UNIT I

Functions of Complex Variables:Analytic functions, Harmonic Conjugate, Cauchy -Riemann Equations, Line integral, Cauchy's theorem, Cauchy's Integral formula, Singular points, Poles and Residues, Residue theorem, Evaluation of Real Integral, Bilinear Transformation.

Numerical Analysis:Difference operators, Errors and Approximations, Interpolation, Inverse interpolation, Numerical differentiation, Numerical Integration by using Simpson’s method, Weddel’srule and Gauss legendre open quadrate formula.

Solutions of algebraic and transcendental equations:Regular False,Newton-Raphson Iterative, Graffe’s root squaring methods), Solutions of simultaneous algebraic equations, Solutions of ordinary differential equations ( Tailor’s Series, Picard’s Method, Modified Euler’s method, RungeKutta Method, Predictor-Corrector Method), Solution of Partial differential equation.

Introduction to optimization by linear programming:only two variable problems solution by graphical and simplex method, concept of degeneracy and duality; simple three variable transport and assignment problems and modeling into LPP.

introduction to Q theory and Markovian process:time independent property of exponential distribution, solution of only M/M/1 (∞/∞/FCFS) Queues; introduction to design of experiments,factorial design, sampling methods, Taguchi Loss Function, robust design methods, variance reduction and six (±3)σ outliers in quality.