Numerical Methods:
Partial differential equation, Newton Raphson Method, Finite Difference, Finite element, method of characteristics, different methods, successive over relaxation method.
Optimization:
Classification and Importance in Environmental studies. Single and multivariable optimization without and with constraints.
Linear Programming:
Different methods, linear approximation of non-linear optimization.
Statistics:
Significance test, Frequency distribution, characteristics of distribution, Method of least squares and regression, Multiple regression.
Applied Partial Differential Equations:
Classification of second order partial differential equations, Canonical forms - Hyperbolic, Parabolic, Elliptical Equations.
Laplace Transform Method:
Transforms of derivatives, Differential equations and simultaneous equations. Transform of Dirac Delta function, Inverse Transform - examples.
Fourier Transform Method:
Properties of Fourier Transforms, Sine and Cosine Fourier Transforms.
Probability Theory:
Review of basic probability theory. Definition of random variables and probability distribution, Probability mass and density function, expaction, moments, central moments, characteristic functions, probability generating and moment generating functions - illustrations. Binomial, Poisson, Exponential, Gaussian and Rayleigh distribution examples.
Joint Probability Distribution:
Definition and properties of CDF, PDF, PMF, conditional distributions. Expection, covariance and Correlation. Independent Random variables, statement of central limit theorem - illustrative examples. Random Process: Classification, stationary and ergodic random process. Auto correlation function properties, Gaussian random process.