Numerical Methods for Scientists and Engineers

Richard W. Hamming (1915-1998) was first a programmer of one of the earliest digital computers while assigned to the Manhattan Project in 1945, then for many years he worked at Bell Labs, and later at the Naval Postgraduate School in Monterey, California. He was a witty and iconoclastic mathematician and computer scientist whose work and influence still reverberates through the areas he was interested in and passionate about. Three of his long-lived books have been reprinted by Dover: Numerical Methods for Scientists and Engineers, 1987; Digital Filters, 1997; and Methods of Mathematics Applied to Calculus, Probability and Statistics, 2004.

• PrefaceI Fundamentals and Algorithms1 An Essay on Numerical Methods2 Numbers3 Function Evaluation4 Real Zeros5 Complex Zeros*6 Zeros of Polynomials7 Linear Equations and Matrix Inversion*8 Random Numbers9 The Difference Calculus10 Roundoff*11 The Summation Calculus*12 Infinite Series13 Difference EquationsII Polynomial Approximation-Classical Theory14 Polynomial Interpolation15 Formulas Using Function Values16 Error Terms17 Formulas Using Derivatives18 Formulas Using Differences*19 Formulas Using the Sample Points as Parameters20 Composite Formulas21 Indefinite Integrals-Feedback22 Introduction to Differential Equations23 A General Theory of Predictor-Corrector Methods24 Special Methods of Integrating Ordinary Differential Equations25 Least Squares: Practice Theory26 Orthogonal Functions27 Least Squares: Practice28 Chebyshev Approximation: Theory29 Chebyshev Approximation: Practice*30 Rational Function ApproximationIII Fournier Approximation-Modern Theory31 Fourier Series: Periodic Functions32 Convergence of Fourier Series33 The Fast Fourier Transform34 The Fourier Integral: Nonperiodic Functions35 A Second Look at Polynomial Approximation-Filters*36 Integrals and Differential Equations*37 Design of Digital Filters*38 Quantization of SignalsIV Exponential Approximation39 Sums of Exponentials*40 The Laplace Transform*41 Simulation and the Method of Zeros and PolesV Miscellaneous42 Approximations to Singularities43 Optimization44 Linear Independence45 Eigenvalues and Eigenvectors of Hermitian MatricesN + 1 The Art of Computing for Scientists and EngineersIndex* Starred sections may be omitted.