|
Unit1.
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.
Unit2. 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.
Unit3. 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.
Unit4. STATISTICS & PROBABILITY: Elementary theory of probability,
Baye’s theorem with simple applications, Expected value. Theoretical
probability distributions – Binomial, Poisson and Normal distributions
Unit5. STATISTICS & PROBABILITY: Lines of regression, co-relation
and rank correlation. TRANSFORMS: Z-transforms, its inverse, simple
properties and application to difference equations.
|