In a few weeks, we will be triple integrals.
几个星期后，我们会学习三重积分。
Well, remember we were trying to do triple integrals.
我们学过了三重积分。
Other kinds of integrals we have seen are triple integrals.
我们学过的另一种积分是三重积分。
So now we're going to triple integrals in spherical coordinates.
现在，在球坐标中进行三重积分。
See, this is actually good practice to remember how we set up triple integrals.
这是建立三重积分的绝佳练习。
OK, so triple integrals over a region in space, we integrate a scalar quantity, dV.
那么在一个空间上的区域的三重积分，对标量dV做积分。
OK, so I'm going to divide my blackboard into three pieces, and here I will write triple integrals.
我要把我的黑板分成三部分，在这我将要写三重积分。
And so that was stuff about double and triple integrals and vector calculus in the plane and in space.
也就是二重和三重积分的内容，以及平面和空间中的向量积分。
OK, so these are just formulas to remember for examples of triple integrals It doesn't change conceptually.
这些都是三重积分的例子，从概念上讲是相同的。
We have been working with triple integrals and seeing how to set them up in all sorts of coordinate systems.
我们目前已经学习了三重积分，以及如何在各种坐标系中建立它们。
When we do triple integrals in space, well, it is the same kind of story, except now we have, of course, more coordinate systems.
做三重积分，和二重一样，当然，我们会有更多的坐标系。
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。
In this paper, some relationships between improper double integral and improper iterated are discussed, and the corresponding results are generalized into the improper triple integrals.
本文通过讨论广义重积分与广义逐次积分之间的关系，得出一些结论，并将相应结果推广到广义三重积分与广义三次积分中。
This paper gives the general description of the definition of curve, curved surface and triple integrals, and derives a theorem on simplified integration by using their symmetry property.
本文给出了线、面、体积分定义的一般描述，并导出了利用对称性简化积分计算的定理。
This paper gives the general description of the definition of curve, curved surface and triple integrals, and derives a theorem on simplified integration by using their symmetry property.
本文给出了线、面、体积分定义的一般描述，并导出了利用对称性简化积分计算的定理。
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