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1·And instead I will want to reduce things to a surface integral.

相反，我想要把它变成面积分。

2·And so it will be a surface integral, not a line integral anymore.

所以要用面积分，而非线积分。

3·It is a surface integral, so we need to have two variables in there.

它是一个面积分，所以这里需要两个变量。

4·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。

5·Whenever you do a surface integral for flux you have two parts of the story.

每当做通量的曲面积分时，你要做两件事。

6·This relates a line integral for one field to a surface integral from another field.

这把一个向量场的线积分，和另外一个向量场的曲面积分联系起来。

7·If you end up with a dx, dy, dz in the surface integral, something is seriously wrong.

如果在这个曲面积分中是以dx, dy, dz结尾的，则表明出现了很大的问题。

8·And, the way in which you would compute the surface integral is just as with any surface integral.

计算这个曲面积分的方法，和其他任何曲面积分的一样。

9·The results are of use value for simplifying the computation of line integral and surface integral.

这一结果，对于简化线积分、面积分的计算具有使用价值。

10·And this is finally where I have left the world of surface integrals to go back to a usual double integral.

也就是最终要摆脱曲面积分，回到常规的二重积分。

面积分

1·It is a surface integral, so we need to have two variables in there.

它是一个面积分，所以这里需要两个变量。