Complex Variable

Complex number system, General functions of a complex variable, Limits and continuity of a function of complex variable and related theorems, Analytic functions, Complex differentiation, Sufficient condition for analyticity and Cauchy Riemann equations, Harmonic functions and conjugate harmonic functions, Construction of analytic functions when either part is given (Milne-Thomson method), Different types singularities, Line integral of a complex function, Cauchy’s integral theorem and converse of Cauchy’s theorem.

Vector Analysis

Transformation of vectors on a plane: Scaling, Rotation, Translation, Linear dependence and independence of vectors, Scalar and vector fields, Differentiation of vectors together with elementary applications, Gradient, Divergence and curl of point functions and related forms, Green’s, Stokes’ and Gauss’ theorem and their applications.

Statistics

Moment, Skewness and kurtosis, Random variables, Probability mass functions and probability density functions.

Expectation

Expected value and variance with their properties.

Discrete Probability Distributions

The Bernoulli and Poisson process, Binomial and Poisson probabilities, Distribution and properties.

Continuous Probability Distributions

Normal variate and normal distribution, Properties of normal distribution, Standard normal variate and standard normal distribution, Properties of standard normal distribution, Uniform distribution and it’s properties.
Complex variable, Vector Analysis and Statistics