Complex variable, function of complex variable, limit, continuity, and differentiability of a function of a complex variable. Analytic functions, Cauchy - Riemann equations, Orthogonal curves, harmonic functions, conformal mapping, bilinear transformation (Mobius transformation), Cauchy integral theorem, Caucy integral formula, Cauchy’s inequality Taylor theorem, Laurent’s theorem.

Periodic function, Fourier series, Dirichlet’s conditions for a Fourier series. Advantages of Fourier series and determination of Fourier coefficients, Fourier series of function of periods 2, change of interval, Even Odd functions, half range sine and cosine series, practical harmonic analysis, Fourier transformation, Fourier sine and cosine transform, properties of Fourier transform.

Laplace transformation, properties of Laplace transformation, first shift theorem, Laplace transform of the derivative of f(t), multiplication and division by t. Unit step function, Laplace transformation of unit function, second shifting theorem, Laplace transform of function and periodic function. Inverse Laplace transformation Multiplication by s, division by s, first shifting property, second shifting property, inverse Laplace transform of derivatives, solution of differencial equations by Laplace transform.

Scatter diagram, Linear Correlation, Measures of Correlation. Karl Pearson’s Coefficient of correlation, Limits for correlation coefficients, Coefficient of correlation for bivariate frequency distribution, Rank correlation, Linear Regression, Equations to the line of Regression. Regression coefficient. Angle between two lines of Regression.

Discrete and Continuous probability distribution’s. Mathematical expectation, Mean and Variance, Moments, Moments generating function, probability distribution, Binomial, Poisson and Normal distribution, Test of significance sassed on chi-square, T, F, and Z distribution degree of freedom, conditions for applying X2 test, student’s test.