Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
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。
Now, an important difference between curl here and curl in the plane is that now the curl of a vector field is again a vector field.
和平面上的旋度的一个重要的不同点是，这里向量场的旋度，仍然是一个向量场。
You have seen that in the plane it is already pretty hard to draw a vector field.
正如大家所知，在平面中画出向量场已经很困难了。
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。
One is to say that the vector field is a gradient in a certain region of a plane.
一个是向量场,在给定平面区域内是梯度场。
Just to remind you, a vector field in space is just the same thing as in the plane.
提醒大家，空间中的向量场与平面中的相同。
That was a vector field in the plane.
它是一个在平面上的向量场。
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。
In this paper, We have given the historical summary of the definition of vector and some application of vector Analyis on the field of vectors in a plane.
本文从数学史角度研究矢量的定义，以及矢量分析在平面夫场上的一些应用。
The obtained velocity vector distribution in the measured plane coincided with the flow visualization results under the same test condition. In addition these vortex flow field was analysed.
流场横截面内的速度矢量分布与相同实验条件下的流态显示结果相符合，并对涡流场加以分析。
The obtained velocity vector distribution in the measured plane coincided with the flow visualization results under the same test condition. In addition these vortex flow field was analysed.
流场横截面内的速度矢量分布与相同实验条件下的流态显示结果相符合，并对涡流场加以分析。
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