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。
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 。
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。
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。
Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point.
那意味着，梯度向量在这点上，垂直于切平面或者是等值面。
It tells you, if you take the line integral of the gradient of a function, what you get back is the function.
它说，如果你对一个函数的梯度做线积分，就能得到原函数。
And I can rewrite this in vector form as the gradient dot product the amount by which the position vector has changed.
可以把这些用向量形式重新写下来，就是梯度向量和位置改变量的点积。
The Fraunhofer device depends on a temperature gradient: the greater the gradient, the more electricity generated.
该装置根据温度变化率工作：温度变化率越大，产生的电能就越多。
So, I claim, in fact, we could have done this without the gradient, or using the gradient in a somehow disguised way.
事实上，我们可以不用梯度来求这个，或者说变相的利用梯度。
For example, the electric field or gravitational field is given by the gradient of the gravitational or electric potential.
例如由重力势梯度给出的重力场，或由电势梯度给出的电场。
Make sure that the gradient matches the one in the image below, you will have to adjust the colour location accordingly.
确保渐变条设置得与下图吻合，为此你要相应地去调整每个颜色的位置。
The final piece to defining the example login screen in Figure 2 is to draw the gradient background with the curved line.
定义图2中登录屏幕例子的最后工作是用曲线绘制渐变背景。
Then grab the gradient tool (shorcut ‘G’ on the keyboard) and setup a white to gray to white gradient like the one referenced below.
选择渐变工具（快捷键“G”），设置一个白-灰-白的渐变，如下图。
OK, so if I go in that direction, which gives me the fastest increase, then the corresponding slope will be the length of the gradient.
也就是说，如果朝该方向运动，函数值变动得最剧烈，那么相应的斜率就是梯度向量的模长。
OK, so that's the general method of calculation, but we've seen a shortcut for work when we can show that the field is the gradient of potential.
这就是计算的一般方法，但求功的时候，如果向量场是某个势的梯度,是有捷径可走的。
OK, so the new definition for today is the definition of the gradient vector. And, our goal will be to understand a bit better what does this vector mean?
所以今天我们的新定义，就是梯度向量，目的就是更好的理解这一定义，这个向量的含义是什么？
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