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21MATME41 – M4 VTU Notes for ME & Allied Engineering Branches

Complex Analysis, Probability and Linear Programming (21MATME41)

Subject code

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.

Textbooks Prescribed by VTU

1. Advanced Engineering Mathematics, E. Kreyszig: John Wiley & Sons, 10th Ed. (Reprint), 2016.

2) Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44th Edition, 2017

3) S.D. Sharma: "Operations Research" Kedarnath Publishers Ed. 2012

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