Examples of using Vector field in English and their translations into Arabic
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Computer
Continuous vector fields.
And our vector field is going to be a little unusual;
And let's say we also have a vector field.
That's what this vector field would look like.
So I mean, this vector field might look something like this.
But this is really any arbitrary vector field.
Now last video, we dealt with a vector field that only had vectors in the i direction.
So here I have drawn,I'm going to just draw a two-dimensional vector field.
Line integral of this vector field, along some path.
So that's what the field isgoing to look like if I were to draw a bunch of vector field lines.
Let's build with another vector field that only has vectors in j direction, or the vertical direction.
More technically,the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
It only had an x-component, the vector field, but we have just simplified this line integral to being equivalent to-- maybe.
And then next two videos after this, we will try to see what this actually does to the line integral, one for a scalar field, and then one for a vector field.
You can almost imagine F being the addition of our vector fields, P and Q, that we did in the last two videos.
The neat thing here is using a vector field that only had an x-component, we were able to connect its line integral to the double integral over region-- oh, and I forgot something very important.
In the next video,I'm going to do the same exact thing with the vector field that only has vectors in the y-direction.
And this is a vector field that I'm drawing, where I'm just randomly picking points and showing the vector of the field at that point, that it's pointed outward, and at any given radius away from the circle.
The Seifert conjecture(1950), is that all vector fields on the three-sphere have at least one closed orbit.
For nematic liquid crystals, there is no difference between orienting a molecule in the n direction or in the-n direction, and the vector field n is then called a"director field".
And it's a neat way to relate a line integral of a vector field that has these partial derivatives, assuming it has these partial derivatives, to the region, to a double integral of the region.
What I want to do in the next few videos is try to see what happens to a line integral,either a line integral over a scalar field or a vector field, but what happens that line integral when we change the direction of our path?
So let's say that q, the vector field q of xy, say it's equal to capital Q of xy times j, and we are going to concern ourselves we're going to concern ourselves with though closed line integral around the path c of q dot dr.
In vector calculus,divergence is a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar.
These polynomial vector fields were studied by Poincaré, who had the idea of abandoning the search for finding exact solutions to the system, and instead attempted to study the qualitative features of the collection of all possible solutions.
A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. .
F(r, t) is a vector field at the spatial position r at time t, Σ is a moving surface in three-space bounded by the closed curve ∂Σ, dA is a vector element of the surface Σ, ds is a vector element of the curve ∂Σ, v is the velocity of movement of the region Σ, ∇⋅ is the vector divergence, × is the vector cross product, The double integrals are surface integrals over the surface Σ, and the line integral is over the bounding curve ∂Σ.
The second part of Hilbert's 16th problem is to decide an upperbound for the number of limit cycles in polynomial vector fields of degree n and, similar to the first part, investigate their relative positions.
An equipotential of a scalar potential function in n-dimensional space is typically an(n- 1)dimensional space.The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being'of equipotential' or simply be called'an equipotential'.