That is called the curl of a vector field.
这个量叫向量场的旋度。
The curl of a vector field in space is actually a vector field, not a scalar function. I have delayed the inevitable.
空间中的向量场的旋度，是一个向量场，而不是一个标量函数，我必须告诉你们。
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。
And that is indeed going to be the curl of F. in practice, if you have to compute the curl of a vector field, you know, don't try to remember this formula.
这就是F的旋度，在实际应用中，如果你必须计算一个向量场的旋度，不要尝试记忆这个公式。
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。
So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.
其中一种说明了，在向量场上，沿逆时针方向，向量做的功等于，平面区域上旋度F的二重积分。
So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.
其中一种说明了，在向量场上，沿逆时针方向，向量做的功等于，平面区域上旋度F的二重积分。
应用推荐