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Asymptotic methods in mechanics of s...

Bauer, Svetlana M.

Asymptotic methods in mechanics of solids

Record Type:	Electronic resources : Monograph/item
Title/Author:	Asymptotic methods in mechanics of solidsby Svetlana M. Bauer ... [et al.].
other author:	Bauer, Svetlana M.
Published:	Cham :Springer International Publishing :2015.
Description:	xxi, 325 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equationsAsymptotic theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-18311-4
ISBN:	9783319183114 (electronic bk.)

Asymptotic methods in mechanics of solids
Asymptotic methods in mechanics of solids[electronic resource] /by Svetlana M. Bauer ... [et al.]. - Cham :Springer International Publishing :2015. - xxi, 325 p. :ill., digital ;24 cm. - International series of numerical mathematics,v.1670373-3149 ;. - International series of numerical mathematics ;v. 136..

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.

ISBN: 9783319183114 (electronic bk.)

Standard No.: 10.1007/978-3-319-18311-4doiSubjects--Topical Terms:

245835
Differential equations
--Asymptotic theory.

LC Class. No.: QA372

Dewey Class. No.: 515.35

Asymptotic methods in mechanics of solids
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300 $a xxi, 325 p. : $b ill., digital ; $c 24 cm.
490 1 $a International series of numerical mathematics, $x 0373-3149 ; $v v.167
505 0 $a 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.
520 $a 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.
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650 1 4 $a Mathematics. $3 184409
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Partial Differential Equations. $3 274075
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