Titlebook: Asymptotology; Ideas, Methods, and Igor V. Andrianov,Leonid I. Manevitch,Michiel Haze Book 2002 Springer Science+Business Media Dordrecht

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Asymptotic Methods and Physical Theories,nary eye, but where an experienced eye is able to find the signs of the preceding work of past ages. Thus, it would be wrong to think that theories which went out of fashion were futile and unnecessary” (Poincaré, 1946).

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Fathers of Asymptotic Methods, should be included in all textbooks devoted to asymptotic analysis. This has much to do with searching for the motivations of the various concepts which are necessary for real penetration into the essence of a subject.

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A Little History,ne, J.-H. Poincaré, B. van der Pol, U.J.J. Le Verrier, L.I. Mandelshtam, N.D. Papaleksi, N.M. Krylov, N.N. Bogoliubov, and others. We are only going to trace some of the stages of development of this method.

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https://doi.org/10.1007/978-1-4419-9162-1Mathematica; applied mathematics; history of mathematics; perturbation; perturbation theory

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978-1-4613-4816-0Springer Science+Business Media Dordrecht 2002

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https://doi.org/10.1007/978-3-642-56775-9 of the theory and for its further development the simplest limit cases, which allow analytical solutions, are of particular importance. In those limits the number of equations usually decreases, their order reduces, nonlinear equations are replaced by linear ones, the initial system becomes average