Interpolation: Existence, Uniqueness of interpolating polynomial, error of interpolation – unequally spaced data; Lagrange’sformula, Newton’s divided difference formula. Equally spaced data: finite difference operators and their properties, Gauss’s forward and backward, Sterling’s formulae – Inverse interpolation – Hermite interpolation.
Differentiation: Finite difference approximations for first and second order derivatives.
Integration: Newton-cotes closed type methods; particular cases, error terms – Newton cotes open type methods – Romberg integration Gaussian quadrature; Legendre formulae.
Solution of nonlinear and transcendental equations: RegulaFalsi method, Newton-Raphson method, Newton Raphson method for system of nonlinear equations.
Solution of linear algebraic system of equations: LU Decomposition, Gauss-Seidal methods; solution of tridiagonal system. Ill conditioned equations. Eigen values and eigenvectors : Power and Jacobi methods.
Solution of ordinary differential equations: Initial value problems: Single step methods; Taylor’s, Euler’s, Runge-Kutta methods, Implicit RungeKutta methods Boundary value problems: Finite difference methods, Shooting method.