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.
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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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