Complex Analysis, Probability and Linear Programming (21MATME41)
Module - 1
Calculus of complex functions: Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences. Applications to flow problems
Construction of analytic functions: Milne-Thomson method-Problems.
Module - 2
Conformal transformations: Introduction. Discussion of transformations Bilinear transformations- Problems.
Complex integration: Line integral of a complex function- Cauchy’s theorem and Cauchy’s integral formula and problems.
Module - 3
Probability Distributions: Review of basic probability theory. Random variables (discrete and continuous), probability mass/density functions. Mean- Variance and Standard Deviations of a random variable. Binomial, Poison, exponential and normal distributions- problems. (8 hours)
Module - 4
Linear Programming Problems (L.P.P): General Linear programming Problem, Canonical and standard forms of L.P.P. Basic solution, Basic feasible solution, Optimal solution, Simplex Method-Problems. Artificial variables, Big-M method, Two-Phase method-Problems. (8 hours)
Module - 5
Transportation and Assignment Problems: Formulation of transportation problems, Methods of finding initial basic feasible solutions by North-West corner method, Least cost method, Vogel approximation method. Optimal solutions-Problems. Formulation of assignment problems, Hungarian method-Problems.