  We present a derivation of a coarse-grained model from the Langevin dynamics.
The focus is placed on the memory kernel function and the
fluctuation-dissipation theorem. Also presented is an hierarchy of
approximations for the memory and random noise terms, using rational
approximations in the Laplace domain. These approximations offer increasing
accuracy. More importantly, they eliminate the need to evaluate the integral
associated with the memory term at each time step.
