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    $\begingroup$ I'm curious, where have you seen that equation with $\pm\vec{F}$? I have never seen it with a plus sign. $\endgroup$
    – David Z
    Commented Dec 30, 2011 at 1:40
  • $\begingroup$ pretty much in any calculus book? $\endgroup$
    – Lemon
    Commented Dec 30, 2011 at 2:37
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    $\begingroup$ Not just any calculus book, or at least not the ones I've used as far as I remember. If you give a specific reference I can elaborate... but that should be done in Physics Chat. $\endgroup$
    – David Z
    Commented Dec 30, 2011 at 2:51
  • $\begingroup$ OP writes $\vec{\nabla}(\pm U) =\vec{F}$. The whole question seems to be just a sign flip $U\leftrightarrow -U$. $\endgroup$
    – Qmechanic ♦
    Commented Dec 30, 2011 at 14:08