Handbook of Computational Methods for Integration
This book, excellent in its structure and the ideas that it contains, is devoted to the often occurring problem of computation of integrals in one variable. There are many integration and quadrature rules given and the material covers most of the areas of practice in which numerical integration is required. The book is not only an overview of rules but it also explains the ideas for which the given formula were previously derived and studied. Some application areas are overviewed such as differential and integral equations, Fourier integrals and transforms, the Hartley transform, fast Fourier and Hartley transforms and wavelets. The first chapter provides some useful definitions and results needed in the book. The topics treated in other chapters include interpolatory and Gaussian quadratures, improper and singular integrals, Fourier integrals and transforms, inversion of Laplace transforms, wavelets and integral equations. The enclosed CD-R contains over 5800 formulas for indefinite and definite integrals, quadrature tables in ASCII format and computer codes in C++, f90, MATLAB and Mathematica, all in ASCII format. The reviewer is convinced that the book is a very useful resource for researchers in many fields of mathematics and for graduate students.