Page 6 - REC :: M.E. CS Curriculum and Syllabus - R2019

SYLLABUS

SEMESTER I

Subject Subject Name Category L T P C
Code
MH19105 APPLIED MATHEMATICS FOR COMMUNICATION FC 3 1 0 4
ENGINEERS

Objectives:
 To develop the ability to use the concepts of Linear algebra for solving problems related to Networks.
 To formulate and construct a mathematical model for a linear programming problem in real life situation;
 To expose the students to solve ordinary differential equations by various techniques.

UNIT-I LINEAR ALGEBRA 12
Vector spaces – norms – Inner Products – Eigen values using QR transformations – QR factorization - generalized
eigenvectors – Canonical forms – singular value decomposition and applications - pseudo inverse – least square
approximations --Toeplitz matrices and some applications.
UNIT-II LINEAR PROGRAMMING 12
Formulation – Graphical solution – Simplex method – Two phase method - Transportation and Assignment Models
UNIT-III ORDINARY DIFFERENTIAL EQUATIONS 12
RungeKutta Methods for system of IVPs, numerical stability, Adams-Bashforth multistep method, solution of stiff
ODEs, shooting method, BVP: Finite difference method, orthogonal collocation method, orthogonal collocation with
finite element method, Galerkin finite element method.
UNIT-IV TWO DIMENSIONAL RANDOM VARIABLES 12
Joint distributions – Marginal and Conditional distributions – Functions of two dimensional random variables –
Regression Curve – Correlation.
UNIT-V QUEUEING MODELS 12
Poisson Process – Markovian queues – Single and Multi-server Models – Little‟s formula - Machine Interference
Model – Steady State analysis – Self Service queue.
Total Contact Hours : 60

Course Outcomes:
On completion of the course, students will be able to
 Analyze and solve system of equations using the techniques of matrix decomposition and least square sense
 Make decisions using the principles of optimality on the problems of dimensionality.
 Solve differential equation using various numerical techniques.
 Apply the concept of correlation and regression in real life situation.
 Analyze and solve those problems that arise in the field of network theory through Queueing models.

Reference Books(s) / Web links:
Veerarajan T, Probability, statistics and random process with queueing theory and queueing networks, 4th edition,
1
McGraw - Hill Publishing Company Limited.
2 Richard Bronson, “Matrix Operation”, Schaum‟s outline series, 2nd Edition, McGraw Hill, 2011.
3 Taha H.A., “Operations Research: An introduction”, Pearson Education Asia, New Delhi, Ninth Edition, 2012.
4 Richard Bronson, Gabriel B.Costa, “Linear Algebra”, Academic Press, Second Edition, 2007.
th
Richard Johnson, Miller & Freund, “Probability and Statistics for Engineers”, 7 Edition, Prentice – Hall of India,
5
Private Ltd., New Delhi (2007).
nd
Donald Gross and Carl M. Harris, “Fundamentals of Queueing Theory”, 2 Edition, John Wiley and Sons, New
6
York.