"In the Green-function treatment of particle motion, a unit impulse is represented by a force F(t) = δ(t–t′) and is the analogue of the unit point source in spatial problems. The initial conditions play the role of boundary conditions."
In mathematics and particularly in dynamical systems, an initial condition is the initial value of a differential equation, difference equation, or other "time"-dependent equation which evolves in time. The most fundamental case, an ordinary differential equation of order k, generally requires k initial conditions to trace the equation's evolution through time. In other contexts, the term may refe
"The surprising discovery of Newton’s age is just the clear separation of laws of nature on the one hand and initial conditions on the other. The former are precise beyond anything reasonable; we know virtually nothing about the latter. ,,, … how can we ascertain that we know all the laws of nature relevant to a set of phenomena? If we do not, we would determine unnecessarily many initial conditions in order to specify the behavior of the object."
"Inflation has attracted cosmologists because of its potential to free the standard big bang model from its worst flaw, the need for special initial conditions and, in particular, the requirement of initial acausal homogeneity. Naturally one must check whether inflation itself depends critically on initial conditions. Several “no hair” theorems and perturbation calculations have indicated that inflation is stable, and that it will take place when the initial conditions are perturbed. This has led to the belief that inflation will start in any generic universe."