This background has a gradient applied to it.
背景应用有渐变。
Salts are enriched around electriferous groups of polymer molecules in solution, which formed a salt concentration gradient.
溶液中的盐份富集在聚合物分子的带电基团附近，并形成盐浓度梯度分布。
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。
Now it should be a gradient field.
那么它应该就是一个梯度场。
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。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
为什么要说F是一个梯度场？
Yes? How do I know the direction of a gradient?
我怎样知道梯度的方向？
So, indeed, this is not a gradient field.
因此这不是一个梯度场。
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。
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。
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。
Yes? How do you determine whether something is a gradient or not?
怎样确定一个场是不是梯度？
Well, you take the gradient of a function.
作出一个函数的梯度。
So, if you have a gradient field, it's what's called conservative.
如果有一个梯度场，它也是一个保守场。
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。
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。
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。
也就是梯度场。
So, actually on Tuesday we'll see how to decide whether a vector field is a gradient or not, and if it is a gradient, how to find the potential function.
周二我们就知道，怎样确定一个场是不是梯度，如果确实是梯度的话，怎样算出势函数。
The question is for which value of a is this a gradient?
问题是a取多少时，这是一个梯度场？
It is a gradient field. We need three conditions.
这是一个有势场，我们需要三个条件。
Using the gradient Tool (g) with a Black to 0% opacity gradient, click and drag a gradient from the bottom up into the planet for the bottom and from the top down for the top of the planet.
使用渐变工具，设置黑色到0%不透明的渐变，从画布底部向上点击拖拉渐变到行星位置，然后，从画布顶部点击拖拉渐变到行星顶端。
Note that this is a radial gradient, whereas earlier you saw a linear gradient.
注意，这是一个放射状渐变，而此前您看到的是一个线性渐变。
So, in particular, only if you have a conservative field, a gradient field.
特别地，仅当是保守场，即有势场时才可以使用。
So as you can see below, here we're adding a Gradient Overlay from black to white, faded out a bit and on Overlay mode.
你在下面可以看到，这里我们正在添加一个从黑到白的梯度覆盖，在覆盖模式下淡化一点。
An image is used in the background to provide a gradient to white.
在背景中使用一个图像提供到白色的逐变。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
如果一个向量场不可能是梯度场，那我们就不应该尝试去找势函数。
添加一个渐变。
添加一个渐变。
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