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Results tagged with vector-fields
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user 1168760
In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space.
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Is $\frac{∂}{x_{j}} \phi(\vec{r})$ at $\vec{ r}=0$ the same as $\frac{∂}{∂x_{j}} \phi(0)$ ca...
In the attached picture, the author evaluated first $ \frac{∂}{∂x_{j}} \phi(\vec{r})$ then to evaluate, in the line below it, $\frac{∂}{∂x_{j}} \phi(0)$, he simply substituted $\vec{r}=0$ in the calc …
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Shouldn't the numerator of the second term in the summation in the last result be $-3\alpha ...
Shouldn't the numerator of the second term in the summation in the last result be $-3\alpha x_{j0}(x_{k}-x_{k0})$?
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If $\vec{\nabla}× \vec{A}$=0, does this qualify as the necessary and sufficient condition fo... [duplicate]
If $\vec{\nabla} × \vec{A}=\vec{0}$, does this qualify as the necessary and sufficient condition for being able to writ $\vec{A}=\vec{\nabla}$ f where f is any scalar function?
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