Approximate Calculation of Integrals

 
9780023669309: Approximate Calculation of Integrals

A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.
The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to the problem of calculation of definite integrals. This section considers three basic topics: the theory of the construction of mechanical quadrature formulas for sufficiently smooth integrand functions, the problem of increasing the precision of quadratures, and the convergence of the quadrature process. The final part explores methods for the calculation of indefinite integrals, and the text concludes with helpful appendixes.

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An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.

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