Abstract
In this chapter we present the fundamental idea of separation of fast and slow variables introduced by H. Poincare in his studies on celestial mechanics. The case study conductivity problem is used to illustrate the method of two-scale asymptotic expansions. This method, which is based on the idea of separation of slow and fast variables, proved to be extremely efficient not only in homogenization problems but also in the variety of other applications. In the context of the case study conductivity problem we also introduce the so-called corrector problem which is the heart of the homogenization method.
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