COMPLEX ANALYSIS, PROBABILITY AND LINEAR PROGRAMMING (21MATME41)

COMPLEX ANALYSIS, PROBABILITY AND LINEAR PROGRAMMING

Course Code 21MATME41 
CIE Marks 50
Teaching Hours/Week (L: T:P) (2:2:0) 
SEE Marks 50
Credits 03 
Exam Hours 03

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. (8 hours) Self-Study: Review of a function of a complex variable, limits, continuity, and differentiability. (RBT Levels: L1, L2 and L3)

Module-2

Conformal transformations: Introduction. Discussion of transformations 𝑤 = 𝑧ଶ, 𝑤 = 𝑒௭, 𝑤 = 𝑧 + ଵ ௭ , (𝑧 ≠ 0). Bilinear transformations- Problems. Complex integration: Line integral of a complex function-Cauchy’s theorem and Cauchy’s integral formula and problems. (8 hours) Self-Study: Residues, Residue theorem – problems (RBT Levels: L1, L2 and L3)

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, Poisson, exponential and normal distributions- problems. (8 hours) Self-Study: Two-dimensional random variables, marginals pdf’s, Independent random variables (RBT Levels: L1, L2 and L3)

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) Self-Study: Formulation of an L.P.P and optimal solution by Graphical Method. (RBT Levels: L1, L2 and L3)

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. (8 hours) Self-Study: Degeneracy in Transportation problem. (RBT Levels: L1, L2 and L3)

Suggested Learning Resources:
Text Books:

 B. S. Grewal: “Higher Engineering Mathematics”, Khanna publishers, 44th Ed.2018

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

 S.D. Sharma: “Operations Research” Kedarnath Publishers Ed. 2012

Reference Books

 V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education,11thEd.

 Mokhtar S.Bazaraa, John J.Jarvis & Hanif D.Sherali(2010), Linear Programming and Network Flows( 4th Edition), John Wiley & sons.

 G.Hadley (2002) Linear Programming, Narosa Publishing House

 F.S. Hillier. G.J. Lieberman: Introduction to Operations Research- Concepts and Cases, 9th Edition, Tata Mc-Graw Hill, 2010.

 Srimanta Pal & Subodh C. Bhunia: “Engineering Mathematics” Oxford University Press,3rdReprint, 2016.

 N.P Bali and Manish Goyal: “A textbook of Engineering Mathematics” Laxmi Publications, Latest edition.

 C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co. New York, Latested.

 H.K. Dass and Er. RajnishVerma:“Higher EngineeringMathematics”S.ChandPublication(2014).

Web links and Video Lectures (e-Resources):

 http://.ac.in/courses.php?disciplineID=111

 http://www.class-central.com/subject/math(MOOCs)

 https://www.coursera.org/learn/operations-research-modeling

 https://www.careers360.com/university/indian-institute-of-technology-madras/introduction-operations- research-certification-course

 http://people.whitman.edu/~hundledr/courses/M339.html

 VTU e-Shikshana Program

 VTU EDUSAT Program

Activity-Based Learning (Suggested Activities in Class)/ Practical Based learning

 Quizzes

 Assignments

 Seminars