MA4103 Applied Mathematics for Embedded Systems Technologists Syllabus:

MA4103 Applied Mathematics for Embedded Systems Technologists Syllabus – Anna University PG Syllabus Regulation 2021

OBJECTIVES :

 To understand the techniques of Fourier transform to solve partial differential equations.
 To become familiar with graph theory for modelling the embedded system.
 To understand various optimization techniques for utilizing system and network resources.
 To understand the basic concepts of probability to apply in embedded technology.
 To understand the basic concept of random variables and queuing theories to address stochastic and dynamic environment in embedded technology.

UNIT I FOURIER TRANSFORM TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

Fourier transform : Definitions – Properties – Transform of elementary functions – Dirac delta function – Convolution theorem – Parseval’s identity – Solutions to partial differential equations : Heat equation – Wave equation – Laplace and Poison’s equations.

UNIT II GRAPH THEORY

Introduction to paths, trees, vector spaces – Matrix coloring and directed graphs – Some basic algorithms – Shortest path algorithms – Depth – First search on a graph – Isomorphism – Other Graph – Theoretic algorithms – Performance of graph theoretic algorithms – Graph theoretic computer languages.

UNIT III OPTIMIZATION TECHNIQUES

Linear programming – Basic concepts – Graphical and simplex methods – Big M method – Two phase simplex method – Revised simplex method – Transportation problems – Assignment problems.

UNIT IV PROBABILITY AND RANDOM VARIABLES

Probability – Axioms of probability – Conditional probability – Baye’s theorem – Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Exponential, Normal distributions – Two dimensional random variables – Poisson process.

UNIT V QUEUEING THEORY

Single and multiple servers – Markovian queuing models – Finite and infinite capacity queues – Finite source model – Queuing applications.

TOTAL : 60 PERIODS

OUTCOMES:

Upon Completion of the course, the students will be able to
 Apply Fourier transform techniques to solve PDE technology.
 Model the networks in embedded systems using graph theory.
 Use the ideas of probability and random variables in solving engineering problems.
 Address stochastic and dynamic behavior of data transfer using queuing theories in embedded systems technologies.

REFERENCES:

1. Taha H .A., ” Operations Research: An Introduction ” , 9th Edition, Pearson Education Asia, New Delhi, 2016.
2. Walpole R.E., Myer R.H., Myer S.L., and Ye, K., ” Probability and Statistics for Engineers and Scientists “, 7th Edition, Pearson Education, Delhi, 2002.
3. Sankara Rao, K., “ Introduction to Partial Differential Equations ”, Prentice Hall of India Pvt. Ltd., New Delhi, 1997.
4. Narasingh Deo, ” Graph Theory with Applications to Engineering and Computer Science “, Prentice Hall India,1997.
5. S. S. Rao, ” Engineering Optimization, Theory and Practice “, 4th Edition, John Wiley and Sons, 2009.