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UNIT 1 :
NUMERICAL 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.
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