What does the notation Div with an arrow on top mean in PDE studies?

In summary, the conversation discusses the notation "Div with an arrow on top" used in PDE studies. It is clarified that this notation represents the divergence operator in Cartesian coordinates, and is often denoted by {\vec \nabla} or \nabla. The exact meaning of this notation may vary depending on the text, but it generally represents a vector-valued function.
  • #1
island-boy
99
0
I encountered this notation in my PDE studies, but I was confused by what it meant. What does the notation Div with an arrow on top (of the word) mean? I figured meant the divergence of something...but am curious about its exact meaning.
 
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  • #2
island-boy said:
I encountered this notation in my PDE studies, but I was confused by what it meant. What does the notation Div with an arrow on top (of the word) mean? I figured meant the divergence of something...but am curious about its exact meaning.
The divergence operator in Cartesian coordinates is
[tex] {\vec \nabla} = {\hat i} {\partial \over \partial x} + {\hat j} {\partial \over \partial y}+{\hat k} {\partial \over \partial z} [/tex]
 
  • #3
so [tex]div \rightharpoonup [/tex] = [tex]{\vec \nabla} [/tex] right?
hmm, makes sense. Thanks!
 
  • #4
Yes- since div f is a vector-valued function, many (but not all) texts use
[tex]{\vec \nabla} [/tex]
to represent it. Other texts use just [itex]\nabla[/itex].
 

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