MSE-101 ADVANCED COMPUTATIONAL MATHEMATICS

UNIT 1

Linear Algebra: Linear transformation, vector spaces, hash function, Hermite

polynomial, Heavisite’s unit function and error function. Elementary concepts of

Modular mathematics

UNIT 2

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 3

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 4

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 5

Operations of fuzzy sets, fuzzy arithmetic & relations, fuzzy relation equations, fuzzy

logics. MATLAB introduction, programming in MATLAB scripts, functions and their

application.

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. Advance Engg Mathematics, O’ Neil, Cengage (Thomson)

4. Introductory Methods of Numerical Analysis by S.S. Shastry,

5. Introduction of Numerical Analysis by Forberg

6. Numerical Solution of Differential Equation by M. K. Jain

7. Numerical Mathematical Analysis By James B. Scarborogh

8. Fourier Transforms by J. N. Sheddon

9. Fuzzy Logic in Engineering by T. J. Ross

10. Fuzzy Sets Theory & its Applications by H. J. Zimmersoms