201. Mathematics III 


FIRST TERM:
1. Ordinary Differential Equations and some special function:
	Series solutions of ordinary differential equations.
	Lagendre and B.assel function and their properties.		-8 lects
2. Partial Differential Equations:
   	Second order linear and liner partial differential equations,
	elliptic, parabolic and hyperbolic types;
 	boundary and initial conditions, 
	solutions of Dirichiet and Neumann problems for Laplace equation 
	and of heat conduction problems by Fourier method. 
	DIA lembert solution of 1-D wave equation and 
	solution of Cauchy's problem.		-8 Lects,

3. Functions of a complex variable:
	Review of complex numbers, formulae of Euler & Demoivre,
	analytic functions, Cauchy Riemann
	elementary complex functions and analytic functien in term of a power series;
	Laur series, residue theorem, contour integration.			-8 Lects.

SECOND TERM:

1. Probability and statistics:
	Axiomatic definition of probability, 
	laws of probabilities classical occupancy problem with illustrations;
	conditional, probability multiplication law, independence of eveents,
	Baves, rule,
	discrete & continuous random variables-cumulative distribution functions,
	probability mass function, probability density function,
	mathematical expectation, mean; 
	variance, momemt generating function and characteristic function,
	standard probability models-binomial, Poisson, exponential, Weibull,
	normal and Iongnormal. 
	Sampling and sampling distribution -z, t, Chi-square, F;
	estimation of parameters, use of t, 
	Chi-square. and F in tests of significance-			-24 lects.

Texts / References

	1.	Advanced Engineering Mathematics By E. Kreyszig, 
								Wiley Eastern Pvt. Ltd. (India)

Reference Books
	1	Advanced Engineering Mathematics, By C.R. Wylse
	2	Mathematics of Physics and Modern Engineering, By Sckolonikoff & Redhehlfer
	3	Advanced Mathematics for Engineers & Physicists, By L.A. Pipes.