UMA032 NUMERICAL AND STATISTICAL METHODS
Numerical Methods (60% Weightage).
Floating-Point Numbers: Floating-point representation, Rounding, Chopping, Error analysis, Condition and instability.
Bisection, Secant, Fixed-point iteration and Newton-Raphson methods, Order of
Linear Systems and Eigen-Values: Gauss-elimination method (using Pivoting strategies) and Gauss-Seidel Iteration method. Rayleigh’s power method for eigen-values and eigen-vectors.
Interpolation: Finite differences, Newton’s Forward and Stirling interpolating polynomials, Lagrange and Newton’s divided difference interpolation formula with error analysis.
Numerical Integration: Newton-Cotes quadrature formulae (with error) and Gauss - Legendre quadrature formulae.
Differential Equations: Solution of initial value problems using Taylor Series, Euler’s and Runge-Kutta (up to fourth order) methods.
Statistical Methods (40% Weightage)
Random Variables: Definition, Distribution Function, Discrete and Continuous Random Variables, Probability functions, Cummulative distributions functions, Mathematical expectation.
Probability Distributions: Binomial, Poisson, Geometric, Uniform, Normal, Exponential and Log- Normal distribution.
Sampling Distributions: Sampling distribution of Means and variance, Chi-Square distribution, t - distribution and F - distribution.
Hypothesis Testing: General concepts, Testing a Statistical Hypothesis, one and two tailed tests, Critical region, Confidence interval estimation. Single and two sample tests on proportion, mean and variance.
Linear Regression and Correlation: Linear Regression, Least Square principal and the Fitted models, Karl Pearson’s Correlation Coefficient, Rank Correlation, Lines of Regression (two variables only).
Programming exercises on numerical and Statitical methods using C or C++ languages.