MA7163 APPLIED MATHEMATICS FOR ELECTRICAL ENGINEERS

MA7163  APPLIED MATHEMATICS FOR ELECTRICAL ENGINEERS          

  

UNIT I      MATRIX THEORY

The Cholesky decomposition - Generalized Eigen vectors, Canonical basis - QR factorization - Least squares method - Singular value decomposition. 

  

UNIT  II    CALCULUS OF VARIATIONS

Concept of variation and its properties – Euler’s equation – Functional dependant on first and higher order derivatives – Functionals dependant on functions of several independent variables – Variational problems with moving boundaries – problems with constraints - Direct methods: Ritz and Kantorovich methods.  

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    LINEAR PROGRAMMING

Formulation – Graphical solution – Simplex method – Two phase method - Transportation and Assignment  Models  

UNIT  V    FOURIER SERIES    

Fourier Trigonometric series: Periodic function as power signals – Convergence of series – Even and odd function: cosine and sine series – Non-periodic function: Extension to other intervals - Power signals: Exponential Fourier series – Parseval’s theorem and power  spectrum – Eigen value  problems and orthogonal functions – Regular Sturm-Liouville systems – Generalized Fourier series.

REFERENCES: 

1. Richard Bronson, “Matrix Operation”, Schaum’s outline series, 2nd Edition, McGraw Hill,  2011. 2. Gupta, A.S., Calculus of Variations with Applications, Prentice Hall of India Pvt. Ltd.,  New Delhi, 1997. 

3. Oliver C. Ibe, “Fundamentals of Applied Probability and Random Processes, Academic   Press, (An imprint of Elsevier), 2010. 

4. Taha, H.A., “Operations Research, An introduction”, 10th edition, Pearson education, New Delhi, 2010. 

5. Andrews L.C. and Phillips R.L., Mathematical Techniques for Engineers and Scientists, Prentice Hall of India  Pvt.Ltd., New Delhi, 2005. 

6. Elsgolts, L., Differential Equations and the Calculus of Variations, MIR Publishers, Moscow,   1973. 

7. Grewal, B.S., Higher Engineering Mathematics, 42nd edition, Khanna Publishers, 2012. 

8. O'Neil, P.V., Advanced Engineering Mathematics, Thomson Asia Pvt. Ltd., Singapore, 2003. 

9.    Johnson R. A. and Gupta C. B., “Miller & Freund’s Probability and Statistics for Engineers”,         Pearson Education, Asia, 7th Edition, 2007.