Examples of using Vector field in English and their translations into Polish
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So this is the vector field.
Vector field is always 5.
You could have a vector field.
So the vector field on this region, it might look something like this.
So this is the vector field.
Let v be a vector field on M with isolated zeroes.
Let me draw this vector field f.
So the curl, you might guess,is equal to the cross product of our Dell operator and the vector field.
You start with the vector field, right?
You wouldn't get a temperature and a direction,so it's not a vector field.
So let's say my vector field is 5i.
The curl is the same throughout this entire vector field.
That's what this vector field would look like.
So we're done analyzing this vector field.
Let's say that this vector field shows the velocity of a fluid at various points.
Let's say I have a vector field.
So this velocity field or vector field will look something like this.
And let's say that we also have a vector field f.
When we took the dot product of this with a vector field, we got the divergence of the vector field. .
Or I gave you a scalar field and you got a vector field.
So that's consistent with what we found out, that the vector field gets very small at this point.
So div of v is the same thing as our del operator dot our vector field, v.
Let's say I have the vector field v.
We got our points,we figured out what coordinates are the magnitude of the vector field 0.
And actually, this is called an irrotational-- I think that's the word-- vector field. Where you're not going to have any rotation here.
But this is really any arbitrary vector field.
Let me draw another vector field.
Let me actually change it to my new vector field.
So if I had an infinitesimally small circle, or sphere, in this vector field, I would have no net density increasing.
Poincaré-Hopf theorem: a generalization of the hairy-ball theorem,which states that there is no smooth vector field on a sphere having no sources or sinks.