In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as where is a very small parameter and is a 1-periodic coefficient:, . Frequently, inhomogeneous materials (such as composite materials) possess microstructure and therefore they are subjected to loads or forcings which vary on a length scale which is far bigger than the characteristic length scale of the microstructure. In this situation, one can often replace the equation above with an equation of the form from 1-periodic functions satisfying: