Approximate Calculation of Integrals

by V. I. Krylov

Overview

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.

Product Details

ISBN-13:	9780486154671
Publisher:	Dover Publications
Publication date:	01/27/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	368
File size:	40 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface
Translator's Preface
Part I. Preliminary Information
Chapter 1. Bernoulli Numbers and Bernoulli Polynomials
2. Orthogonal Polynomials
3. Interpolation of Functions
4. Linear Normed Spaces. Linear Operators
Part II. Approximate Calculation of Definite Integrals
5. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature
6. Interpolatory Quadratures
7. Quadratures of the Highest Algebraic Degree of Precision
8. Quadrature Formulas with Least Estimate of the Remainder
9. Quadrature Formulas Containing Preassigned Nodes
10. Quadrature Formulas with Equal Coefficients
11. Increasing the Precision of Quadrature Formulas
12. Convergence of the Quadrature Process
Part III. Approximate Calculation of Indefinite Integrals
13. Introduction
14. Integration of Functions Given in Tabular Form
15. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand
16. Methods Which Use Several Previous Values of the Integral
Appendix A. Gaussian Quadrature Formulas for Constant Weight Function
Appendix B. Gaussian-Hermite Quadrature Formulas
Appendix C. Gaussian-Laguerre Quadrature Formulas
Index