ADVANCE MATHEMATICS (MEPS-101)

M.E. POWER SYSTEM 1ST SEM ADVANCE MATHEMATICS (MEPS-101)SYLLABUS

UNIT I
Solution of Partial Differential Equation (PDE): by separation of variable method,numerical solution of PDE (Laplace, Poisson’s, Parabola) using finite difference methods, Elementary properties of FT, DFT, WFT, Wavelet transform,Haar transform.
UNIT II 
Probability:compound probability and discrete random variable.Binomial,Normal and Poisson’s distributions, Sampling distribution,elementary concept of estimation and theory of hypothesis, recurred relations.
UNIT III 
Stochastic process:Markov process transition probability transition probability matrix, just and higher order Markov process, Markov chain. Queuing system,transient and steady state, traffic intensity, distribution queuing system, concepts of queuing models (M/M/1: Infinity/ Infinity/ FC FS), (M/M/1: N/ Infinity/ FC FS),(M/M/S: Infinity/ Infinity/ FC FS)
UNIT IV 
Operations of fuzzy sets:fuzzy arithmetic & relations,fuzzy relation equations,fuzzy logics. MATLAB introduction, programming in MATLAB scripts, functions and their application.
UNIT V
Introduction and definition of reliability:derivation of reliability functions,Failure rate, Hazard rate, mean time t future & their relations,concepts of fault tolerant analysis, Elementary idea about decision theory and goal programming.
REFERENCE BOOKS:

1. Higher Engineering Mathematics by B.V. Ramana, Tata Mc Hill.
2. Advance Engineering Mathematics by Ervin Kreszig, Wiley Easten Edd.
3. Applied Numerical Methods with MATLAB by Steven C Chapra, TMH
4. Introductory Methods of Numerical Analysis by S.S. Shastry, 
5. Numerical Solution of Differential Equation by M. K. Jain 
6. Numerical Mathematical Analysis By James B. Scarborogh 
7. Fourier Transforms by J. N. Sheddon 
8. Fuzzy Logic in Engineering by T. J. Ross 
9. Fuzzy Sets Theory & its Applications by H. J. Zimmersoms