Dr. Sathish Kumar A. >>Subject -III

MAL205                     Numerical Methods  & Probability Theory                       3-0-0-6

 

Numerical Analysis:  Solutions of algebraic and transcendental equations by Iteration method,  method of false position, Newton-Raphson method and their convergence.

Solutions of system of linear equations by Gauss elimination method, Gauss Seidal method, LU decomposition method.  Newton-Raphson method for system of nonlinear equations.

Eigen values and eigen vectors :  Power and Jacobi methods.

Numerical solution of ordinary differential equations: Taylor’s series method, Euler’s modified method, Runge-Kutta method, Adam’s Bashforth and Adam’s Moulton, Milne’s predictor corrector method.

Boundary value problems: Shooting method, finite difference methods.

Probability theory: 

Random variables, discrete and continuous random variable, probability density function; probability distribution function for discrete and continuous random variable joint  distributions.

Definition of mathematical expectation, functions of random variables, The variance and standard deviations, moment generating function other measures of central tendency and dispersion, Skewness and Kurtosis.

Binomial, Geometric distribution, Poisson distribution, Relation between Binomial and Poisson’s distribution, Normal distribution, Relation between Binomial and Normal distribution.

Random processes, continuous and discrete, determinism, stationarity, ergodicity etc. correlation functions, autocorrelation and cross-correlation, properties and applications of correlation functions.

 

Text Books:

  1. Jain, Iyengar and Jain : Numerical Methods  for  Engineers and Scientists,   Wiley Eastern,1995
  2. V.K. Rohatgi and A.K.M. Ehsanes Sateh: An Introduction to Probabability and Statistics, John Wiley & Sons.

Reference Books

  1. S. D. Cante and C. de Boor, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.
  2. Gerald and Wheatley : Applied Numerical Analysis,   Addison-Wesley, 1999.
  3. Spiegel, M.R.; Theory and problems of Probability and statistics; McGraw-Hill Book Company; 1980.
  4. K.S. Trivedi: Probability Statistics with Reliability, Queuing and Computer Science applications, Prentice Hall of India Pvt. Ltd, 2000.