提出了矢量函数积分中的坐标选择问题。
The coordinate selection in vector functional integration is raised.
分析无穷空间点源扰动函数积分形式的解。
The solution in integral form of Green's function of a point source in infinite space is analysed.
研究一类非线性函数积分方程解的存在唯一性。
This paper deals with the existence and uniqueness of the solution of a class of nonlinear functional integral equations.
积分区域和被积函数结构是函数积分的两个关键点。
The integral range and the integrand structure are the two key points of the function integral.
故本算法对双重贝塞尔函数积分的计算效率有明显提高。
This algorithm has improved efficiency of calculation obviously for dual Bessel integration.
提出了一种计算宽光谱间隔的普朗克函数积分值的简单近似方法。
A simple approximate method for calculating the values of integration of the Planck function over broad spectral intervals is presented.
该方法易掌握，特别是使用该方法对无理函数积分更容易求得结果。
This method is easy to grasp. especially. the integral result of irrational function is easy obtained with this method.
同时，由透射光场的格林函数积分得出了基尔霍夫近似下光场的表达式。
We also obtain the expression for the transmissive light waves from the Green 's-function integral in the case of Kirchhoff's approximation.
本文采用修正格林函数积分方程的矩量法数值解技术求解静电场边值问题。
A new approach to numerical solution of the boundary-value problems of static-electric fields, the Modified Green Function kernel integral equation and its moment-method solution, is presented.
如果要计算cos, sin，的高次函数积分，则公式将会在注释中给出。
If there is a need to integrate some big power of cosine or sine then the formula will be given to you the way it is in the notes.
利用极限理论，给出了复函数积分中值公式的“中值点”的渐近性的简洁证明。
By using the limit theory, we discuss and prove the asymptotic properties of mean point in integral mean value formula for a complex function.
在可测模糊随机函数及模糊值函数积分的基础上，研究了模糊值函数的有界控制收敛定理。
This paper gives the control convergent theorem of integral for fuzzy random functions on basis fuzzy functions and fuzzy integral.
对求解过程中的关键问题进行了全面阐述，如目标的几何建模，基函数、权函数的选择，格林函数积分奇异性的加减同阶奇异项处理方法等。为后面的研究工作打下良好的基础。
The key points in the calculation are introduced such as the selection of the basis function and testing function, the way to solve the integral singularity of Green function and so on.
那么我就能名正言顺地,用R上的某个函数的二重积分来替代通量的线积分。
Then I can actually -- --replace the line integral for flux by a double integral over R of some function.
我要说的是取其一，积分得到包括另一变量的函数的结果，然后对结果求导，进行比较看得到什么。
But what I am saying is just take one of them, integrate, get an answer that involves function of the other variable, then differentiate that answer and compare and see what you get.
就二重积分来讲,它是对区域里函数值求总和。
The way we actually think of the double integral is really as summing the values of a function all around this region.
一种考虑这个问题的办法是，如果你还觉得，二重积分是求体积的话，那这个度量的，就是函数1的图形下的体积。
One way to think about it, if you're really still attached to the idea of double integral as a volume what this measures is the volume below the graph of a function one.
一般cp和，都是温度的函数，因此实际上，我们可以将这个积分计算出来。
Cv So, for Cp and Cv, these are often quantities that are measured as a function of temperature, and one could, in fact, calculate this integral.
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.
那么，你会说那很简单，积分就可以了，除非你不知道函数是什么。
So, you'd say, oh, it's easy. Let's just integrate, except you don't have a function.
可能是积分边界容易确定，但函数可能就比较困难，因为它含有这些sin,cos在里面。
Maybe it will be easier to set up bounds but maybe the function will become harder because it will have all these sines and cosines in it.
无论函数是什么，如果你的函数除了原点处处为，在原点是其他的值，那积分还是0的。
no matter what value you put for a function, 0 if you have a function that's zero everywhere except at the origin, and some other value at the origin, the integral is still zero.
你们都知道，要求这个面积是非常简单的，如果你们想的话，可以积分除了椭圆函数以外的任何函数。
So, you know, if you find that the area is too easy, you can integrate any function other than ellipse, if you prefer.
我们有这个积分常数，但是除去它，我们应该从这里能得到一个势函数。
We have this integration constant, but apart from that we know that we should be able to get a potential from this.
通常，你只会在这两种情况下用替代法，或者这可以极大地简化被积函数，或者就是这可以简化，积分的上下限。
I mean, normally, you would only do this kind of substitution if either it simplifies a lot the function you are integrating, or it simplifies a lot the region on which you are integrating.
微积分基本定理，不是曲线积分的，告诉我们，如果对函数的导数积分，就会得回原函数。
So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.
但是微积分，主要是学习函数的。
一旦需要计算这个积分，只需要计算这个函数的三重积分。
Once you have computed what this guy is, it's really just a triple integral of the function.
它说，如果你对一个函数的梯度做线积分，就能得到原函数。
It tells you, if you take the line integral of the gradient of a function, what you get back is the function.
作为引子，你们可能已经知道了，一元微积分里面的一个小把戏，也就是求隐函数微分法。
And, just to motivate that, let me remind you about one trick that you probably know from single variable calculus, namely implicit differentiation.
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