1.The difference calculus. 2.Roundoff noise. 3.The summation calculus. 4.Evaluation of infinite series. 5.Finite difference equations. 6.The finite Fourier series. 7.Introduction to polynomial approximations. 8.Polynomial interpolation-arbitrarily spaced data. 9.Polynomial interpolation-Equally spaced data. 10.A uniform method for finding formulas. 11.On finding the error term of a formula. 12.Formulas for definite integrals. 13.Indefinite integrals. 14.Introduction to differential equations. 15.A general theory of predictor-corrector methods. 16.Special methods of integrating ordinary differential equations. 17.Least squares: theory. 18.Least squares: practice. 19.Chebyshev polynomials. 20.Rational functions. 21.Periodic functions-Fourier approximation. 22.The convergence of Fourier series. 23.Nonperiodic functions-the Fourier integral. 24.Linear filters- smoothing and differentiating. 25.Integral and differential equations. 26.Exponential approximation. 27.Exponential approximation. 28.On finding zeros. 29.Simultaneous linear algebraic equations. 30.Inversion of matrices and eigenvalues. 31.Some examples of the simulation of situations and processes. 32.Randow numbers and monte clarlo engineers.