# Small quantities in mathematica

by JohnSimpson
Tags: mathematica, quantities
 P: 91 Hi, I'm doing a calculation in which I have a small parameter $$\epsilon$$ floating around, and I want to automatically remove terms of order $$\epsilon^2$$ and higher. Is this possible to do?
 P: 91 Thanks!! One more question. Lets say I had something like $$\left( \begin{array}{cc} -2 \varepsilon & 1-\varepsilon \\ -1+\varepsilon & -1+2 \varepsilon \end{array} \right)$$ How could I retain the multiplicative terms but ditch the additive terms, so that this simplifies to $$\left( \begin{array}{cc} -2 \varepsilon & 1 \\ -1 & -1 \end{array} \right)$$
 P: 91 Right, sorry. What I want to do is say that epsilon is small compared to some other number, in this case 1, but to keep epsilon finite. $$0 < \varepsilon << 1$$ Therefore, -1 + 2epsilon is ROUGHLY -1. So the first matrix above simplifies under this approximation to the second one. EDIT: Hmmm, actually, I don't think the power series expansion is quite what I'm looking for. I'd like to have $$f(x) = \sqrt{x^2 + \varepsilon + \varepsilon^2} \simeq \sqrt{x^2 + \varepsilon}$$ since terms of eps^2 are very small compared to terms of power eps, but x is comparable to epsilon for small enough x. Unless I'm very confused a power series expansion in epsilon will not give me this. Any thoughts would be appreciated.