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UNIT-II: Transportation and Assignment Problems (15 Hours)

Definition of transportation problem, finding initial basic feasible solution using Northwest corner
method, Least-cost method, and Vogel approximation method; Algorithm for solving
transportation problem; Hungarian method of solving assignment problem.

UNIT-III: Two-Person Zero-Sum Games (12 Hours)
Introduction to game theory, rectangular games, Mixed strategies, Dominance principle;
Formulation of game to primal and dual linear programming problems.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

1. Thie, Paul R., & Keough, G. E. (2014). An Introduction to Linear Programming andGame
Theory. (3rd ed.). Wiley India Pvt. Ltd.
2. Taha, Hamdy A. (2017). Operations Research: An Introduction (10th ed.). Pearson.
3. Hadley, G. (1997). Linear Programming. Narosa Publishing House. New Delhi.
4. Hillier, F. S., & Lieberman, G. J. (2021). Introduction to Operations Research (11th
ed.)McGraw-Hill Education (India) Pvt. Ltd.

Math.323 Complex Analysis 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is:
 To study the techniques of complex variables and functions together with their derivatives,
Contour integration and transformations.
 To study complex power series, classification of singularities, calculus of residues and its
applications in the evaluation of integrals, and other concepts and properties.

LEARNING OUTCOMES:

This course will enable the students to: S
 Understands the fundamental concepts of complex variable theory and skill of contour
integration to evaluate complicated real integrals via residue calculus.
 Apply problem-solving using complex analysis techniques applied to diverse situations in
physics, engineering, and other mathematical contexts.

THEORY (45 Hours)

UNIT I (15 Hours)

Limits, Limits involving the point at infinity, continuity. Properties of complex numbers, regions
in the complex plane, functions of complex variable, mappings. Derivatives, differentiation
formulas, Cauchy-Riemann equations, sufficient conditions for differentiability.

UNIT-II (15 Hours)
Analytic functions, examples of analytic functions, exponential function, Logarithmic function,
trigonometric function, derivatives of functions, definite integrals of functions.
UNIT-III (15 Hours)

Contours, Contour integrals and its examples, upper bounds for moduli of contour integrals.
Cauchy- Goursat theorem, Cauchy integral formula. Liouville‘s theorem and the fundamental
theorem of algebra. Convergence of sequences and series, Taylor series and its examples.

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