4CE6.3                   ADVANCED MATHEMATICS                                                                    L-3

UNIT 1

Elementary Statistics & Probability:

Elementary theory of probability, Baye’s Theorem with its simple

applications, Theoretical probability distributions – Binomial, Poisson, Normal distribution.

UNIT 2

Advance Statistics:

Chisquare test as test of goodness of fit. Line of regression, Coefficient of correlation

and rank correlation.

UNIT 3

Tensor Analysis

: Definition of a tensor, Transformation of co-ordinates, contra variant and co-variant

vectors, addition and multiplication of tensors, contraction of tensors, inner product, fundamental tensors,

Christoffel symbols, covariant differentiation

UNIT 4

Bessel's Functions:

Bessel functions of first and second kind, simple recurrence relations, orthogonal,

property of Bessel’s function.

UNIT 5

Legendre’s function

:  Legendre’s function, simple recurrence relations, Rodrigues formula, orthogonal

property of Legendre’s function, generating function.