• We have a line integral along a curve.

    对于沿曲线线积分

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  • And, I still want to compute the line integral along a closed curve.

    仍然沿着封闭曲线线积分计算

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  • Graphics are included not merely as a means of making the information easier for the student to grasp, but as an integral part of the way social scientists think.

    加入图形不仅是让学生更容易掌握信息手段也是社会科学家思考方式一个组成部分

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  • A name is an integral part of anyone's personal and professional identityjust like the town you're born in and the place where you're raised.

    名字任何人个人职业身份不可分割一部分——出生城镇和你长大的地方一样。

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  • A line integral for flux just becomes this.

    通量的线积分变成这样了。

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

    个向量线积分另外一个向量场的曲面积分联系起来。

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  • If you manage your project from a good plan — and an integral part of that plan is a good estimate — there is going to be significant cost savings.

    如果采用好的计划管理项目——其中完整部分就是一个好的评估——那么您将能够节省大量的开销。

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  • Flux looks quite different in the plane and in space because, in the plane, it is just another kind of line integral, while in space it is a surface integral.

    平面中的通量空间中的通量有很大区别平面中,通量仅仅线积分另一种形式在空间中,表现曲面积分。

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  • Remember, you have to know how to set up and evaluate a line integral of this form.

    注意大家需要知道如何建立计算这种形式线积分

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  • And, then I have a single variable integral.

    然后就变成一个变量积分。

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  • Then I can actually -- --replace the line integral for flux by a double integral over R of some function.

    那么就能名正言顺地,R某个函数的二重积分替代通量线积分。

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  • Not a very big one, not a very complicated integral, but imagine it could get potentially much harder.

    不是大的麻烦,也不是一个非常复杂积分估计可能变得更加困难。

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  • If we have to compute a line integral, we have to do it by finding a parameter and setting up everything.

    如果我们必须计算线积分必须通过寻找一个参数建立一切

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

    每当通量曲面积分时,

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  • So, that's a really strange statement if you think about it because the left-hand side is a line integral.

    那么如果仔细,会有奇特的结论,因为左面一个线积分。

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  • So, what it does actually is it computes a line integral.

    实际上计算线积分

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  • Once you have computed what this guy is, it's really just a triple integral of the function.

    一旦需要计算这个积分需要计算这个函数三重积分。

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  • So, using Green's theorem, the way we'll do it is I will, instead, compute a double integral.

    那么使用格林公式我们计算二重积分

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

    相反要把它变成面积分。

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  • No matter which form it is, it relates a line integral to a double integral Let's just try to see if we can reduce it to the one we had yesterday.

    不管哪种形式线积分和二重积分联系在一起,看看能不能通过化简得到昨天公式。

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  • What ends up happening is it gives you this integral times a certain number.

    结果这个积分乘以某个

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  • And so, this becomes the integral from a to b.

    那么也就成为ab积分了。

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  • Integral in going from a to B, integral in going from a to B.

    ab积分,从ab的积分。

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  • So, we need to set up the flux integral for a vector field dot ndS.

    需要建立向量场点乘nds通量积分

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  • Or, if you prefer, that's negative integral from a to b of M of dx.

    或者喜欢的话,就是积分负值,abMdX的积分。

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  • So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.

    其中一种说明向量场上沿逆时针方向,向量等于,平面区域旋度F二重积分

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  • S if we have a closed surface with a normal vector pointing outwards, and we want to find a flux integral for it, well, we can replace that with a triple integral.

    的法向量似乎是指向外部。,And, the,normal, vector, to,s, seems, to, be, pointing, out wards, everywhere。,如果我们个法向量指向外部的封闭曲面并且我们要求的一个通量积分那么我们可以一个三重积分来代替这个通量积分。

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  • Business is complex and fast-moving, and designers need to make themselves an integral part of a collaborative process.

    商业复杂快速过程设计师需要自己变成其中有机部分

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  • Business is complex and fast-moving, and designers need to make themselves an integral part of a collaborative process.

    商业复杂快速过程设计师需要自己变成其中有机部分

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