6 ME 6-NUMERICAL METHODS AND APPLIED STATISTICS |
Units: I |
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,
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Units: II |
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, |
Units: III |
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).
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Units: IV |
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.
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Units: V |
Tests of Significance; t-distributions, chi square distributions, F-distributions.
Regression And Correlation; Linear regression; correlation, multiple correlation & partial
correlation Confidence Limits; Large samples, small samples, error bands in regression
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