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 (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
2 distribution,cDistributions
: Binomial distribution, Poisson distribution and normal 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. 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”.
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