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Why is it that
[tex]\vec{A}\cdot\nabla \neq \nabla\cdot\vec{A}[/tex]
?
edit: sorry about that. fixed the typo.
[tex]\vec{A}\cdot\nabla \neq \nabla\cdot\vec{A}[/tex]
?
edit: sorry about that. fixed the typo.
Last edited:
Why is it that
[tex]\vec{A}\cdot\nabla \neq \vec{A}\cdot\nabla[/tex]
?
Why is it that
[tex]\vec{A}\cdot\nabla \neq \nabla\cdot\vec{A}[/tex]
?
edit: sorry about that. fixed the typo.
"Dot Del" is what is technically referred to as an "abuse of notation". Of course, some people consider del to be an abuse of notation in itself.
You see, by itself [tex]\nabla[/tex] is just [tex](\frac{\partial}{\partial x_1},\frac{\partial}{\partial x_2}, \ldots , \frac{\partial}{\partial x_n})[/tex]. It's nice but all the derivatives have the same coefficient on them (i.e. one).
To allow for more general operators we use [tex]A \cdot \nabla[/tex] to stand for [tex](a_1 \frac{\partial}{\partial x_1} , a_2 \frac{\partial}{\partial x_2} , \ldots , a_n \frac{\partial}{\partial x_n})[/tex]