UNIT-I : Function of Complex Variable
Analytic function, C-R equations, Harmonic Functions, Cauchy's integtal theorem, Cauchy's integral formula, Derivatives of analytic functions, Taylor's and Laurent's series, Singularities, Zeroes and Poles, Residue theorem, Evaluation of real integrals of the type and .
UNIT-II : Statistical Techniques
Moments, Moment generating functions, Skewness, Kurtosis, Curve fitting, Method of least squares, Fitting of straight lines, Polynomials, Exponential curves, Correlation, Linear, non-linear and multiple regression analysis, Binomial, Poisson and Normal distributions, Tests of significations : Chi-square test, t-test.
UNIT-III : Numerical Techniques-I
Zeroes of transcendental and polynomial equations using Bisection method, Regula-falsi method and Newton-Raphson method, Rate of convergence of above methods. Interpolation : Finite differences, Newton's forward and backward interpolation, Lagrange's and Newton's divided difference formula for unequal intervals.
UNIT-IV : Numerical Techniques-II
Solution of system of linear equations, Matrix Decomposition methods, Jacobi method, Gauss - Seidel method. Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson's one third and three-eight rules, Solution of ordinary differential equations (first order, second order and simultaneous) by Euler's, Picard's and fourth-order Runge- Kutta methods.
UNIT-V : [This unit contains two parts. Students have to read only one part of this unit as question paper will contain questions from both the parts with choice.]
Numerical Techniques-III : Boundary Value Problem, Finite Difference Method, Eigen Value'Problems, Condition Number, Polynomial Method, Power Method, Numerical solution of partial differential equations, Elliptic, parabolic and Hyperbolic equations.
Integral Transforms : Fourier integral, Complex Fourier transform, Inverse Transforms, Convolution Theorems, Fourier sine and cosine transform, Applications of Fourier transform to simple one dimensional heat transfer equations, wave equations and Laplace equations, Z- transform and its application to solve difference equations.