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

Couverture
Springer Science & Business Media, 29 oct. 1999 - 593 pages
6 Avis
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

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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 ... Consulter l'avis complet

Table des matières

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
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