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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.

For this inexpensive paperback edition of a groundbreaking classic, the author has extensively rearranged, rewritten and enlarged the material. Book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: Fundamentals and Algorithms; Polynomial Approximation Classical Theory; Fourier Approximation Modern Therory; Exponential Approximation.