Asymptotic Methods For Integrals - Couverture rigide

Temme, Nico M

 
9789814612159: Asymptotic Methods For Integrals
Couverture rigide
ISBN 10 : 9814612154 ISBN 13 : 9789814612159
Editeur : World Scientific Publishing Co Pte Ltd, 2014

Synopsis

The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners. Zentralblatt Math This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

“The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt Math This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.

Revue de presse

The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners. --Zentralblatt MATH

I recommend this substantial text, complementing existing treatments, not only as an introductory text for graduate students but as a mine of information for experts. --Sir Michael Berry, University of Bristol, UK

This book compiles many of the relevant asymptotic methods for integrals, classical and modern, known nowadays. As the author is an expert, not only in asymptotics of integrals, but also in special functions, the book pays special attention to the application of asymptotic methods of integrals in the approximation of special functions. --Mathematical Reviews

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
World Scientific Publishing Co Pte Ltd
Date d'édition
2014
Langue
anglais
ISBN 10 
9814612154
ISBN 13 
9789814612159
Reliure
Relié
Nombre de pages
628
Coordonnées du fabricant
non disponible
Personne responsable
non disponible