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:
1.Johnson, R.A., Miller, I and Freund, J., “Miller and Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 8th Edition, 2015. (UNIT-I, II)
2. 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. (UNIT-I, II)
3. Kandasamy, P., Thilagavathy. K and Gunavathy, K., "Numerical Methods", 3rd Edition, S.Chand& Company Pvt. Ltd, 2013.(UNIT-III, IV, V).
4. Gerald, C.F. and Wheatley, P.O. “Applied Numerical Analysis”, 8th Edition, Pearson Education, Asia, New Delhi, 2014 (UNIT-III, IV, V)
5.Chapra, S.C and Canale, R.P. “Numerical Methods for Engineers”, 6th Edition, Tata McGraw Hill Edition, 2014 (UNIT-III,IV,V)
Text Book:
1.Milton, J. S. and Arnold, J.C., "Introduction to Probability and Statistics", Tata McGraw Hill, 4th Edition, 2007. (UNIT-I, II)
2. Grewal, B.S and Grewal, J.S, “Numerical methods in Engineering and Science”, 9th Edition, Khanna Publishers, New Delhi, 2012 (UNIT-III,IV,V)
