| Titre : |
Approximate calculation of integrals |
| Type de document : |
texte imprimé |
| Auteurs : |
Vladimir Ivanovich Krylov, Auteur ; Arthur H. Stroud, Traducteur |
| Editeur : |
New York : Dover publications |
| Année de publication : |
2005 |
| Importance : |
X, 357 p. |
| Présentation : |
ill. |
| Format : |
22 cm |
| ISBN/ISSN/EAN : |
978-0-486-44579-3 |
| Note générale : |
Trad. du russe :"Priblizhennoe Vychislenie Integralov". Notes bibliogr. Index |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Intégrales -- Calculs numériques
Approximation, Théorie de l'
Intégration de fonctions
Integrals
Approximation theory |
| Index. décimale : |
517.3 Calcul intégral. Intégration |
| Résumé : |
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. |
| Note de contenu : |
In summary :
I. Preliminary Information
1. Bernoulli Numbers and Bernoulli Polynomials
2. Orthogonal Polynomials
3. Interpolation of Functions ...
II. Approximate Calculation of Definite Integrals
1. Quadrature Sums and Problems Related to Them...
2. Interpolatory Quadratures
3. Quadratures of the Highest Algebraic Degree of Precision ...
III. Approximate Calculation of Indefinite Integrals
1. Integration of Functions Given in Tabular Form
2. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand
3. Methods Which Use Several Previous Values of the Integral... |
Approximate calculation of integrals [texte imprimé] / Vladimir Ivanovich Krylov, Auteur ; Arthur H. Stroud, Traducteur . - New York : Dover publications, 2005 . - X, 357 p. : ill. ; 22 cm. ISBN : 978-0-486-44579-3 Trad. du russe :"Priblizhennoe Vychislenie Integralov". Notes bibliogr. Index Langues : Anglais ( eng)
| Mots-clés : |
Intégrales -- Calculs numériques
Approximation, Théorie de l'
Intégration de fonctions
Integrals
Approximation theory |
| Index. décimale : |
517.3 Calcul intégral. Intégration |
| Résumé : |
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. |
| Note de contenu : |
In summary :
I. Preliminary Information
1. Bernoulli Numbers and Bernoulli Polynomials
2. Orthogonal Polynomials
3. Interpolation of Functions ...
II. Approximate Calculation of Definite Integrals
1. Quadrature Sums and Problems Related to Them...
2. Interpolatory Quadratures
3. Quadratures of the Highest Algebraic Degree of Precision ...
III. Approximate Calculation of Indefinite Integrals
1. Integration of Functions Given in Tabular Form
2. Calculation of Indefinte Integrals Using a Small Number of Values of the Integrand
3. Methods Which Use Several Previous Values of the Integral... |
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