PROBABILITY AND RANDOM VARIABLES
Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Exponential and Normal distributions.
Sampling distributions – Statistical hypothesis – Tests for single mean, proportion, Difference of means (large and small samples) – Tests for single variance and equality of variances – Chi square test for goodness of fit.
Newton Raphson method –Pivoting Gauss Jordan methods – Iterative methods of Gauss-Seidal – Matrix Inversion by Gauss-Jordan method.
INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL INTEGRATION
Lagrange’s interpolation – Newton’s forward and backward difference interpolation – Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal and Simpson’s 1/3rd rules.
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Single step methods: Taylor’s series method – Euler’s method – Modified Euler’s Method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods: Milne’s predictor-corrector methods for solving first order equations.
Reference Book:
Johnson, R.A., Miller, I and Freund, J., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 8th Edition, 2015.
Walpole, R.E., Myers, R.H., Myers, S.L. and Ye. K., “Probability and Statistics for Engineers and Scientists”, Pearson Education, Asia, 8th Edition, 2007.
Kandasamy, P., Thilagavathy. K and Gunavathy, K., "Numerical Methods", 3rd Edition, S.Chand& Company Pvt. Ltd, 2013.
Gerald, C.F. and Wheatley, P.O. “Applied Numerical Analysis”, 8th Edition, Pearson Education, Asia, New Delhi, 2014.
Chapra, S.C and Canale, R.P. “Numerical Methods for Engineers”, 6th Edition, Tata McGraw Hill Edition, 2014.
Text Book:
Milton, J. S. and Arnold, J.C., "Introduction to Probability and Statistics", Tata McGraw Hill, 4th Edition, 2007.
Grewal, B.S and Grewal, J.S, “Numerical methods in Engineering and Science”, 9th Edition, Khanna Publishers, New Delhi, 2012.
