عنوان
پدید آورنده
موضوع
رده
QA311 .K713 2005
QA311
.
K713
2005
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
048615467X
(Number (ISBN
9780486154671
Erroneous ISBN
0486445798
Erroneous ISBN
9780486445793
NATIONAL BIBLIOGRAPHY NUMBER
Number
b753303
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Approximate calculation of integrals /
General Material Designation
[Book]
First Statement of Responsibility
Vladimir Ivanovich Kraylov ; translated by Arthur H. Stroud.
EDITION STATEMENT
Edition Statement
Dover ed.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Mineola, N.Y. :
Name of Publisher, Distributor, etc.
Dover Publications,
Date of Publication, Distribution, etc.
2005.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (x, 357 pages) :
Other Physical Details
illustrations
SERIES
Series Title
Dover books on mathematics
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Cover; Title Page; Copyright Page; Preface; Translator's Preface; Contents; Part One. Preliminary Information; Chapter 1. Bernoulli Numbers and Bernoulli Polynomials; 1.1. Bernoulli Numbers; 1.2. Bernoulli Polynomials; 1.3. Periodic Functions Related to Bernoulli Polynomials; 1.4. Expansion of an Arbitrary Function in Bernoulli Polynomials; Chapter 2. Orthogonal Polynomials; 2.1. General Theorems About Orthogonal Polynomials; 2.2. Jacobi and Legendre Polynomials; 2.3. Chebyshev Polynomials; 2.4. Chebyshev-Hermite Polynomials; 2.5. Chebyshev-Laguerre Polynomials.
Text of Note
10.2. Uniqueness of the Quadrature Formulas of the Highest Algebraic Degree of Precision with Equal Coefficients10.3. Integrals with a Constant Weight Function; Chapter 11. Increasing the Precision of Quadrature Formulas; 11.1. Two Approaches to the Problem; 11.2. Weakening the Singularity of the Integrand; 11.3. Euler's Method for Expanding the Remainder; 11.4. Increasing the Precision When the Integral Representation of the Remainder Contains a Short Principle Subinterval; Chapter 12. Convergence of the Quadrature Process; 12.1. Introduction.
Text of Note
5.3. The Remainder in Approximate Quadrature and its RepresentationChapter 6. Interpolatory Quadratures; 6.1. Interpolatory Quadrature Formulas and Their Remainder Terms; 6.2. Newton-Cotes Formulas; 6.3. Certain of the Simplest Newton-Cotes Formulas; Chapter 7. Quadratures of the Highest Algebraic Degree of Precision; 7.1. General Theorems; 7.2. Constant Weight Function; 7.3. Integrals of the Form and a Their Application to the Calculation of Multiple Integrals; 7.4. The Integral; 7.5. Integrals of the Form; Chapter 8. Quadrature Formulas with Least Estimate of the Remainder.
Text of Note
8.1. Minimization of the Remainder of Quadrature Formulas8.2. Minimization of the Remainder in the Class Lq(r); 8.3. Minimization of the Remainder in the Class Cr; 8.4. The Problem of Minimizing the Estimate of the Remainder for Quadrature with Fixed Nodes; Chapter 9. Quadrature Formulas Containing Preassigned Nodes; 9.1. General Theorems; 9.2. Formulas of Special Form; 9.3. Remarks on Integrals with Weight Functions That Change Sign; Chapter 10. Quadrature Formulas with Equal Coefficients; 10.1. Determining the Nodes.
Text of Note
Chapter 3. Interpolation of Functions3.1. Finite Differences and Divided Differences; 3.2. The Interpolating Polynomial and Its Remainder; 3.3. Interpolation with Multiple Nodes; Chapter 4. Linear Normed Spaces. Linear Operators; 4.1. Linear Normed Spaces; 4.2. Linear Operators; 4.3. Convergence of a Sequence of Linear Operators; Part Two. Approximate Calculation of Definite Integrals; Chapter 5. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature; 5.1. Quadrature Sums; 5.2. Remarks on the Approximate Integration of Periodic Functions.
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SUMMARY OR ABSTRACT
Text of Note
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.
SYSTEM REQUIREMENTS NOTE (ELECTRONIC RESOURCES)
Text of Note
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
OTHER EDITION IN ANOTHER MEDIUM
Title
Approximate calculation of integrals.
UNIFORM TITLE
General Material Designation
Priblizhennoe vychislenie integralov.
Language (when part of a heading)
English
TOPICAL NAME USED AS SUBJECT
Approximation theory.
Integrals.
Approximation theory.
Integrals.
MATHEMATICS-- Functional Analysis.
DEWEY DECIMAL CLASSIFICATION
Number
515/
.
43
Edition
22
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA311
Book number
.
K713
2005
PERSONAL NAME - PRIMARY RESPONSIBILITY
Krylov, V. I., (Vladimir Ivanovich),1902-1994.
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Stroud, A. H.
ORIGINATING SOURCE
Date of Transaction
20201204125033.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
