Asymptotic Expansions - Brossura

Erdelyi, A.

Brossura

ISBN 10: 0486603180 ISBN 13: 9780486603186

Casa editrice: Dover Pubns, 2003

Riassunto

Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.

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Contenuti:

Introduction; References Chapter I. Asymptotic Series 1.1 O-symbols 1.2 Asymptotic sequences 1.3 Asymptotic expansions 1.4 Linear operations with asymptotic expansions 1.5 Other operations with asymptotic expansions 1.6 Asymptotic power series 1.7 Summation of asymptotic series References Chapter II. Integrals 2.1 Integration by parts 2.2 Laplace integrals 2.3 Critical points 2.4 Laplace's method 2.5 The method of steepest descents 2.6 Airy's integral 2.7 Further examples 2.8 Fourier integrals 2.9 The method of stationary phase References Chapter III. Singularities of Differential Equations 3.1 Classification of singularities 3.2 Normal solutions 3.3 The integral equation and its solution 3.4 Asymptotic expansions of the solutions 3.5 Complex variable. Stokes' phenomenon 3.6 Bessel functions of order zero References Chapter IV. Differential Equations with a Large Parameter 4.1 Liouville's problem 4.2 Formal solutions 4.3 Asymptotic solutions 4.4 Application to Bessel functions 4.5 Transition points 4.6 Airy functions 4.7 Asymptotic solutions valid in the transition region 4.8 Uniform asymptotic representations of Bessel functions References

Product Description:

Asymptotic Expansions

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2003
• ISBN 10: 0486603180
• ISBN 13: 9780486603186
• Rilegatura: Copertina flessibile
• Numero di pagine: 128