## MA3301 Syllabus - Fourier Series And Linear Programming - 2021 Regulation Anna University

MA3301

FOURIER SERIES AND LINEAR PROGRAMMING

LTPC

3104

COURSE OBJECTIVES:
• To introduce Fourier series analysis which is central to many applications in engineering apart from its use in solving boundary value problems.
• To acquaint the student with Fourier series techniques in solving heat flow problems used in various situations.
• To acquaint the student with Fourier transform techniques used in wide variety of situations.
• To have knowledge in solving linear programming problems
• To acquaint knowledge to solve transportation and assignment problems.
• To familiar with the method of solving nonlinear programming problems.

UNIT I

FOURIER SERIES

9+3

Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series and cosine series – Root mean square value - Parseval’s identity–– Harmonic analysis.

UNIT II

FOURIER TRANSFORMS

9+3

Statement of Fourier integral theorem– Fourier transform pair – Fourier sine and cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

UNIT III

LINEAR PROGRAMMING PROBLEMS

9+3

Mathematical formulation - Graphical method - Simplex method - Artificial variable techniques - Big M Method - Two phase Simplex method - Duality - Dual Simplex method

UNIT IV

TRANSPORTATION AND ASSIGNMENT PROBLEMS

9+3

Matrix form - Loops in T.P - Initial basic feasible solutions - Transportation algorithm - Degeneracy in T.P - Assignment and Routing problems.

UNIT V

NON-LINEAR PROGRAMMING PROBLEMS

9+3

Lagrange multipliers – Equality constraints – Inequality constraints – Kuhn – Tucker Conditions – Quadratic programming.

TOTAL: 60 PERIODS

COURSE OUTCOMES:
1. Apply Fourier series techniques used in wide variety of situations in which the functions used are not periodic and to solve boundary value problems.
2. Apply the Fourier transform techniques to solve boundary value problems.
3. Develop a fundamental understanding of linear programming models, able to develop a linear programming model from problem description, apply the Simplex method for solving linear programming problems.
4. Analyze the concept of developing , formulating , modeling and solving transportation and assignment problems. 5. Determine the optimum solution for non-linear programming problems.

TEXT BOOKS:
1. Grewal B.S., “Higher Engineering Mathematics", 44th Edition, Khanna Publishers, New Delhi, 2018.
2. H.A. Taha, "Operations Research - An introduction”, 10th Edition, Pearson Education, New Delhi, 2017.
3. Kanti Swarup, Guptha P.K. and Man Mohan, "Operations Research”, 5th Edition, Sultan Chand & Sons, New Delhi, 2010.

REFERENCES:
1. Kreyszig E, "Advanced Engineering Mathematics", 10th Edition, John Wiley, New Delhi, India, 2016.
2. Ravindran, Philips and Solberg "Operations Research, Principles and Practice", 2 nd Edition, Wiley, , New Delhi, 2007.
3. Frederick S Hillier and Gerald J. Lieberman, "Introduction to Operations Research”, Mc Graw Hill, New Delhi, 2017.
4. J.K.Sharma , " Operations Research - Theory and Applications ", Mac Millan India Ltd , 2 nd Edition , New Delhi , 2003.
5. Richard Bronson & Govindasami Naadimuthu, "Operations Research” (Schaum’s Outlines – TMH Edition) Tata McGraw Hill, 2nd Edition, New Delhi, 2004.