Complex variables: Analytic functions; CauchyRiemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series. 
Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median,mode and standard deviation; random variables, binomial, Poisson and normal distributions 
Numerical Methods: Numerical solutions of linear and nonlinear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multistep methods for differential equations. 

Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard
Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution,
Binomial distribution, Correlation analysis, Regression analysis. 
Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss, Green and Stokes theorems. 
Calculus: Functions of single variable; Limit, continuity and differentiability; Mean value theorems, local maxima and minima; Taylor series; Evaluation of definite and indefinite integrals, application of definite integral
to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities;
Directional derivatives; Line, Surface and Volume integrals. 
Ordinary Differential Equation (ODE): First order (linear and nonlinear) equations; higher order linear equations with constant coefficients; EulerCauchy equations; initial and boundary value problems.Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of one dimensional diffusion equation; first and second order onedimensional wave equation and twodimensional Laplace equation. 
Probability and Statistics: Sampling theorems; Conditional probability; Descriptive statistics  Mean, median, mode and standard deviation; Random Variables – Discrete and Continuous, Poisson and Normal Distribution;Linear regression. 
Numerical Methods: Error analysis. Numerical solutions of linear and nonlinear algebraic equations; Newton
and Lagrange polynomials; numerical differentiation; Integration by trapezoidal and Simpson’s rule; Single and multistep methods for first order differential equations. 

