MCA-204 Computer Oriented Numerical & Statistical Methods Course Contents:
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 (Striplings) and divided difference formulas, lagrangie’s interpolation, Inverse interpolation for equal and unequal intervals.
Numerical Integration : Newton Cote’s formula, Simpson’s 1/3rd and 3/8th 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, 2 distribution, Rectangular distribution, hypergeometric distribution.
Hypothesis testing for sampling: Small samples, t, z and f tests. Chi-square test.
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”.
1. Iyengyr 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.