# Advanced Mathematical Methods for Scientists and Engineers: Assymptotic Methods and Perturbation Theory

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

Valutazione media 4,4
( su 20 valutazioni fornite da GoodReads )

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.

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Recensione:

"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics.

This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic."  (A.D. Wood, Mathematical Reviews)

Contenuti:

I Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index

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## 1.Advanced Mathematical Methods for Scientists and Engineers I: v. 1

Editore: Springer-Verlag New York Inc. 1999-10-01, New York, NY (1999)
ISBN 10: 0387989315 ISBN 13: 9780387989310
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Descrizione libro Springer-Verlag New York Inc. 1999-10-01, New York, NY, 1999. hardback. Condizione libro: New. Codice libro della libreria 9780387989310

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## 2.Advanced Mathematical Methods for Scientists and Engineers I

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Descrizione libro Condizione libro: Brand New. New. SoftCover International edition. Different ISBN and Cover image but contents are same as US edition. Customer Satisfaction guaranteed!!. Codice libro della libreria SHUB98051

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## 3.Advanced Mathematical Methods for Scientists and Engineers I

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Descrizione libro Condizione libro: New. New. International edition. Perfect condition. Ship by express service to USA, Canada, Australia, France, Italy, UK, Germany and Netherland. Customer satisfaction our priority. Codice libro della libreria ABE-FEB-98051

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## 4.Advanced Mathematical Methods for Scientists and Engineers I

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## 5.Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

Editore: Springer (1999)
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Descrizione libro Springer, 1999. Hardcover. Condizione libro: New. book. Codice libro della libreria 0387989315

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## 6.Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (v. 1)

Editore: Springer (1999)
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Descrizione libro Springer, 1999. Hardcover. Condizione libro: New. 1999. This item is printed on demand. Codice libro della libreria DADAX0387989315

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## 7.Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory: v. 1

Editore: Springer (1999)
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Descrizione libro Springer, 1999. Condizione libro: New. Codice libro della libreria UA9780387989310

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## 8.Advanced Mathematical Methods for Scientists and Engineers I. Asymptotic Methods and Perturbation Theory

Editore: Springer (1999)
ISBN 10: 0387989315 ISBN 13: 9780387989310
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Descrizione libro Springer, 1999. Hardback. Condizione libro: NEW. 9780387989310 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0276951

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## 9.Advanced Mathematical Methods for Scientists and Engineers I: v. 1

Editore: Springer-Verlag New York Inc. (1999)
ISBN 10: 0387989315 ISBN 13: 9780387989310
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Descrizione libro Springer-Verlag New York Inc., 1999. HRD. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria I1-9780387989310

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## 10.Advanced Mathematical Methods for Scientists and Engineers I

Editore: Springer Okt 1999 (1999)
ISBN 10: 0387989315 ISBN 13: 9780387989310
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Descrizione libro Springer Okt 1999, 1999. Buch. Condizione libro: Neu. 235x155x38 mm. Neuware - 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 comput er-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. 612 pp. Englisch. Codice libro della libreria 9780387989310

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