Say that it is a gradient field.
如果F是梯度场。
为什么要说F是一个梯度场?
What is meant by social gradient?
社会梯度是什么?
Now it should be a gradient field.
那么它应该就是一个梯度场。
请讲?,哦,不是梯度。
也就是梯度场。
Switch to the Gradient Tool (G).
切换到渐变工具(G)。
What is the gradient of this function?
这个函数的梯度是什么?
This is the social gradient in health.
这就是健康方面的社会梯度。
它不是梯度。
So, indeed, this is not a gradient field.
因此这不是一个梯度场。
Well, you take the gradient of a function.
作出一个函数的梯度。
The normal vector will just be the gradient.
法向量就是梯度向量。
Well, so, what's the gradient of this function?
那么,这一函数的梯度是什么?
Yes? How do I know the direction of a gradient?
我怎样知道梯度的方向?
OK.So what is our test for gradient fields?
那么怎样验证有势场呢?
Find the gradient. Find an approximation formula.
求梯度和近似公式。
Yes, that's right. The gradient tool is evil.
好,我用渐变工具完成了水管、山、砖块。
This background has a gradient applied to it.
背景应用有渐变。
The problem is not every vector field is a gradient.
问题是,不是所有向量场都是梯度。
So, the way to do it is that we compute the gradient.
方法应该是去计算出梯度。
It is a gradient field. We need three conditions.
这是一个有势场,我们需要三个条件。
But, so here's the first cool property of the gradient.
现在我们来看看梯度的第一个好性质。
We have said if we have a gradient field then we have this.
如果有一个梯度场,那就能得到这个。
So, if you prefer, that's where the gradient vector is zero.
认为梯度向量为零也是可以的。
Well, the gradient is also a way to package partials together.
同样地,梯度也是把偏导数糅合到一起。
When I am at a minimum, the two gradient vectors are parallel.
当在最小值点的时候,两个梯度向量就垂直了。
If you have a gradient field then it should have this property.
如果给定一个梯度场,那么它就应该满足这个性质。
You know it's a gradient, f and you know the function, little f.
如果知道一个梯度,相应地就有一个函数。
Altitude measurements mean the road's gradient can be determined.
海拔测量还可以判定出道路的坡度。
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