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

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The discussion revolves around the notation "Div" with an arrow on top, specifically in the context of partial differential equations (PDEs). Participants are exploring its meaning and implications within mathematical notation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to clarify the meaning of the notation and its relation to the divergence operator. There are questions about whether it represents a vector-valued function and how different texts may present this notation.

Discussion Status

The discussion includes some participants confirming that the notation is indeed related to the divergence operator and discussing variations in its representation across different texts. There is an ongoing exploration of these interpretations without a definitive consensus.

Contextual Notes

Some participants note that the divergence operator can be represented in various ways, which may lead to confusion. The context of PDE studies is emphasized, highlighting the specific area of mathematics being discussed.

island-boy
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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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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]
 
so [tex]div \rightharpoonup[/tex] = [tex]{\vec \nabla}[/tex] right?
hmm, makes sense. Thanks!
 
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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