R.G.P.V. BHOPAL
M.TECH 1ST SEM ADVANCE PRODUCTION
MMCM-101 ADVANCE MATHEMATICS
UNIT I
Linear Algebra: Linear transformation, vector spaces, hash function, Hermite polynomial,
Heavisite’s unit function and error function. Elementary concepts of Modular mathematics
Linear Algebra: Linear transformation, vector spaces, hash function, Hermite polynomial,
Heavisite’s unit function and error function. Elementary concepts of Modular mathematics
UNIT II
Solution of Partial Differential Equation (PDE) by separation of variable method: numerical solution of PDE (Laplace, Poisson’s, Parabolic) using finite difference methods, Elementary properties of FT, DFT, WFT, Wavelet transform, Haar transform.
UNIT III
Probability: compound probability and discrete random variable,Binomial, Normal & Poisson’s distributions, Sampling distribution, elementary concept of estimation and theory of hypothesis, recurred relations.
UNIT IV
Stochastic process: Markov process transition probability transition probability matrix,just and higher order Markov process, Application of Eigen value problems in 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 V
FEM: Variational functionals, Euler Lagrange’s equation, Variational forms, Ritz method, Galerkin’s method, descretization, finite elements method for one dimensional problems.
REFERENCE BOOKS:-
- Higher Engineering Mathematics by B.V. Ramana, Tata Mc Hill.
- Advance Engineering Mathematics by Ervin Kreszig, Wiley Easten Edd.
- Applied Numerical Methods with MATLAB by Steven C Chapra, TMH.
- Advance Engineering Mathematics, O’Neil, Cengage (Thomson)
- Introductory Methods of Numerical Analysis by S.S. Shastry,
- Krishmurthy Finite element TMH
- Buchanan Finite element analysis(Schaum Outline S) TMH
- Numerical Solution of Differential Equation by M. K. Jain
- Numerical Mathematical Analysis By James B. Scarborogh
- Fourier Transforms by J. N. Sheddon
- Advance Mathematics for Engr and Sc, Spiegel, Schaum Series, TMH
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