It is found that the canonical momentum is directly proportional to the gradient of space phase.
发现正则动量与空间相的梯度成正比。
Now, what's the gradient vector?
现在，梯度向量是什么呢？
It points opposite to the gradient.
指向和梯度向量相反。
What is the gradient of this function?
这个函数的梯度是什么？
Well, you take the gradient of a function.
作出一个函数的梯度。
Adding one doesn't change the gradient.
加1并不改变梯度。
Set the gradient style to Radial Gradient .
设置渐变模式为径向(圆形)渐变 。
Well, so, what's the gradient of this function?
那么，这一函数的梯度是什么？
The normal vector will just be the gradient.
法向量就是梯度向量。
Find the gradient. Find an approximation formula.
求梯度和近似公式。
So, the way to do it is that we compute the gradient.
方法应该是去计算出梯度。
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。
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。
Click on the gradient to open up the gradient Editor dialog box.
点击渐变条打开渐变面板。
So, if actually show you the gradient, you can't really see it here.
如果展示梯度的话，在这儿是看不到的。
Notice the gradient backing of the button components in Figure 2.
请注意图2中按钮组件的渐变背景。
We have seen that the gradient is perpendicular to the level surface.
我们已经知道，梯度是垂直于等值面的。
Say that f, our vector field is actually the gradient of some function.
也就是向量场f实际上是一个函数的梯度。
If I fix a point, then the gradient vector at that point is given to me.
确定一点，那么对我来说，这点的梯度向量就是确定的。
You use this downward pointing triangle as the notation for the gradient.
用▽表示,这就是梯度的符号。
That means that the gradient of f is perpendicular to the level set of g.
也就是说f的梯度向量,应该与g的水平集垂直。
But they won't be the level curves of a function for which this is the gradient.
但它们不一定是，某个以该向量场为梯度的函数的等值线。
So, we said when we have a function of two variables, we have the gradient vector.
我们说，当一个二元函数存在时，就有梯度向量。
So now, let's go back to the gradient and see what this tells us about the gradient.
所以现在我们再回头看看梯度，看看它告诉了我们什么。
If you take the gradient of this, you should get again this vector field over there.
对这个函数取梯度，你应该又得到这个向量场。
And we have learned how to package partial derivatives into a vector, the gradient vector.
我们也知道了，如何将各个偏导组合成一个梯度向量。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
The directional derivative in a direction that's perpendicular to the gradient is basically zero.
垂直于梯度的方向上,方向导数为零。
And, maybe I should also say in words, this is the component of the gradient in the direction of u.
再强调一下，这是梯度函数在u方向上的分量。
But we know another vector that is also perpendicular to the level set of g. That is the gradient of g.
但我们知道有另外一个向量也是和g的等值面垂直的，这个向量就是g的梯度。
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