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

Springer, Oct 29, 1999 - Mathematics - 593 pages
This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain 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 converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader 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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#### Review: Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory

User Review  - Joecolelife - Goodreads

I have learned a lot of asymptotic methods from this book, having spent several previous years wondering what that stationary phase method that the physicsts were on about was (by the way B&O poo-poo ... Read full review

### Contents

 II 3 III 5 IV 7 V 11 VI 14 VII 20 VIII 24 IX 27
 XLV 276 XLVI 280 XLVII 302 XLVIII 306 XLIX 319 L 324 LI 330 LII 335

 X 29 XI 30 XII 36 XIII 37 XIV 40 XV 49 XVI 53 XVIII 61 XIX 62 XX 66 XXI 68 XXII 76 XXIII 88 XXIV 103 XXV 107 XXVI 118 XXVII 136 XXVIII 146 XXIX 148 XXX 152 XXXI 171 XXXII 185 XXXIII 196 XXXIV 205 XXXV 206 XXXVI 214 XXXVII 218 XXXVIII 227 XXXIX 233 XL 240 XLI 247 XLII 249 XLIII 252 XLIV 261
 LIII 350 LIV 361 LV 368 LVI 379 LVII 383 LVIII 395 LIX 400 LX 405 LXI 410 LXII 419 LXIII 426 LXIV 431 LXV 435 LXVI 446 LXVII 455 LXVIII 463 LXIX 479 LXX 484 LXXI 493 LXXII 497 LXXIII 504 LXXIV 519 LXXV 524 LXXVI 534 LXXVII 539 LXXVIII 544 LXXIX 549 LXXX 551 LXXXI 560 LXXXII 566 LXXXIII 569 LXXXIV 577 LXXXV 581 Copyright

### References from web pages

JSTOR: Advanced Mathematical Methods for Scientists and Engineers
Advanced mathematical methods for scientists and engineers, by Carl M. Bender and Steven A. Orszag. Pp xiv, 593. 1978. SBN 0 07 004452 X (mcgraw-Hill) The ...

Advanced mathematical methods for scientists and engineers I ...
Advanced Mathematical Methods for Scientists and Engineers I. Asymptotic Methods and Perturbation Theory Volume package: Bender,cm;Orszag,sa: Adv.Math. ...

anziam 2000
Book Review: Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods ond Perturbation Theory. Reviewed by John Billingham ...
www.amsta.leeds.ac.uk/ Applied/ news.dir/ issue20.dir/ art/ art.html

Advanced mathematical methods for scientists and engineers — UWA ...
Advanced mathematical methods for scientists and engineers. Author: Bender, cm and Orszag, sa. Edition:. Publisher: mcgraw Hill. UWA Library Call Number: ...
www.maths.uwa.edu.au/ book-repository/ book.2006-02-24.7449331296

Noise small-correlation-time effects on the dispersion of passive ...
10: BENDER cm AND ORSZAG sa, Advanced Mathematical Methods for Scientists and Engineers (mcgraw-Hill) 1978. 11: CASTIGLIONE P. AND CRISANTI A., ...
www.iop.org/ EJ/ article/ 0295-5075/ 43/ 5/ 522/ node1.html

Advanced Mathematical Methods for Scientists and Engineers ...
Advanced Mathematical Methods for Scientists and Engineers: Asymptotic الهندسة الميكانيكية.

Mathematical Physics
Carl M. Bender and Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, ISBN 0387989315, Springer, 1999. ...
fy.chalmers.se/ ~kinaret/ mathphys.html

Carl M. Bender
He co-authored Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, which, according to J. Ely Shrauner, ...
news-info.wustl.edu/ sb/ page/ normal/ 149.html

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Advanced Mathematical Methods for Scientists and Engineers. This book gives a clear, practical and self-contained presentation of the methods of asymptotics ...