| 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 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: Practice Theory |
| 26 Orthogonal Functions |
| 27 Least Squares: Practice |
| 28 Chebyshev Approximation: Theory |
| 29 Chebyshev Approximation: Practice |
| *30 Rational Function Approximation |
| III Fournier 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 |
| * Starred sections may be omitted. |