We have a connection between that, which is Stokes theorem.
还有一种联系的方式就是Stokes定理。
But for that, I needed to be able to find a surface which to apply Stokes theorem.
但是对于这个，我需要找到一个可以运用Stokes定理的曲面。
So, I'm going to say a couple of words about surface independence in Stokes theorem.
我将讲述一些，关于Stokes定理的曲面独立性。
So, now that tells us we can actually apply Stokes theorem, except it won't fit here.
这告诉我们可以运用Stokes定理，这里写不开了。
Well, to be able to use Stokes theorem, I need, actually, to find a surface to apply it to.
为了能够应用Stokes定理，我需要找一个曲面来应用它。
Methods the method of shooting and bouncing rays was used to calculate the RCS and stokes theorem was used to improve the arithmetic.
研究复杂组合体目标后向散射场问题，并对射线跟踪法的典型算法进行改进，以提高计算精度和运算速度。
And that's why the flux for S1, and the flux for S2 were the same a priori and we didn't have to worry about which one we chose when we did Stokes theorem.
这就是为什么S1的通量，和S2的通量是相同的，当运用Stokes定理时，我们不用担心，选的是哪一个面。
Ok, one last thing I want to show you before we start reviewing, so one question you might have about Stokes theorem is, how come we can choose whatever surface we want?
在开始复习之前，我想讲点东西，大家对Stokes定理可能有一个疑问，我们如何选择我们想要的曲面？
Well, the orientation I should have for Stokes theorem is that Well, if you look at the convention around here, it tells us that the normal vector should be going this way.
对于Stokes定理中的定向——，观察这里，它的法向量应该是这个方向。
So, if we really wanted to apply Stokes theorem, because I've been telling you that space is simply connected, and I will always be able to apply Stokes theorem to any curve, what would I do?
因为我已经告诉过你们空间是单连通的，所以，如果我们真的想要运用Stokes定理，那么我总是可以把它运用于任何曲线，我应该做什么呢？
Yes. I have a yes. Let me explain to you quickly why Stokes is true. How do we prove a theorem like that?
来快速解释一下，为什么Stokes定理是对的，我们怎么来证明这样的一个定理呢？
If we apply Stokes' theorem to compute the work done by the electric field around a closed curve, that means you have a wire in there and you want to find the voltage along the wire.
如果用Stokes定理计算的话，电场对一条封闭曲线做的功，比如说，电厂中有一个金属线圈，想要知道金属线圈的电压是多少。
Then you wouldn't be able to Stokes' theorem at all or at least not directly.
那就不能用Stokes定理,至少不能直接用。
Now, let's instead try to use Stokes' theorem to do the calculation.
现在使用Stokes定理来算。
Well, it turns out we can do the same thing in space and that is called Stokes' theorem. What does Stokes' theorem say?
我们发现，在空间里面也可以做一样的事情，那是Stokes定理，Stokes定理说了什么呢？
Stokes' versus Green. I want to show you how Green's theorem for work that we saw in the plane, but also involved work and curl and so on, is actually a special case of this.
我想让你们看到，格林公式是怎么在这个平面中运用的，但是也牵涉到功和旋度等等，这也是比较特别的地方。
Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.
格林定理及其应用、三重积分、空间中的线积分和面积分、散度定理、斯托克斯定理应用。
Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications.
格林定理及其应用、三重积分、空间中的线积分和面积分、散度定理、斯托克斯定理应用。
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