这是二元函数中的第一个例子。
That was our first example of a function of two variables possibly.
我们将把注意力集中在二元函数上。
So, we are going to focus on the case of functions of two variables.
还有另外的一种方法画出二元函数的图像。
So, there is another way to plot the functions of two variables.
这的确是一个二元函数。
我们说，当一个二元函数存在时，就有梯度向量。
So, we said when we have a function of two variables, we have the gradient vector.
我们学过怎样认识二元函数,从它的图像和等高线的角度来看。
we've seen is how to actually view a function of two variables in terms of its graph and its contour plot.
因此当我们在想像一个图像时，其实那只是一个二元函数的图像。
So, when we think of a graph, really, it is a function of two variables.
冻土中的未冻水的化学势是未冻水含量和温度的二元函数。
As far as the frozen soil is concerned, the chemical of unfrozen is a function of the temperature and the amount of unfrozen water.
对于二元函数的二重极限，重点是极限的存在性及其求解方法。
For double limit of a binary function, the existence of the limit and the methods to seek its solution are emphasis among our focus.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
但这种办法并不普遍，只能用于二元函数，来判断是极小值点、极大值点还是鞍点。
I should say that is for a function of two variables to try to decide whether a given critical point is a minimum, a maximum or a saddle point.
二元函数的极限远比一元函数的极限复杂，但它们之间又有密切的联系。
Limit of function of two variables is more complex than that of one variable.
并且我们已经做过两次了，一次是关于二元函数的，另一次关于三元函数的。
And we have seen them twice. We have seen them once for functions of two variables, once for functions of three variables.
讨论了二元函数中值定理中间值的渐近性质，给出了一个相关反问题的解。
The asymptotic properties of mean value in the mean value of bivariate functions are discussed, a solution is presented for related inverse problem.
本文给出了用定义法证明二元函数可微性的四则运算法则与复合运算法则。
Four Arithmetic Operations of Fuzzy Number by Method of Intersection Point or Discontinuity Point;
经过归纳，总结，找到一些规律：即选择适当路径以确定二元函数极限不存在。
After summing up, summarizing, find some laws: Choosing proper route to confirm the function limit of two variables' doesn't exist.
给出二元函数型来定式的各种值法则，包括一阶极限判定法则和二阶极限判定法则。
This paper gives several determined value rules to type of indeterminate forms of functions of two variables. These contain the first order and the second order decision rules of the limit.
利用多元函数极值的定义和偏导数的定义公式证明二元函数与一元函数在某点取得极值的关系。
This article use the diverse function extremum and the local derivative's definition formula to prove the relation between extremum obtained by the two function and the dollar function at some point.
探讨二元函数的连续性、偏导数、方向导数以及可微性之间的关系，有助于我们对二元函数的学习。
A discussion of the relations between continuity, partial derivative, directional derivative and differentiability of binary function is helpful for us to study binary function.
确切的说，对于某一天的期权报价，隐含波动率是执行价格和存续期的二元函数，呈现曲面的形态。
More precisely, for one day 'quote, the implied volatility is a function of two parameters: the strike price and the time to maturity, exhibiting a surfaced shape.
小波变换作为频率和时间的二元函数，使之可以很方便地在频率和时间域中同时进行地震波能量的吸收衰减补偿。
Wavelet transform involves the two-variate function of frequency and time, which makes it convenient to simultaneously compensate for attenuation of seismic energy in frequency and time domains.
将一元函数和二元函数极值的部分判别方法推广到多元函数极值的判别，提出了判定多元函数极值的几个方法。
The extreme conditions for the monovariate functions were applied to the multivariate functions and then an effective method to decide the extreme values for the multivariate functions was presented.
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ，定义了二元齐次多项式的正定性 ，并基于定义给出了二元函数极值的一个充分条件。
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions, in which a new sufficient condition and its concise proof when critical case is given.
应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。
By using the limits of functions and the exchange limit theorem, we considered the relationship between the double limit of function with two variables and its repeated limits.
我们已经知道，怎样通过图像去了解二元和三元函数。
We have learned how to think of functions of two or three variables in terms of plotting them.
既然这样，一旦CompareOther写好了，只需要写一个二元谓词将比较函数包装起来就可以了。
Now, if I may continue, once the CompareOther function has been written, the faithful needs only to write a binary predicate to wrap the comparison function.
由配分函数求出二元系统的物态方程。
本文利用高阶集团展开方法(三阶)，求出二元系统配分函数的表达式。
In this paper, by using higher term virial expansion method, we get the expression of partial function for Hardsphere system.
本文利用高阶集团展开方法(三阶)，求出二元系统配分函数的表达式。
In this paper, by using higher term virial expansion method, we get the expression of partial function for Hardsphere system.
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