So, that's the divergence theorem.
这就是散度定理。
So, what does the divergence theorem say?
那么散度定理究竟讲的是什么？
And that is called the divergence theorem.
那就是散度定理。
That is Green for flux and that is the divergence theorem.
也就是通量的格林公式——散度公式。
At that part is actually math, namely, the divergence theorem.
那部分是数学的东西，即散度定理。
So, that's by the divergence theorem using the fact that s is a closed surface.
所以那是通过散度定理得到的，其中使用了S是封闭曲面这一事实。
OK, so we have somehow a connection between these which is the divergence theorem.
在某种方式下它们是有联系的,这就是散度定理。
So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.
散度定理为我们提供了一种，计算向量场通过闭曲面的通量的方法。
The convention in the divergence theorem is that we orient the surface with a normal vector pointing always outwards.
在散度定理中的约定是,将曲面的定向取为外法线的方向。
So, instead of proving the divergence theorem, namely, the equality up there, I'm going to actually prove something easier.
我将要证明一些稍简单的结论，而不是证明散度定理，也就是写在这儿的等式，接下来证明点简单的东西。
This one here, the divergence theorem, tells you something similar but now for a region of space bounded by a closed surface.
这个就是散度公式了，告诉大家一些相似的东西，仅仅是对被闭合曲面包围的空间区域来讲的。
And the second piece of information that we got was from the divergence theorem, and that was the one I spent time trying to explain.
第二点信息是，我们从散度定理得到的，这就是我花费时间试图解释的。
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。
There is a similar thing with the divergence theorem, of course, with flux and double integral of div f, you can apply exactly the same argument.
有一个和散度定理很像的东西，当然，对于通量和div,f的二重积分，都可以使用类似的理论。
Topics for the electric field mathematics include: The integral form of Coulomb's Law, Gauss's Law, the equations of Laplace and Poisson, and the divergence theorem.
电场的数学基础包括：库仑定律的积分形式、高斯定理的积分形式，拉普拉斯公式和泊松公式，散度定理。
Now, of course, 02 if you're doing 8.02, then you might actually have seen the divergence theorem already being used for things that are more like force fields, say, electric fields and so on.
自然地，如果你们上过8。,可能已经看到，散度定理的应用,在诸如力场、电场上的应用。
So, remember, when we set up the divergence theorem, we need the normal vectors to point out of our region, which means that on the top surface, n But, on the bottom face, we want n pointing down.
当我们建立散度定理时，我们要使法向量指向区域外，即在上表面时，要指向上方。，we，want，n，pointing，up。,但是，在下表面，要使n指向下面。
So, remember, when we set up the divergence theorem, we need the normal vectors to point out of our region, which means that on the top surface, n But, on the bottom face, we want n pointing down.
当我们建立散度定理时，我们要使法向量指向区域外，即在上表面时，要指向上方。，we，want，n，pointing，up。,但是，在下表面，要使n指向下面。
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