6 ME 6: NUMERICAL METHODS AND APPLIED STATISTICS
3 L + 0T MM 100 Ex. Hrs: 3
Unit 1

Errors and significant digits, Roots of algebraic equations Bisection method, secant method, Newton Raphson method, Graff’s root- squaring method, Iterated synthetic division with quadratic factors method for finding complex roots.
Unit 2

Solutions of systems of equations (Gauss elimination, Gauss Jordan and Partition method for linear system of equations, power method for partition, method for linear system of equations, power method for finding Eigen values), Forward, backward , central and Divided differences, Newton’s formula of interpolation for equal and unequal intervals. Lagrange’s interpolation formula, Stirling’s and Bessell’s formula,
Unit 3

Numerical Differentiation, Numerical Integration: Trapezoidal, Simpson’s rule and Gaussian integration (only formula applications) Differential equations and their solutions, Numerical methods for ordinary differential equations (Picard method, Taylor series method, Euler’s method, Ranga Kutta Method, Predictor- corrector method, Adams- Bashforth method).
Unit 4

Sampling Theory: Introduction, Moments, Moment generating functions, Skewness, Kurtosis, Correlation and Regression, Normal sampling distributions, Binomial distribution, Poisson distribution, Normal distribution, Sampling distribution of the means, sampling distribution of the differences of the means, sampling distributions of proportions.
Unit 5

Tests of Significance: t-distributions, chi square distributions, F-distributions. Regression And Correlation, Linear regression, correlation, multiple correlation and partial correlation Confidence Limits, Large samples, small samples, error bands in regression.
List of Recommended Books:
1. Introductory Methods of Numerical Analysis, Sastry S.S., Prentice Hall India
2. Numerical Methods for Engineering and Scientific Computation, Jain and Jain, New Age International Pvt.
Ltd. New Delhi.
3. Engineering Statistics, Bowker, A.H. and Liberman G.J., Prentice Hall.
4. Probability and Statics in Engineering, Hines, John Willey and Sons.
5. Applied Statistics and Probability for Engineers, Montgomery, John Wiley and Sons.