User:Boris Tsirelson/Sandbox1

In Newtonian mechanics, coordinates of moving bodies are functions of time. For example, the classical equation for a falling body; its height at a time t is

$h(t)=h_{0}-{\frac {1}{2}}gt^{2}$

(here h₀ is the initial height, and g is the acceleration due to gravity). The height changes in time, but the function h does not.

PD Image
A function changes in time

The instantaneous shape of a vibrating string is described by a function (the displacement is a function of the coordinate), and this function changes in time.

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Wave equation (classical physics)

Partial differential equation