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Oscillations and Resonances : Volume I: Oscillations and resonances.
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make a...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin/Boston :
De Gruyter,
2016.
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| Colección: | De Gruyter series in nonlinear analysis and applications.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction ; 1. Asymptotic expansions and series ; 1.1 Definitions of Asymptotic Series and Examples ; 1.1.1 An Example of Divergent Series ; 1.1.2 Order Operators ; 1.1.3 Calibration Sequence. Asymptotic Series ; 1.1.4 Problems ; 1.2 Summation of Asymptotic Series.
- 1.2.1 Asymptotic Representation of Functions 1.2.2 Theorem on the Uniqueness of Asymptotic Expansion ; 1.2.3 Theorem on Existence of a Function with the Given Asymptotic Expansion ; 1.2.4 Problems ; 1.3 Laplace Method and Gamma Function.
- 1.3.1 Asymptotic Expansion of Integral when Subintegral Function Exponent Does Not Contain Extrema 1.3.2 Asymptotic Expansion of Integral, When Integrand Exponent Contains Extrema ; 1.3.3 Derivation of Integral Formula for Gamma Function ; 1.3.4 Moivre-Stirling Formula ; 1.3.5 Problems.
- 1.4 Fresnel Integral and Stationary Phase Method 1.4.1 Riemann Lemma ; 1.4.2 Fresnel Integral Formulae ; 1.4.3 Large Values of Argument ; 1.4.4 Method of Stationary Phase ; 1.4.5 Problems ; 1.5 Airy Function and Its Asymptotic Expansion ; 1.5.1 Airy's Equation.
- 1.5.2 An Integral Representation of General Solution for Airy Equation 1.5.3 Asymptotic Expansion for the Airy Function as z? -8 ; 1.5.4 Saddle-Point Method and the Airy Function Asymptotic Expansion as z?8 ; 1.5.5 Problem ; 1.6 Functions of Parabolic Cylinder.