Includes bibliography.

Part I. The discrete finite difference calculus -- 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 -- Part II. Polynomial approximation: classical numerical analysis -- 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 -- Part III. Nonpolynomial approximation -- 21. Periodic functions: Fourier approximation -- 22. The convergence of Fourier series -- 23. Nonperiodic functions: the Fourier integral -- 24. Linear filters: smoothing and differentiating -- 25. Integrals and differential equations -- 26. Exponential approximation -- 27. Singularities -- Part IV. Algorithms and heuristics -- 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. Random numbers and Monte Carlo methods -- Chapter N+1. The art of computing for scientists and engineers.