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Not sure what square brackets indicate when dealing with partial derivates 
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#1
Dec1212, 04:49 AM

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Hi guys, attached is a picture of my problem and it is also underlined.
I've been reading through this theory and I just don't understand what the square brackets indicate. I understand that ∇phi is the partial derivative with respect to the scalar function phi. But what is ∇phi [r(t)] ? I feel ashamed asking this like I'm going to be laughed at. 


#2
Dec1212, 06:53 AM

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##\nabla\phi## is the the gradient of ##\phi##: it is read "grad phi" or "del phi".
So it involved taking the partial derivative of phi with respect to each coordinate axis. http://en.wikipedia.org/wiki/Gradient ##\phi[\vec{r}(t)]## is just telling you that ##\phi## is a function of ##\vec{r}## which, in turn, is a function of ##t##. What they've done is parameterized the path represented by the C. Having turned ##\phi## into a function of just one variable, the gradient is much simplified. 


#3
Dec1212, 07:51 AM

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They are just using "[ ]" in place of "( )" because they are already using "( )" for the "[itex]\vec{r}(t)[/itex]" and don't want to have "))". There is no difference in meaning.



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