Primarily written as a textbook, this third edition provides a complete course on numerical methods for undergraduate students in all branches of engineering, postgraduate students in mathematics and physics, and students pursuing courses in master of computer applications (mca). Besides students, those appearing for competitive examinations, research scholars and professionals engaged in numerical computations, will treasure this edition for its in-depth analysis, systematic treatment and clarity of approach. The third edition has been updated with new material comprising new methods and concepts and additional chapters on boundary value problems and approximation of functions. It introduces the basics in computing, stresses on errors in computation, discusses various direct and iterative methods for solving algebraic and transcendental equations and a method for solving a system of nonlinear equations, linear system of equations, matrix inversion and computation of eigenvalues and eigenvectors of a matrix. The book provides a detailed discussion on curve fitting, interpolation and cubic spline interpolation, numerical differentiation and integration. It also presents, various single step and predictor - corrector methods for solving ordinary differential equations, finite difference methods for solving partial differential equations with the concepts of truncation error and stability. Finally, it concludes with a treatment of numerical methods for solving boundary value problems, least squares, chebyshev, pade polynomial approximations and fourier series approximation to a real continuous function. This title provides altogether about 300 examples, of which about 125 are worked-out examples. It gives detailed hints and solutions to examples under exercises.