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Viser: Approximate Calculation of Integrals
Approximate Calculation of Integrals
V. I. Krylov og Arthur H. Stroud
(2005)
Sprog: Engelsk
Dover Publications, Incorporated
179,00 kr.
1 stk på lager
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- Paperback: 368 sider
- Udgiver: Dover Publications, Incorporated (December 2005)
- Forfattere: V. I. Krylov og Arthur H. Stroud
- ISBN: 9780486445793
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.
PrefaceTranslator's PrefacePart
I. Preliminary InformationChapter
1. Bernoulli Numbers and Bernoulli Polynomials2. Orthogonal Polynomials3. Interpolation of Functions4. Linear Normed Spaces. Linear OperatorsPart
II. Approximate Calculation of Definite Integrals5. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature6. Interpolatory Quadratures7. Quadratures of the Highest Algebraic Degree of Precision8. Quadrature Formulas with Least Estimate of the Remainder9. Quadrature Formulas Containing Preassigned Nodes10. Quadrature Formulas with Equal Coefficients11. Increasing the Precision of Quadrature Formulas12. Convergence of the Quadrature ProcessPart
III. Approximate Calculation of Indefinite Integrals13. Introduction14. Integration of Functions Given in Tabular Form15. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand16. Methods Which Use Several Previous Values of the IntegralAppendix A. Gaussian Quadrature Formulas for Constant Weight FunctionAppendix B. Gaussian-Hermite Quadrature FormulasAppendix C. Gaussian-Laguerre Quadrature FormulasIndex
I. Preliminary InformationChapter
1. Bernoulli Numbers and Bernoulli Polynomials2. Orthogonal Polynomials3. Interpolation of Functions4. Linear Normed Spaces. Linear OperatorsPart
II. Approximate Calculation of Definite Integrals5. Quadrature Sums and Problems Related to Them. The Remainder in Approximate Quadrature6. Interpolatory Quadratures7. Quadratures of the Highest Algebraic Degree of Precision8. Quadrature Formulas with Least Estimate of the Remainder9. Quadrature Formulas Containing Preassigned Nodes10. Quadrature Formulas with Equal Coefficients11. Increasing the Precision of Quadrature Formulas12. Convergence of the Quadrature ProcessPart
III. Approximate Calculation of Indefinite Integrals13. Introduction14. Integration of Functions Given in Tabular Form15. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand16. Methods Which Use Several Previous Values of the IntegralAppendix A. Gaussian Quadrature Formulas for Constant Weight FunctionAppendix B. Gaussian-Hermite Quadrature FormulasAppendix C. Gaussian-Laguerre Quadrature FormulasIndex
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