Let's think about various USES of double integrals.
来想想二重积分的其他用途吧。
One is setting up and evaluating double integrals.
一个是建立并计算二重积分。
Anyway, that is double integrals in polar coordinates.
这是极坐标系下的二重积分。
So, the first topic will be setting up double integrals.
先来说说关于建立二重积分的事。
That is because we are only doing double integrals so far.
这是由于我们才刚开始做二重积分的缘故。
But most of the time we need to learn how to set up double integrals.
但在大多数情况下，我们需要了解怎样建立二重积分。
The claim is we are able, to do double integrals in polar coordinates.
这也就说明了，可以用极坐标做二重积分。
OK, any questions about how to set up double integrals in xy coordinates?
关于在xy坐标系里建立二重积分有问题吗？
We've learned about double integrals, and we've learned about line integrals.
我们已经学过，二重积分和线积分。
The double integrals in these expressions are reduced to single integrals.
同时把这两种方法中含有二重积分的公式简化为一重积分形式。
OK, now another thing we've seen with double integrals is how to do more complicated changes of variables.
另一件关于二重积分的是，我们已经讲过了，如何做更复杂的变量变换。
OK, if that's not completely clear to you, then I encourage you to go over how we set up double integrals again.
如果你还不是完全清楚，建议你去复习一下，如何建立二重积分。
And whether these line integrals or double integrals are representing work, flux, integral of a curve, whatever, the way that we actually compute them is the same.
不管是线积分或是二重积分，也不管它们表示的是功还是通量，计算它们的方法实际上是一样的。
I am using dS rather than dA because I still want to think of dA as maybe the area in one of the coordinate planes like the one we had in double integrals. You will see later where this comes in.
这里使用dS而不是dA，因为我习惯把dA看成是，坐标平面中的面积元，就像在二重积分中所做的那样，待会大家会了解。
I am using dS rather than dA because I still want to think of dA as maybe the area in one of the coordinate planes like the one we had in double integrals. You will see later where this comes in.
这里使用dS而不是dA，因为我习惯把dA看成是，坐标平面中的面积元，就像在二重积分中所做的那样，待会大家会了解。
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