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BL
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998933
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b753303
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| Uniform Title
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Priblizhennoe vychislenie integralov.English
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| Main Entry
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Krylov, V. I., (Vladimir Ivanovich),1902-1994.
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| Title & Author
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Approximate calculation of integrals /\ Vladimir Ivanovich Kraylov ; translated by Arthur H. Stroud.
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| Edition Statement
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Dover ed.
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| Publication Statement
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Mineola, N.Y. :: Dover Publications,, 2005.
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| Series Statement
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Dover books on mathematics
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| Page. NO
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1 online resource (x, 357 pages) :: illustrations
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| ISBN
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048615467X
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: 9780486154671
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0486445798
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9780486445793
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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.
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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.
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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.
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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.
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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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| Abstract
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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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| Subject
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Approximation theory.
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| Subject
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Integrals.
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Approximation theory.
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| Subject
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Integrals.
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MATHEMATICS-- Functional Analysis.
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| Dewey Classification
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515/.43
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| LC Classification
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QA311.K713 2005
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| Added Entry
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Stroud, A. H.
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