Asymptotic methods in mechanics of solids / Svetlana M. Bauer ... [et al.].
Contributor(s): Bauer, Svetlana M.Material type: BookSeries: International series of numerical mathematics, volume 167.Publisher: Cham, Switzerland : Birkhäuser / Springer International Publishing, c.2015Description: xxi, 325 p. : ill. ; 24 cm.ISBN: 9783319183107; 3319183109.Other title: Asimptoticheskie metody v mekhanike tverdogo tela [Title in Russian on title page verso:].Subject(s): Mathematical physics -- Asymptotic theory | Singular perturbations (Mathematics) | Differential equations -- Asymptotic theory | | Engineering, Electrical August 2016 DDC classification: 515.35 Online resources: Full text available on campus access | Full text available off campus access
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Based on the Russian version." Asimptoticheskie metody v mekhanike tverdogo tela"
Index : p. 323-325.
Bibliography : p. 319-321.
Asymptotic estimates -- Asymptotic estimates for integrals -- Regular perturbation of ordinary differential equations -- Singularly perturbed linear ordinary differential equations -- Singularly perturbed linear ordinary differential equations with turning points -- Asymptotic integration of nonlinear differential equations.
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. --