Asymptotic methods in mechanics of solids [electronic resource] / Svetlana M. Bauer, Sergei B. Filippov, Andrei L. Smirnov, Petr E. Tovstik, Remi Vaillancourt.
2015
QA372
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Title
Asymptotic methods in mechanics of solids [electronic resource] / Svetlana M. Bauer, Sergei B. Filippov, Andrei L. Smirnov, Petr E. Tovstik, Remi Vaillancourt.
ISBN
9783319183114 electronic book
3319183117 electronic book
9783319183107
3319183117 electronic book
9783319183107
Published
Cham : Birkhäuser, 2015.
Language
English
Description
1 online resource (xxi, 325 pages) : illustrations.
Item Number
10.1007/978-3-319-18311-4 doi
Call Number
QA372
Dewey Decimal Classification
515/.35
Summary
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.
Note
"Based on the Russian version."
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 4, 2015).
Added Author
Series
International series of numerical mathematics ; volume 167.
Available in Other Form
Print version: 9783319183107
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Table of Contents
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.
Bibliography
Index.