4EC1-MATHEMATICS-IV |
Units: I-NUMERICAL ANALYSIS |
Finite differences – Forward, Backward and Central differences.
Newton’s forward and backward differences, interpolation formulae. Stirling’s formula, Lagrange’s
interpolation formula.
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Units: II-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 |
Units: III-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
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Units: IV-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.
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Units: V-CALCULUS OF VARIATIONS |
Functional, strong and weak variations simple variation
problems, the Euler’s equation.
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