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Introduction

Part of the Lecture Notes in Mathematics book series (LNM,volume 2114)

Abstract

Chapter 1 provides an easy introduction to perturbation methods. It begins with an algebraic equation and proceeds to a second order ODE. The concept of an initial or boundary layer is introduced. This motivates the method of multiple scales. The idea of slow surfaces and slow integral manifolds is introduced and illustrative examples are given. Then a statement of Tikhonov’s theorem is given which answers the question about the permissibility of the application of a “degenerate” system (\(\varepsilon = 0\)) as a zero-approximation to the full system.

Keywords

  • Asymptotic Expansion
  • Invariant Manifold
  • Order Differential Equation
  • Integral Manifold
  • Secular Term

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Shchepakina, E., Sobolev, V., Mortell, M.P. (2014). Introduction. In: Singular Perturbations. Lecture Notes in Mathematics, vol 2114. Springer, Cham. https://doi.org/10.1007/978-3-319-09570-7_1

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