三重积分

通过Fourier变换，使问题的求解转换为两对三重积分对偶方程。

By using the Fourier transform , the problem can be solved with the help of two pairs of triple integral equations .

三重积分的Simpson公式及其误差估计

Simpson 's Rules and Their Error Estimations for Triple Integral

Ω上三重积分优化复化Simpson数值算法

An optimum numerical method of compound Simpson for the triple integral over the ω region

那么在一个空间上的区域的三重积分，对标量dV做积分。

OK , so triple integrals over a region in space , we integrate a scalar quantity , dV .

计算质量可看成二重或三重积分，这取决于空间维数，取决于密度函数，dA还是。

And mass will be double or triple integral , depending on how many dimensions you have , dV of whatever density function you have , dA or dV .

简单地重复一下吧，我们已经得到了Rz，dv的三重积分。

So , just to recap , we 've got a formula for the triple integral of R sub z dV .

那么，那将是。。。，抱歉，这和区域中，烟雾总量关于t的导数一样，由u的三重积分给出。

So , that should be , sorry , that 's the same thing as the derivative with respect to t of the total amount of smoke in the region , which is given by the triple integral of u.

我将要证明，一个只有z分量的向量场的通量，等于一个三重积分，其中被积表达式为。

I 'm going to prove that the flux of a vector field that has only a z component is actually equal to the triple integral of , RzdV well , the divergence of this is just R sub z dV .

在此基础上通过对Fischer的三重积分的直接求解，建立了新的天然河流纵向分散系数计算公式。

By using the suggested transverse mixing coefficient equation and the direct integration of Fischer 's triple integral , the paper presents a new theoretical equation of the longitudinal dispersion coefficient for natural rivers .

几个星期后，我们会学习三重积分。

In a few weeks , we will be triple integrals .

我们学过的另一种积分是三重积分。

Other kinds of integrals we have seen are triple integrals .

我们学过了三重积分。

Well , remember we were trying to do triple integrals .

运用对称性简化柱面坐标三重积分计算

Making use of symmetry to predigest calculation of cylindrical coordinates triple integral

这等价于在这个区域内部的三重积分。

That 's equal to the triple integral over the region inside .

曲面积分在三重积分中的应用

Application of the curved surface integral in the triple integral

在柱坐标系下三重积分计算法的探讨

Discussion on the Calculation of Threefold Integral in a Cylindrical Coordinate System

三重积分及曲面积分的算法研究

Research of Calculation Method of Triple Integral and Surface Integral

现在，在球坐标中进行三重积分。

So now we 're going to triple integrals in spherical coordinates .

这与三重积分不同。

It is not like in a triple integral .

如果是在4维空间中，通量就表现为三重积分。

If you were in four-dimensional space it would be a triple integral .

这就是空间区域中的标准三重积分。

This is just your standard triple integral over a region in space .

利用平面投影图形确定三重积分的积分限

Determing integral intervals in triple integral by projection

较强条件下三重积分换元公式的一种证法

A kind of indentification method of transform formulation of threefold integration under stronger condition

这和计算其他三重积分的方法是相同的。

It 's just the same way that you would compute any other triple integral .

，这是建立三重积分的绝佳练习。

See , this is actually good practice to remember how we set up triple integrals .

利用函数的奇偶性与积分区域的对称性求三重积分的值

Evaluating Triple Integration with Odd & Even Property of Function and the Symmetry of Integral Area

最后一个联系，是联系二重积分和三重积分的。

OK , and finally , the last bridge , so this was between two and three .

昨天学习了直角坐标系下，以及柱坐标下的三重积分。

So , last week we learned how to do triple integrals in rectangular and cylindrical coordinates .

三重积分积分限的确定一直是教学的难点与重点。

Determing integral intervals in triple integral while calculating is important and difficult part in advanced mathematical teaching .

先看看怎么，在球坐标中建立三重积分。

Well , we have to figure out how to set up our triple integral in spherical coordinates .