Numerical Analysis

Differences, Relation between differences and derivatives,difference of polynomials, Factorial notation,Newton’s forward and backward interpolation formula (including 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 – Quadrature formula-trapezoidal rule, Simpson’s 1/3 ^rd and 3/8 ^th formulae,Gaussian Integration , Newton cotes formula.

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: Gauss elimination method , Jacobi and Gauss Seidal method . Solutitons of ordinary differential equations with initial boundary conditions: Picard’s method, Euler’s and modified Euler’s method, Runge’s Kutta Method.