Titlebook: Linear Turning Point Theory; Wolfgang Wasow Book 1985 Springer Science+Business Media New York 1985 Algebra.Calculation.Invariant.Variable

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Ejaculate

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GUILT

pineal-gland

Uniform Transformations at Turning Points: Formal Theory, potential turning points were removed. In this chapter domains containing turning points will be considered, and the first question is: How far can the differential equation be simplified by . transformations with well understood asymptotic properties in such regions. The essence of Langer’s method

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Extensions of the Regions of Validity of the Asymptotic Solutions,, neighborhoods of a point. Several techniques exist for the study of the asymptotic properties of the solutions in larger domains. Most of those methods have to be adapted to specific examples, because general theories are either too difficult or so cumbersome as to yield little insight. Here is a

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Doubly Asymptotic Expansions,of the asymptotic theory one has to characterize functions of x and ∈ by their behavior near x = ∞ in some unbounded region of the x-plane, the knowledge of doubly asymptotic expansions is extremely helpful. Unfortunately, all known results of some generality in this direction require that the coeff

Affectation

A Singularly Perturbed Turning Point Problem,ins positive are now commonly called “singular perturbation problems.” The condition that the order remain positive for ∈ = 0 is not a very distinguishing property of the differential equation as such. The equation . . a constant,for instance, which will be examined closely in the next section, beco