Asymptotic Methods in Mechanics

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R mi Vaillancourt, Andrei L. Smirnov
American Mathematical Soc., Dec 21, 1993 - Technology & Engineering - 282 pages
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Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
 

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Contents

Asymptotic Expansions
5
Singular Perturbation of Linear Differential Equations
23
CHAPTER 3 Degenerate Boundary Value Problems
61
Asymptotic Solutions of Partial Differential Equations
81
Asymptotic Solutions of Nonlinear Differential Equations
103
Thirteen Papers
141
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Page xvii - This work was supported in part by the Natural Sciences and Engineering Research Council of Canada...