Description
The author attempts in this book to introduce the reader to the principal ideas and results of the contemporary theory of approximate integration and to provide a useful reference for practical computations. In this book we consider only the problem of approximate integration of functions of a single variable. We almost completely ignore the more difficult problem of approximate integration of functions of more than one variable, a problem about which much less is known. Only in one place do we mention double and triple integrals in connection with their reduction to single integrals. But even for single integrals the author has omitted many interesting considerations. Problems not touched upon are, for example, methods of integration of rapidly oscillating functions, the calculation of contour integrals of analytic functions, the application of random methods, and others. The book is devoted for the most part to methods of mechanical quadrature where the integral is approximated by a linear combination of a finite number of values of the integrand.
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