Rank of the matrix, Echelon form, Linearly dependent and independent equations, Solutions for linear equations, Gauss Seidel method, Partition method, Croute's Triangularisation method. Jacobi method,Eigen Values, Eigen Vectors, Bounds on Eigen Values, Given‟s method for symmetric matrices
Simple fixed point iteration methods. Newton Rapson method, Secant Method, Muller‟s method, Graeffe‟s Roots Squaring Method. Aitkin‟s Method, Linear Programming: Simplex method, Sensitivity analysis.
Solution of Ordinary differential equations:
Euler's method, Euler's modified method, and Ranga Kutta 3rd and 4th order method, Taylor‟s series method, Milne‟s Predictor-corrector method.
Solutions for Integral Equations:,
Trapezoidal rule, Simpson‟s 1/3rd and 3/8th rule, and Weddle‟s Rule. Least square approximation, Lagrange Interpolations
Conditional Probability, Random variables and expectations, Binomial Distributions, Poisson Distribution, Normal Distribution, Uniform distribution, Exponential distribution, Joint distribution. Expectation; Inequalities; Convergence of random variables.
Hypothesis testing and p -values; Bayesian inference; Statistical decision theory, Density curves, ANOVA, Sampling, Designing of Experiments (Inference for the Mean of a Population, Sample Proportions, Inference for a Population, Proportion Comparing, Two Means, Comparing Two Proportions, Goodness of Fit Test Two way Tables.