Numerical methods for scientists and engineers (United States of America : McGraw-Hill, 1962)
Preface, There has been much progress in the 10 years since the first edition was written, but of the many books that have appeared on the topic none has put the emphasis on the frequency approach and its use in the solution of problems. For these reasons, a second edition seems necessary. The material has been extensively rearranged, rewritten, and added to, so that in some respects it is a new book; however, the main aims, style, and motto have not changed. As always, the author is greatly indebted to others for much that is in the book. Most important are his management and colleagues at the Bell Telephone Laboratories. Professor Roger Pinkham has over the years been a constant source of stimulation and inspiration. It would take a list of at least 100 names to thank all who have contributed to some extent, and at the top of this list would be M. P. Epstein. My thanks also go to all the unmentioned people on the list and to A. Ralston for many helpful suggestions. Thanks also to Mrs. Jeannie Waddel for typing and helping to organize the manuscript. R. W. HAMMING
I. Fundamentals and algorithms. 1 An Essay on Numerical Methods. - 2 Numbers. - 3 Function Evaluation. -- 4 Real Zeros. -- 5 Complex Zeros. -- 6 Zeros of Polynomials. -- 7 Linear Equations and Matrix Inversion. -- 8 Random Numbers. -- 9 The Difference Calculus. -- 10 Roundoff. -- 11 The Summation Calculus. -- 12 Infinite Series. -- 13 Difference Equations. -- II. Polynomial approximation-classical theory. 14 Polynomial Interpolation. -- 15 Formulas Uaing Funetion Values. -- 16 Error Terms. -- 17 Formulas Using Derivatives. -- 18 Fomulas Using Differences. - 19 Formulas Using the Sample Points as Parameters. -- 20 Composite Formulas. -- 21 Indefinite Integrals-Feedback. -- 22 Introduction to Differential Equations. -- 23 A General Theory of Predictor-Corrector Methods. - 24 Special Methods of Integrating Ordinary Differential Equations. -- 25 Least Squares: Theory. -- 26 Orthogonal Funetions. -- 27 Least Squares: Practice. -- 28 Chebyshev Approximation: Theory. -- 29 Chebyshev Approximation: Practice. -- 30 Rational Function Approximation. -- III. Fourier approximation-modern theory. 31 Fourier Series: Periodic Functions. -- 32 Convergence of Fourier Series. -- 33 The Fast Fourier Transform. -- 34 The Fourier Integral: Nonperiodic Functions. -- 35 A Second Look at Polynomial Approximation -Filters. -- 36 Integrals and Differential Equations. -- 37 Design of Digital Filters. -- 38 Quantization of Signals. -- IV. Exponential approximation. 39 Sums of Exponentials. -- 40 The Laplace Transform. -- 41 Simulation and the Method of Zeros and Poles. -- V. Miscellaneous. 42 Approximations to Singularities. -- 43 Optimization. -- 44 Linear Independence. - 45 Eigenvalues and Eigenvectors of Hermitian Matrices. -- N+1 The Art of Computing for Scientists and Engineers. - Index.
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