MA7157 APPLIED MATHEMATICS FOR ELECTRONICS ENGINEERS

MA7157 APPLIED MATHEMATICS FOR ELECTRONICS ENGINEERS 

UNIT I FUZZY LOGIC

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

UNIT II MATRIX THEORY

Some important matrix factorizations – The Cholesky decomposition – QR factorization – Least squares method – Singular value decomposition -Toeplitz matrices and some applications.

UNIT III ONE DIMENSIONAL RANDOM VARIABLES

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 IV DYNAMIC PROGRAMMING

Dynamic programming – Principle of optimality – Forward and backward recursion – Applications of dynamic programming – Problem of dimensionality.

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.

REFERENCES: 

1. George J. Klir and Yuan, B., Fuzzy sets and fuzzy logic, Theory and applications, Prentice Hall of India Pvt. Ltd., 1997. 

2. Moon, T.K., Sterling, W.C., Mathematical methods and algorithms for signal processing, Pearson Education, 2000. 

3. Richard Johnson, Miller & Freund’s Probability and Statistics for Engineers, 7th Edition, Prentice – Hall of India, Private Ltd., New Delhi (2007). 

4. Taha, H.A., Operations Research, An introduction, 7th edition, Pearson education editions, Asia, New Delhi, 2002. 

5. Donald Gross and Carl M. Harris, Fundamentals of Queuing theory, 2nd edition, John Wiley and Sons, New York (1985).