The eigenvalue equation and approximate formula for cut-off frequencies of guided modes are obtained by vector-field-method.
采用矢量场法，得到了在弱导条件下传导模式的特征方程和截止频率的近似计算公式。
So, this vector field is not conservative.
所以，这个向量场不是保守场。
We dot our favorite vector field with it.
用我们喜欢的向量场来点乘它。
That was a vector field in the plane.
它是一个在平面上的向量场。
I want to find the potential for this vector field.
我想找出这个向量场的势函数。
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。
Vector field visualization is an important part of visualization in scientific computing.
矢量场可视化是科学计算可视化的重要组成部分。
Vector field is important conception in science and engineering, which describes directional information of physical procedure and developing trends of states.
向量场是科学和工程中的重要概念，描述物理过程中的方向信息和状态的变化趋势。
At the origin, the vector field is not defined.
在原点，向量场是没有意义的。
So, in fact, it's a vector field.
事实上，是一个向量场。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
Let's say that our vector field has two components.
假设我们的向量场有两个分量。
Well, our vector field, is actually vertical.
向量场是竖直的。
That is called the curl of a vector field.
这个量叫向量场的旋度。
OK, so my vector field does something like this everywhere.
这个向量场处处都是这样。
One is the vector field whose flux you are taking.
一个是要取通量的向量场。
It's a vector field that just rotates around the origin counterclockwise.
这是一个绕原点逆时针旋转的向量场。
My vector field is really sticking out everywhere away from the origin.
即给定的向量场是以原点为心向外延伸的。
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。
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。
I have a curve in the plane and I have a vector field.
这有一条平面曲线和一个向量场。
OK, so you take the divergence of a vector field.
取一个向量场的散度。
F I have my surface and I have my vector field f.
有一个曲面，还有一个向量场。
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。
Well, I want to figure out how much my vector field is going across that surface.
下面我们要搞清楚，这个向量场是如何穿过曲面的。
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。
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。
Let's say that I have a plane curve and a vector field in the plane.
有一条平面曲线和这个平面上的向量场。
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。
We have a sphere of radius a. I have my vector field.
先作出半径为a的球面，再画出给定的向量场。
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