Statistics (Theory of Estimation and Testing of Hypothesis) Sampling Distributions: Distributions of Sampling Statistics, Chi-square, t and F distributions (only definitions and use). Central Limit Theorem.

Theory of estimation: Point Estimation, Unbiased estimator- Maximum Likelihood Estimator- Interval Estimation.

Testing of Hypothesis: Large and small sample tests for mean and variance – Tests based on Chi-square distribution. Probability Theory

Probability Concepts: Review of probability concepts – Bayes’ Theorem.

Random Variable and Distributions: Introduction to random variable – discrete and continuous distribution functions- mathematical expectations – moment generating functions and characteristic functions. Binomial, Poisson, Geometric, Uniform, Exponential, Normal distribution functions (MGF, mean, variance and simple problems) – Chebyshev’s theorem

Two dimensional Random variables: Discrete and continuous random variables – stochastic independence of random variables – Transformation of random variables (functions of one and two random variables)- Correlation and Regression.

Numerical Methods for PDE: Elliptic, Parabolic and Hyperbolic Partial differential equations, Neumann method for irregular boundary