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＜電子ブック＞
Asymptotic methods in mechanics of solids / by Svetlana M. Bauer, Sergei B. Filippov, Andrei L. Smirnov, Petr E. Tovstik, Rémi Vaillancourt
(International Series of Numerical Mathematics. ISSN:22966072 ; 167)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2015
本文言語	英語
大きさ	XXI, 325 p. 88 illus : online resource
著者標目	*Bauer, Svetlana M author Filippov, Sergei B author Smirnov, Andrei L author Tovstik, Petr E author Vaillancourt, Rémi author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mechanics FREE:Differential Equations FREE:Classical Mechanics
一般注記	Asymptotic Estimates.- Asymptotic Estimates for Integrals.- Regular Perturbation of ODE's.- Singularly Perturbed Linear ODE's.- Linear ODE's with Turning Points.- Asymptotic Integration of Nonlinear ODE's -- Bibliography -- Index The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic HTTP:URL=https://doi.org/10.1007/978-3-319-18311-4

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