用面积原理证明了原函数存在定理；
Application of the area principle may enable some problems to be visual and eaSy.
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.
它们意味着我们可以，用一些相近的线性公式来替代原函数。
They mean that we replace the function, actually, by some closest linear formula that will be nearby.
如果把这两个看做等价的，实际上，就是用函数的线性近似式来代替原函数。
And, if we set these things equal, what we get is actually, we are replacing the function by its linear approximation.
如果你想要严格的近似等式,那就意味着我们要用切线逼近来取代原函数。
If you want strict equalities in approximations means that we replace the function by its tangent approximation.
定义了n重导数，n元绝对连续函数，广义n重原函数及牛顿n重积分。
It defines n-ple derivative, n-ary absolutely continuous function, generalized n-ple primitive function and Newton n-ple integral.
从理论上给出了微观系统在有限温度下态密度用松原函数表示的表达式。
A state density representative of microscopic system related to Matsubara function is theoretically given under finite temperature.
应用这种方法不仅可以改善滤波特性曲线的光滑度，还可近似地保持原函数的形状。
Adopting this method, we can not only improve the smoothness of filtering curve but also approximately preserve the shape of original function.
应用这种方法不仅可以改善滤波特性曲线的光滑度，还可近似地保持原函数的形状。
Adopting this method, we can not only improve the smoothness of filtering curve but also approximately preserve...
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.
插值算法以某种方法描述数据点之间的关系，在进行高次插值时会出现与原函数不一致的现象；
The interpolation algorithm in some way describe the relationship between the data points, carrying out high-order interpolation would appear inconsistent with the original function of the phenomenon;
第三章给出一类新的拉伸函数，其从原函数的一个局部极小点出发应用拉伸函数法修正目标函数。
In the third chapter, a new auxiliary function method is proposed, and then a stretching function technique is used to modify the objective function with respect to the obtained local minimum.
本文通过对导函数若干性质的分析，采用简洁的方法，对原函数存在的条件进行了探讨，给出了几个便于使用的结论．。
This paper analyses several characters of derivative function, presents effective methods to discuss existential conditions of primitive function and gives number of facilitated conclusions.
本文通过对导函数若干性质的分析，采用简洁的方法，对原函数存在的条件进行了探讨，给出了几个便于使用的结论．。
This paper analyses several characters of derivative function, presents effective methods to discuss existential conditions of primitive function and gives number of facilitated conclusions.
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