Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory

Bender, Carl M. M.; Orszag, Steven A.

ISBN 10: 1441931872 / ISBN 13: 9781441931870

Edité par Springer, 2010

A propos de cet article

N° de réf. du vendeur I-9781441931870

Détails bibliographiques

• Titre: Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory
• Éditeur: Springer
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 1441931872
• ISBN à 13 chiffres: 9781441931870
• Reliure: Couverture souple
• État de l'article: New

A propos de ce titre

Synopsis

Intended for graduate students and advanced undergraduates, this book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute- force numerical methods may not provide useful solutions.

Présentation de l'éditeur

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.