Estimating the order of magnitude of derivatives in physics by means of characteristic lengths and times

摘要

It is shown that, for many mathematical functions f or A used in physics, the order of magnitude of derivatives such as df/dt, dA/dt, delf, del . A, or del X A can be estimated relative to the order of magnitude of f or A, with the help of the characteristic times or characteristic lengths of f or A. This result provides a mathematical justification for the informal use of characteristic times and lengths often encountered in physics. The method is not applicable to all functions, however, and, when applicable, it cannot be applied blindly. (C) 2004 American Association of Physics Teachers.