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。
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。
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