4EE6.1 ADVANCED MATHEMATICS

Unit-1

Numerical Analysis:

Finite differences - Forward backward and central difference. Newton’s

forward and backward differences interpolation formulae. Sterling’s formulae, Lagrange’s

interpolation formula. Solution of non-linear equations in one variable by Newton Raphson

and Simultaneous algebraic equation by Gauss and Regula Falsi method. Solution of

simultaneous equations by Gauss elimination and Gauss Seidel methods. Fitting of curves

(straight line and parabola of second degree) by method of least squares.

Unit-2

Numerical Analysis:

Numerical differentiation, numerical integration trapezoidal rule,

Simpson’s one-third and one eighth rule. Numerical Integration of ordinary differential

equations of first order, Picard’s method, Euler’s & modified Euler’s methods. Miline’s

method and Runga Kutta fourth order method. Simple linear difference equations with

constant coefficients.

Unit-3

Special Functions:

Bessel’s function of first and second kind, simple recurrence relations,

orthogonal property of Bessel functions, Transformation, Generating functions, Legendre’s

function of first kind, simple recurrence relations, orthogonal property, Generating functions.

Unit-4

Statistics & Probability:

Elementary theory of probability, Baye’s theorem with simple

applications, Expected value.

Theoretical probability distributions – Binomial, Poisson and

Nor mal distributions.

Unit-5

Statistics & Probability:

Lines of regression, co-relation and rank correlation.

Transforms

: