MA4101 Applied Mathematics for Electronics Engineers Syllabus:

MA4101 Applied Mathematics for Electronics Engineers Syllabus – Anna University PG Syllabus Regulation 2021

COURSE OBJECTIVES:

 To introduce the fundamentals of fuzzy logic.
 To understand the basics of random variables with emphasis on the standard discrete and continuous distributions.
 To understand the basic probability concepts with respect to two dimensional random variables.
 To make students understand the notion of a Markov chain, and how simple ideas of conditional probability and matrices can be used to give a thorough and effective account of discrete – time Markov chains.
 To provide the required fundamental concepts in queueing models and apply these techniques in networks, image processing.

UNIT I FUZZY LOGIC

Classical logic – Multivalued logics – Fuzzy propositions – Fuzzy qualifiers.

UNIT II PROBABILITY AND RANDOM VARIABLES

Probability – Axioms of probability – Conditional probability – Bayes theorem – Random variables – Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a random variable.

UNIT III TWO DIMENSIONAL RANDOM VARIABLES

Joint distributions – Marginal and conditional distributions – Functions of two dimensional random variables – Regression curve – Correlation.

UNIT IV RANDOM PROCESSES

Classification – Stationary random process – Markov process – Markov chain – Poisson process – Gaussian process – Auto correlation – Cross correlation.

UNIT V QUEUEING MODELS

Poisson process – Markovian queues – Single and multi server models – Little’s formula – Machine Interference model – Steady state analysis – Self service queue.

TOTAL : 60 PERIODS

COURSE OUTCOMES:

At the end of the course, students will be able to
 apply the concepts of fuzzy sets, fuzzy logic, fuzzy prepositions and fuzzy quantifiers and in relate.
 analyze the performance in terms of probabilities and distributions achieved by the determined solutions.
 use some of the commonly encountered two dimensional random variables and extend to multivariate analysis.
 classify various random processes and solve problems involving stochastic processes.
 use queueing models to solve practical problems.

REFERENCES:

1. Ganesh M., “Introduction to Fuzzy Sets and Systems, Theory and Applications”, Academic Press, New York, 1997.
2. George J. Klir and Yuan B,” Fuzzy sets and Fuzzy logic” Prentice Hall, New Delhi, 2006.
3. Devore J.L, “Probability and Statistics for Engineering and Sciences”, Cengage learning, 9th Edition, Boston, 2017.
4. Johnson R.A. and Gupta, C.B., “ Miller and Freunds Probability and Statistics for Engineers”, Pearson India Education, Asia, 9th Edition, New Delhi, 2017.
5. Oliver C. Ibe,” Fundamentals of applied probability and Random process”, Academic press, Boston, 2014.
6. Gross D. and Harris C.M., “Fundamentals of Queuing theory”, Willey student, 3rd Edition, New Jersey, 2004.