MCA-204 COMPUTER ORIENTED NUMERICAL AND STATISTICAL METHODS SYLLABUS

RAJIV GANDHI PROUDYOGIKI VISHWAVIDYALAYA

  (University of Technology of Madhya Pradesh)

COURSE OF STUDY AND SCHEME OF EXAMINATION

MASTER OF COMPUTER APPLICATIONS (MCA)

W.E.F. 2005-2006

MCA-204 COMPUTER ORIENTED NUMERICAL AND STATISTICAL METHODS SYLLABUS

 

UNIT – I

Numerical approximation, Representation of integers and real numbers in computers, fixed and floating point arithmetic, normalized floating point numbers, Round off and truncation errors, relative and absolute errors. Iterative methods: Zeros of single transcendental equations and zeros of polynomials using bisections, false position, Newton Raphson methods.  Convergence of solutions.

Unit – II

Interpolation : Forward, Backward, central (Stirlings) and divided difference formulas, lagrangie’s interpolation, Inverse interpolation for equal and unequal intervals.

Numerical Integration : Newton cote’s formula, simpson’s 1/3^rd   and 3/8^th rule. Gauss legendre (two and three points)  integration formula.

Unit – III

Simultaneous linear equations: Solutions of simultaneous linear equations – Gauss elimination method and pivoting, ill conditioned equations and refinement of solutions, Gauss-seidal iterative methods.

Solution of differential equation: Runge-Kutta fourth order method. Euler’s method, Picard’s, Taylor’s series.

 

Unit - IV

Distributions : Binomial distribution, Poisson distribution and normal distribution, c² distribution,  Rectangular distribution, hypergeometric distribution.

Unit -V

Hypothesis testing for sampling: Small samples, t, z and f tests. Chi-square test.

Large samples : Comparision of large samples, testing the significance of the difference between the means of two large samples.

BOOKS

1.      E. Balaguruswamy  “Numerical Methods” , TMH, ISBN – 07-463311-2, 1999.

2.      B.S. Grewal  “Numerical Methods in Engineering & Science”.

3.      Miller “Mathematical Statistics with applications” 7 ed, Pearson.

4.      Gupta & Kapoor, Introduction to Statistics, Chand & Co.

5.      V. Rajaraman “Computer Oriented Numerical Methods”.

6.      M.Ray and Har Swarup Sharma “ Mathematical Statistics”.

REFERENCE BOOKS

1.      Iyenoyr M.K. Jain & R.K. Jain  “Numerical Methods for scientific and engineering computation”, Wiley Eastern (New Age), 1995

2.      E.V. Krishnamurthy & S.K. Sen  “Computer Based Numerical Algorithms”.

3.      Miller & Freund’s “Probability and Statistics for Engineers”.

Note : Paper is to be set unit wise with internal choice & emphasis is to be given on computerized implementation.