measurement of Errors

Solving Equations: Introduction, Bisection Method, Regula Falsi Method, Secant Method, Convergence of the iterative methods.

Unit – II

Interpolation: Introduction, Lagrange Interpolation, Finite Differences, Truncation Error in Interpolation

Curve Fitting: Introduction, Linear Regression, Polynomial Regression, Fitting Exponential and Trigonometric Functions

Unit – III

Numerical Differentiation and Integration: Introduction, Numerical Differentiation Formulae, Numerical Integration Formulae, Simpson's Rule, Errors in Integration Formulae, Gaussian Quadrature Formulae, Comparison of Integration Formulae

Solving Numerical Differential Equations: Introduction, Euler's Method, Taylor Series Method, Runge-Kutta Method, Higher Order Differential Equations.

Unit – IV

Introduction to Statistical Computation: History of Statistics, Meaning and scope of Statistics, Various measures of Average, Median, Mode, Geometric Mean, Harmonic Mean, Measures of Dispersion, Range, Standard Deviation

Probability Distributions: Introduction, Counting Techniques, Probability, Axiomatic or Modern Approach to Probability, Theorems on Probability, Probability Distribution of a Random Variable, Mean and Variance of a Random Variable, Standard Probability Distributions, Binomial Distribution, Hyper geometric Distribution Geometrical Distribution, Uniform Distribution (Discrete Random Variable), Poisson Distribution, Exponential Distribution, Uniform Distribution (Continuous Variable), Normal Distribution

Unit – V

Estimation: Sampling Theory, Parameter and Statistic, Sampling Distribution of Sample Mean, Sampling Distribution of the Number of Successes, The Student's Distribution, Theory of Estimation, Point Estimation, Interval Estimation

Hypothesis Testing: Test of Hypothesis, Test of Hypothesis Concerning Mean, Test of Hypothesis Concerning Proportion, Test of Hypothesis Concerning Standard Deviation