NUMERICAL ANALYSIS
Differences, Relation between differences and derivatives, Difference of polynomials, Factorial notation, Newton’s forward and backward interpolation formula (with proof).
Divided differences: Newton’s and Lagrange’s divided differences formulae. Central differences: Gauss’s, Stirling’s and Bessel’s interpolation formulae, Numerical differentiation.
Numerical integration: Newton-Cotes quadrature formula, Trapezoidal formula, Simpson’s 1/3rd and 3/8th formulae, Gaussian integration.
Inverse Interpolation, Numerical solution of algebraic and transcendental equations: Bisection method, Regula-falsi method, Method of iteration and Newton Raphson’s Method. Newton’s iterative formula for obtaining square and inverse square root.
Solution of system of linear equations: Direct methods (Gauss elimination method, LU-decomposition method), Iterative methods (Jacobi and Gauss Seidal method, SOR method), Theorems based on iterative methods, Solutions of first order ordinary differential equations: Picard’s method, Euler’s method, Runge-Kutta method.
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(Note: Non-Programmable scientific calculator up to 100 MS is permitted)
