Ordinary and Partial Differential Equations
Simultaneous first order linear equations with constant coefficients – linear equations of second order with constant and variable coefficients – Formation of partial differential equations – Classification of second order partial differential equations
Solution of Systems of Linear Equations:
Partition method, Croute’s Triangularisation method. Eigen values and Eigen vectors. Bounds on Eigen Values. Jacobi method for symmetric matrices.
Ortoganality and Least Squarers
Orthogonal vectors, orthogonal bases, orthonormal sets, orthogonal projection, QR factorization. Gram-Schmidt orthogonalization process and Applications to linear models- Least squares lines.
Probability Theory
Probability: Random variables, Probability distributions: Binomial, Poisson, Normal distributions, Joint probability distribution (discrete)- examples.
Sampling Theory
Sampling distributions - Tests based on t-distribution, chi-square and F-distributions - Analysis of variance - One-way and two-way classifications.