Let's say that you're at a hair salon and you have very fine hair.
假设你正在一家理发店，你有一头非常漂亮的头发。
Let's say that you are in a movie theater and you have forgotten your sweater or jacket.
假设你在电影院，你忘记带上你的毛衣或外套。
Let's say that you have a really good relationship with your mom and you rarely ever fight.
我们假设你跟你母亲关系特别好，很少有口角。
Let's say that you're going through your mom's jewelry box and you're having a conversation about a piece of jewelry.
我们假设你们正在翻看你妈妈的珠宝盒，你们正在讨论一件珠宝。
Now let's say that we were in space.
现在假设在空间中。
Now, let's say that I know how to do that.
现在知道怎么做了。
And let's say that it is of uniform density.
它的密度是常数。
Let's say that I have — It is a close cousin.
假设我们已知——这是一个相近的题型。
Let's say that my circle is not at the origin.
假设圆心不是在原点。
Well, let's say that I have a curve like that.
假设有这么一条曲线。
Let's say that we are at constrained min or Max.
假如我们在某个限制上的最小点或者最大点。
C So, let's say that I have a curve, c, in space.
假设有一条在空间中的曲线。
Let's say that my surface is just a slanted plane.
比如说我们的曲面就是一个倾斜的平面。
Let's say that our vector field has two components.
假设我们的向量场有两个分量。
Let's say that you have just got fired from your job.
让我们来假设你刚被解雇了。
But now, let's say that I have a general vector field.
但是现在，假设有一个一般向量场。
Let's say that we have twelve iterations worth of data.
让我们假定我们有12个迭代数据值。
Let's say that I take some path that starts at the origin.
比方说取从原点开始的路径。
Let's say that actually I do want to keep the right Angle.
假设，我想保留这个直角。
Let's say that I gave you this curve bounding this surface.
给你这个曲面和这个曲线作为它的边。
Let's say that you are a writer who wants to finish a book.
比如说你是一个要完成一本书的作者。
Let's say that we had the same c, but now the vector field.
假设c还是一样的，但现在的向量场变为。
Well, let's say that I know the value of my potential here.
假设我们知道这里的势。
Let's say that a particular family has an account at my ISP.
假设有一个特殊家庭在我的ISP拥有帐户。
So let's say that our R&D department is developing a new drug.
所以我们可以认为我们的R&D部门在开发一种新的药物。
Now let's say that we're into polymers. We know what plastic is.
现在假设我们知道聚合物，我们就知道塑料是什么。
OK, so let's say that we have a slightly more complicated function.
下面研究一个稍微复杂的函数。
Let's say that I have a plane curve and a vector field in the plane.
有一条平面曲线和这个平面上的向量场。
Let's say that I am going to do it with the normal pointing upwards.
比方说我打算让它法向量指向向上。
Let's say that you really, really want to reap some future prosperity.
让我们假设你真的很想去收获一些未来的辉煌。
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