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.
为什么这不可以友元函数访问私有变量？
Why can't this friend function access the private variables?
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.
当我需要使用友元函数而不是成员函数?。
When do I have to use a friend function rather than a member function?
积分上限函数是一元函数微分学的基本概念。
Integral upper limit function is a basic concept in function differential calculus.
元函数对与谱向量对通过反射阵建立映射关系。
By reflection matrix the mapping relation of element function pair and spectral vector pair can be established.
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.
当然我们还不能看到，三元函数的图像，因为它处在一个四维空间里。
Except, of course, we haven't see the graph of a function of three variables because that would live in 4-dimensional space.
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.
实验测试结果表明，该算法对一元函数和多元函数都有很好的效果。
Simulation test illustrates that the presented algorithm is efficient for both one-variable functions and multi-variable functions.
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.
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.
本文将一元函数的罗尔定理推广到多元函数中，并给出了一个简洁、颖的证明。
In this paper, the Rolle's theorem of a variadle function is extended to multiple-variable functions. The paper, then, gives a new and simple proof.
给出了一元函数在区间上一致连续的一个等价条件，并运用它证明了一些函数的一致连续性。
AN equivalent condition of function's consistent continuity is proved. Application of it in several examples is showed.
并根据数学分析中一元函数和多元函数的极限的相关知识，在理论上证明了该指标的有效性。
According to unary function limit and multivariate function limit of mathematical Analysis, the validity of the index Vnew is proved in theory.
为了访问一个用户定义的类里的私有数据，你必须声明全局函数为友元函数，并且在类中定义。
But to be able to reach any private data within a user defined class you have to declare the global function as a friend within the definition of the class.
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.
课程内容包括函数、极限与连续、一元函数微分学、一元函数积分学和常微分方程等几大板块。
This course consists of several major parts, such as Functions, Limits and Continuity, The Derivative, Integration and Ordinary Differential Equation.
课程内容包括函数、极限与连续、一元函数微分学、一元函数积分学和常微分方程等几大板块。
This course consists of several major parts, such as Functions, Limits and Continuity, The Derivative, Integration and Ordinary Differential Equation.
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