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Divergence of a vector field 
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#1
Apr2312, 09:52 PM

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1. The problem statement, all variables and given/known data
F(x,y,z) = (x+y)i + (y+z)j + (z+x)k Find divergence 2. Relevant equations 3. The attempt at a solution The gradient is i + j + k Dotting that with F, I get x  y + y + z + z  x = 2z My book lists the answer as 1. What the heck are they talking about? (they did not ask me to evaluate for any point) 


#2
Apr2312, 10:15 PM

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#4
Apr2312, 10:19 PM

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Divergence of a vector field
Is it correct to say that it's like taking grad F, then adding up the resulting components for a scalar?



#5
Apr2312, 10:23 PM

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#6
Apr2312, 10:36 PM

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I see my misunderstanding now. The del operator is not the gradient of anything in particular. It's just (d/dx)i + (d/dy)j + (d/dz)k. Dot product that with F leads to the correct definition.
This actually clears up a lot of the past notation. Since del is not a gradient of anything in particular, when we say [itex]\nabla f[/itex], since f is a scalar being multiplied by some vector, del, the result is a vector, which is the gradient of f. Cool. :) 


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Apr2312, 10:39 PM

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