What does " to first order" mean ?

[dyn]

Hi. When using approximations such as g = n + h where h is much less than n ; what does " valid to first order in h" mean ? Does it mean include terms linear in h or does it mean drop those terms ?
Thanks

 

[andrewkirk]

It's the former. It's based on the idea of the amount - g in this case - being expressed as a Taylor series in h. To first order means including the constant term and the term that has $h^1$ but excluding all other terms that have $h^k$ for $k>1$.