So, in fact, it's a vector field.
事实上，是一个向量场。
这是向量场。
That was a vector field in the plane.
它是一个在平面上的向量场。
It is proportional to this vector field.
它与向量场成比例。
We dot our favorite vector field with it.
用我们喜欢的向量场来点乘它。
向量场。
So, this vector field is not conservative.
所以，这个向量场不是保守场。
That is called the curl of a vector field.
这个量叫向量场的旋度。
Well, our vector field, is actually vertical.
向量场是竖直的。
At the origin, the vector field is not defined.
在原点，向量场是没有意义的。
Let's say I want to do it for this vector field.
比如说，我想对这个向量场来求解。
F I have my surface and I have my vector field f.
有一个曲面，还有一个向量场。
OK, so you take the divergence of a vector field.
取一个向量场的散度。
One is the vector field whose flux you are taking.
一个是要取通量的向量场。
I want to find the potential for this vector field.
我想找出这个向量场的势函数。
Let's say that our vector field has two components.
假设我们的向量场有两个分量。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
We have a sphere of radius a. I have my vector field.
先作出半径为a的球面，再画出给定的向量场。
I have a curve in the plane and I have a vector field.
这有一条平面曲线和一个向量场。
We had a curve in the plane and we had a vector field.
平面上有一曲线，且存在着向量场。
But now, let's say that I have a general vector field.
但是现在，假设有一个一般向量场。
But it's a new vector field that you can build out of f.
这是一个新的向量场，可以用f来建立。
OK, so my vector field does something like this everywhere.
这个向量场处处都是这样。
We have a vector field that gives us a vector at every point.
有一个向量场来描述每一个点上的向量。
So, it's an example of a vector field that is not conservative.
这是一个非保守场的例子。
We need, actually, a vector field that is well-defined everywhere.
实际上我们需要，一个处处有定义的向量场。
s Let's say that we have a vector field and s, a surface in space.
假设空间中存在一个向量场和一个曲面。
OK, so let's assume that we have a vector field whose curl is zero.
假设有一个旋度为零的向量场。
Let's say that I have a plane curve and a vector field in the plane.
有一条平面曲线和这个平面上的向量场。
That would be an example of a vector field that comes up in physics.
这是物理学中向量场的例子。
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