This book presents the classical results of the two-scale convergence theory and explains -
using several figures - why it works. It then shows how to use this theory to homogenize
ordinary differential equations with oscillating coefficients as well as oscillatory singularly
perturbed ordinary differential equations. In addition it explores the homogenization of
hyperbolic partial differential equations with oscillating coefficients and linear oscillatory
singularly perturbed hyperbolic partial differential equations. Further it introduces readers
to the two-scale numerical methods that can be built from the previous approaches to solve
oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates
how they can be used efficiently. This book appeals to master's and PhD students interested in
homogenization and numerics as well as to the Iter community.
