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Approximate Calculation of Integrals 1st Edition by Krylov 9780486445793 0486445798

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Approximate Calculation of Integrals V. I. Krylov Digital Instant Download

Author(s): V. I. Krylov, Arthur H. Stroud
ISBN(s): 9780486445793, 0486445798
Edition: Kindle
File Details: PDF, 5.39 MB
Year: 2006
Language: english
SKU: EB-1968346 Category: Tags: ,

Approximate Calculation of Integrals 1st Edition by Krylov – Ebook PDF Instant Download/Delivery: 9780486445793, 0486445798

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Product details:

ISBN 10: 0486445798

ISBN 13: 9780486445793

Author: V. I. Krylov

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.

Table of contents:

Part One: Preliminary Information

  1. Bernoulli Numbers and Bernoulli Polynomials

  2. Orthogonal Polynomials

  3. Interpolation of Functions

  4. Linear Normed Spaces. Linear Operators

Part Two: Approximate Calculation of Definite Integrals

  1. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature

  2. Interpolatory Quadratures

  3. Quadratures of the Highest Algebraic Degree of Precision

  4. Quadrature Formulas with Least Estimate of the Remainder

  5. Quadrature Formulas Containing Preassigned Nodes

  6. Quadrature Formulas with Equal Coefficients

  7. Increasing the Precision of Quadrature Formulas

  8. Convergence of the Quadrature Process

Part Three: Approximate Calculation of Indefinite Integrals

  1. Introduction

  2. Integration of Functions Given in Tabular Form

  3. Calculation of Indefinite Integrals Using a Small Number of Values of the Integrand

  4. Methods Which Use Several Previous Values of the Integral

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Tags: Krylov, Approximate, Calculation, Integrals