4EC1 MATHEMATICS-IV

UNIT 1 :

N

UMERICAL ANALYSIS -

Finite differences – Forward, Backward and Central differences.

Newton’s forward and backward differences, interpolation formulae. Stirling’s formula, Lagrange’s

interpolation formula.

UNIT 2 :

NUMERICAL ANALYSIS- Integration

-Trapezoidal rule, Simpson’s one third and three-eighth

rules. Numerical solution of ordinary differential equations of first order - Picard’s mathod, Euler’s and

modified Euler’s methods, Miline’s method and Runga-Kutta fourth order method.,Differentiation

UNIT 3 : SPECIAL FUNCTIONS –

Bessel’s functions of first and second kind, simple recurrence

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

first kind. Simple recurrence relations, Orthogonal property, Generating function.

UNIT 4 : STATISTICS AND PROBABILITY -

Elementary theory of probability, Baye’s theorem with

simple applications, Expected value, theoretical probability distributions-Binomial, Poisson and Normal

distributions. Lines of regression, co-relation and rank correlation.

UNIT 5 : CALCULUS OF VARIATIONS -

Functional, strong and weak variations simple variation

problems, the Euler’s equation.