Numerical solution of algebraic and transcendental equations, Iterative algorithms, Convergence, Newton Raphson procedure, Solutions of polynomial and simultaneous linear equations, Gauss method, Relaxation procedure, Error estimates, Numerical integration, Euler-Maclaurin formula. Newton-Cotes formulae, Error estimates, Gaussian quadratures, Extensions to multiple integrals. Numerical integration of ordinary differential equations: Methods of Euler, Adams, Runge-Kutta and predictor - corrector procedures, Stability of solution. Solution of stiff equations. Solution of boundary value problems: Shooting method with least square convergence criterion, Quasilinearization method, Parametric differentiation technique and invariant imbedding technique. Solution of partial differential equations:Finite-difference techniques, Stability and convergence of the solution, Method of characteristics. Finite element and boundary element methods.