Numerical methods for scientists and engineers/ R.W. Hamming.

Preface; 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 Using Function Values; 16 Error Terms; 17 Formulas Using Derivatives; 18 Formulas Using Differences. 19 Formulas Using the Sample Points as Parameters20 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 Functions; 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 Transform34 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; Bibliography; Index.