| Difference quotient and dimensionality -
04-04-2006, 07:05 PM
In calculus you have the difference quotient dy/dt = lim h->0 f(t+h)-f(t) / h
Consider f as a function of two variables, x and h.
f(t,h) = t+h
and f(x) seperately
This limit then defines an infinitesimal advance in the dimensionality of the equation. You essentially are adding a dimension represented by a variable that you are varying towards 0 (h). You are using this "trick" of adding a dimension to find out how it's changing in 2 dimensions - y,t,h - (if the equation has one dependent variable (y) and one independent variable (t).) Since the position function s(t) is the derivitive of the velocity function v(t), I believe that time as a changing quantity must be infinitesimally-dimensional, under this definition. |