University of Madras - Syllabus of Bachelor of Computer Applications (BCA) IInd Year - Semester III - BCA211 - Numerical and Statistical Methods

UNIVERSITY OF MADRAS

Bachelor in Computer Applications (BCA)

SEMESTER SYSTEM WITH CREDITS

(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - BCA211 - Numerical and Statistical Methods

Lecturer/Lab Hours per Week: 6

Duration: 3 hrs

Max Makrs: 100

Credit: 4

Unit - I

Roots of Equations: Graphical Method -Bisection Method - False-Position Method - Fixed-Point
Iteration - Newton-Raphson Method Secant Method - Roots of Polynomials: Conventional Methods - Muller’s Method - Bairstow’s Method. Algebraic Equations: Gauss Elimination -Gauss-Jordan - LU
Decomposition - Matrix Inverse -Gauss-Seidel.

Unit - II

Numerical Differentiation - Integration: Trapezoidal Rule - Simpson’s Rule - Romberg Integration
- Differential equations: Taylor’s method - Euler’s method -Runge-Kutta 2^{nd} and 4^{th} order methods Predictor - corrector methods.

Unit - III

Diagrammatic and Graphical representation of Numerical Data - Formation of frequency distribution - Histogram, Cumulative Frequency - Polygon and Ogives - Measures of central tendencies - Mean, Median, Mode - Measures of dispersion - Mean deviation, Standard deviation, variance, Quartile deviation and coefficient of variation - Moments (upto 4th) - Measures of Skewness and Kurtosis for grouped and ungrouped data.

Unit - IV

Sample space - Events - Definition of probability - combinatorial problems - conditional probability and independence - Random variables, distributions and Mathematical expectations - Discrete distributions - Binomial - Poisson - Continuous distributions - Normal and Exponential distributions - Moments and Moment generating functions.

Unit - V

Correlation and Regression analysis: product moment correlation -coefficient - rank correlation coefficient - simple regression - method of least squares for estimation of regression coefficient. Concept of sampling and Sampling distributions - Sampling from Normal distributions - Standard error - Tests of significance - Large sample test for population mean and proportions - Test for populations means: single - two sample and paired t - test - Chi square tests for goodness of fit and test for independence of attributes in contingency table.

Books for Study and Reference:

1. Snedecor G.W. and Cochran W.G. (1989): Statistical methods, 8 ed., Affiliated East West.

2. Trivedi K.S. (1994): Probability and Statistics with Reliability, Queueing and computer Science applications, Prentice Hall of India.

3. Balaguruswamy E. (1988): Computer oriented Statistical and Numerical methods, Macmillan India Ltd.

4. S. C. Chopra and R. P.Canale - Numerical Methods for Engineers - Third Edition - McGraw Hill International Edition - 1998.

5. S. S. Sastri, Introductory Methods of Numerical Analysis, Prentice Hall