那用什么坐标系来计算这个积分呢？
这是极坐标系下的二重积分。
WKT和SVG在坐标系中定义不同的原点。
WKT and SVG define different origins for the coordinate systems.
关于在xy坐标系里建立二重积分有问题吗？
OK, any questions about how to set up double integrals in xy coordinates?
我们必须总是用,我们所谓的-,“右手坐标系
You will always, always have to work with what we call "a right- handed coordinate system."
这道题最合适的方法，应该在极坐标系里面计算。
OK, the right way to do this will be to integrate it in polar coordinates.
如果实体是圆形状的话，那就可以考虑用极坐标系。
If my solid is actually just going to be round then I might want to use polar coordinates.
我们有直角坐标系，有柱坐标系和球坐标系。
We have rectangular coordinates, we have cylindrical coordinates and we have spherical coordinates.
怎么在坐标系中计算呢？，或者说，怎样用分量来做呢？
How do we do the calculation in coordinates, or I should say using components?
通常你转换到极坐标系下，有可能积分区域更容易建立。
I mean usually you will switch to polar coordinates either because the region is easier to set up.
做三重积分，和二重一样，当然，我们会有更多的坐标系。
When we do triple integrals in space, well, it is the same kind of story, except now we have, of course, more coordinate systems.
所以说球坐标系,其实就是在rz平面再建立一个极坐标。
So the idea of spherical coordinate is you're going to polar coordinates again in the rz plane.
但还是可以建立这个积分，然后转换到极坐标系下去求结果。
But still we could set this up and then switch to polar coordinates to evaluate this integral.
而旋度度量了，运动中的旋转情况，这跟坐标系的选择有关。
And when I say that the curl measures the rotation in a motion, well, that depends on which coordinates you use.
请说，你想知道极坐标系下的积分边界，这是一个二重积分。
Yes? In case you want the bounds for this region in polar coordinates, indeed it would be double integral.
不过，您需要为位于其父组件局部坐标系中的组件显示工具提示。
However, you need to show the tooltip for a component that lies in the local-coordinate system of its parent.
下面的图表描述了几种常见的方法在坐标系中的位置。
The following chart illustrates where several popular methods appear along these dimensions.
这个是做不成的，事实上我们也许可以有更好的坐标系？
You will never get there. What happens is actually maybe we need better coordinates. Why do we need better coordinates?
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。
We have been working with triple integrals and seeing how to set them up in all sorts of coordinate systems.
如果你想使用。,螺旋锥法则,必须保证自己是,在用右手坐标系。
You must work... if you use the right-hand corkscrew rule make sure you work with the right-handed coordinate system.
相对简单的、找出边界的办法,就是在u、v坐标系下画出积分区域。
And to find the bounds perhaps the easiest is to draw a picture of a region in u, v coordinates.
另一种选择，也就是我要选的那种，是转换坐标系，让这个点变成原点。
The other option, which is the one I will choose, is to change the coordinate so that this point become the origin.
使用plot命令，gnuplot可以在直角二维坐标系中进行操作。
With the plot command, gnuplot can operate in rectangular or polar coordinates.
您需要使用其他方法将该子元素从局部坐标系转换到内容坐标系。
You need some extra methods to convert that item from its local-coordinate system to its content-coordinate system.
我们在直角坐标系中处理，在这里dV有可能变成，或者它们的其他排列。
Well, we can do that in rectangular coordinates dz dx dy where dV becomes something like, maybe, dz dx dy, or any permutation of these.
如果给出了积分区域，你就要找出积分边界，也许通过选择适当的坐标系来做。
If it is the region of integration then it will go into the bounds of the integral and maybe in the choice of the coordinate system that you use for integrating.
接下来有个坏消息就是，不仅要会在xy坐标系里做，还要会在极坐标系里做。
So, the bad news is we have to be able to do it not only in xy coordinates, but also in polar coordinates.
然后，在uv坐标系内，把面积元素定义为dA，只是为了让他们看起来不同。
And, the area element in uv coordinates, let me call that dA prime just to make it look different.
事实上，Guugu Yimihirr根本没有使用到以自己为中心的坐标系。
In fact, Guugu Yimithirr doesn't make any use of egocentric coordinates at all.
地理和投影坐标系都包含对地球形状的假设(一个略扁的球体)；这称为大地基准点。
Both geographic and projected coordinate systems include a definition of the assumed shape of the earth (a flattened sphere); this is called the geodetic datum.
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