Interpolation by polynomials, divided di_erences, error of the interpolating polynomial, piecewise linear and cubic spline interpolation. Numerical integration, composite rules, error formulae. Solution of a system of linear equations, implementation of Gaussian elimination and Gauss-seidel methods, partial pivoting, row echelon form, LU factorization Cholesky’s method, ill-conditioning, norms. solution of a nonlinear equation, bisection and secant methods. Newton’s method, rate of convergence, solution of a system of nonlinear equations, numerical solution of ordinary di_erential equations, Euler and Runge-Kutta methods, multi-step methods, predictor-corrector methods, order of convergence, _nite di_erence methods, numerical solutions of elliptic, parabolic, and hyperbolic partial di_erential equations. Eigenvalue problem, power method, QR method, Gershgorin’s theorem. Exposure to software packages like IMSL subroutines, MATLAB.