NUMERICAL METHODS AND OPERATION RESEARCH TECHNIQUES
UNIT I: Error Analysis, absolute, relative and percentage errors. A general error formula and error in series approximation, Solution of Nonlinear and polynomial equations: Bisection Method, False Position method, secant, Newton Raphson methods.
UNIT II: Solution of Linear Systems of Equation: Gauss elimination method, Gauss Jordon Method, Gauss Seidel Iterative Method, Gaussian elimination, Matrix Inversion Method, LU factorization method. Regression, Curve fitting: Least Square Method, Correlations.
UNIT III: Integration and Differential equations: Numerical Integration- Trapezoidal, Simpson’s one third and three eight rules, Romberg’s Method. Newton’s forward and backward interpolation formula. Numerical differentiation: Maximum and minimum values. Lagrange’s Interpolation Method, Euler’s method, Runge-Kutta methods, Predictor Corrector method, Taylor Series.
UNIT IV: Operations Research Models and Dynamic Programming: Operations research models- classification of problems, phases of operation research, scope and limitation of operations research. Dynamic programming: Investment problem Stagecoach Problem, Equipment Replacement problem, conversion of final value problem into an initial value problems.
UNIT V: Linear Programming and Sequencing: Linear programming – Concept of Linear Programming, simplex method, Big-M Method, Two Phase Simplex Method, concept of duality, transportation problems, Assignment Problem, Hungarian Method. Sequencing Problem: Two-Machine, N- Jobs, and Three Machine Problem.
UNIT VI: PERT and CPM: Pert Networks, ET, TE, TL, SE and Critical path, Probability of completion. Decision theory: Introduction, Minimax decision procedure, Bayes decision procedure with and without data, Regret function Vs. Loss function.