So, in fact, it's a vector field.
事实上，是一个向量场。
这是向量场。
That was a vector field in the plane.
它是一个在平面上的向量场。
向量场。
So, this vector field is not conservative.
所以，这个向量场不是保守场。
Well, our vector field, is actually vertical.
向量场是竖直的。
Let's say I want to do it for this vector field.
比如说，我想对这个向量场来求解。
F I have my surface and I have my vector field f.
有一个曲面，还有一个向量场。
OK, so you take the divergence of a vector field.
取一个向量场的散度。
I want to find the potential for this vector field.
我想找出这个向量场的势函数。
Let's say that our vector field has two components.
假设我们的向量场有两个分量。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
We had a curve in the plane and we had a vector field.
平面上有一曲线，且存在着向量场。
But now, let's say that I have a general vector field.
但是现在，假设有一个一般向量场。
But it's a new vector field that you can build out of f.
这是一个新的向量场，可以用f来建立。
Let's say that my vector field has components p, Q and r.
假定我的向量场。
OK, so my vector field does something like this everywhere.
这个向量场处处都是这样。
Let's say that we had the same c, but now the vector field.
假设c还是一样的，但现在的向量场变为。
That actually is what we will call later a vector field.
这就是后面我们要讲的向量空间。
So, it's an example of a vector field that is not conservative.
这是一个非保守场的例子。
We need, actually, a vector field that is well-defined everywhere.
实际上我们需要，一个处处有定义的向量场。
OK, so let's assume that we have a vector field whose curl is zero.
假设有一个旋度为零的向量场。
That would be an example of a vector field that comes up in physics.
这是物理学中向量场的例子。
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。
We are just integrating a vector field that has nothing to do with that.
其实是要对一个与其无关的向量场积分，其实是要对一个与其无关的向量场积分。
OK, and that surface integral, well, it's not for the same vector field.
这个曲面积分，不是同一个向量场。
Vector field visualization has been a focus of visualization research.
向量场可视化是可视化研究的一个焦点。
Establishing a new model for non-motorized vehicle: vector field model.
建立了新的非机动车微观模型：矢量场模型。
Remember that was the vector field that looked like a rotation at the unit speed.
我们记得，这是个以单位速度旋转的向量场。
An attempt is to provide a clear overall picture of vector field visualization.
试图为矢量场可视化研究领域提供一个清晰的概貌。
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