给出了非初等函数的几种判断方法。
给出实例说明初等函数的导数可以是非初等函数。
Give examples to show that the derivate of elementary function may be unelementary function.
函数为初等函数的必要条件是函数在定义域内为连续函数。
The necessary condition of a function being an elementary function is that the function is a continuous function in the field of definition.
定义域、间断点、或与且等问题是初等函数经常遇到的问题。
The problems of definition domain, break point, or and even etc often occur in elementary function.
采用正则摄动法，求出了由有限项初等函数所构成的渐近解。
The asymptotic solutions composed of finite terms of elementary functions are obtained by regular perturbation method.
第三种方法是把待求级数用基本初等函数的幂级数展开式表示出来；
The third one is to let series be expressed by basic elementary function's power series expansion;
从初等函数入手，以极限定义为基础，按照极限的定义来进行论证和阐述。
Proceed with elementary function, prove and explain promptly since defining for the foundation , according to the bottom of limit with limit.
用求解常微分方程及其初值问题的方法得到由函数方程表示的基本初等函数。
The basic elementary functions represented by functional equations were obtained by using the methods of solving ordinary differential equations and initial value probe.
在生产活动和科学技术分析中，需要一些常用的简单初等函数来拟合经验公式。
In productive activity and scientific analysis, some common simple primary functions are used to fit empirical equation.
以高斯光束的变换为例，推导出了一个表示为初等函数之和的近似解析传输公式。
The transformation of Gaussian beams is taken as an example, an approximate analytical propagation expression in terms of a sum of elementary functions is derived.
三角函数反映了圆运动和直线运动的相互转化与对应关系，是初等函数中唯一的周期函数。
Trigonometrical function reflects Yuan Movement and the Movement of mutual conversion and the corresponding linear relationship is the only primary function of the cycle function .
将初等函数定义的两种提法进行比较，对分段函数与初等函数与初等函数的关系进行了探讨。
The two formulations of the initial function definition are compared and the relation between section function and initial function is discussed.
运用微积分的方法，对基本初等函数的若干特征性质进行了证明。从而给出了基本初等函数的等价表征。
This paper, using the method of differential equation, proves some characters properties of basic elementary function, and then concludes an equivalent representation about basic elementary function.
给出了定点计算三角函数、开平方等初等函数的误差分析，并对该算法进行了改进，使计算精度达到火控总体的要求。
Also the error analysis of elementary functions, such as trigonometric and square root functions for fixed point computing, is given.
在大多数章节有数学要求，不过通常只是初等代数和函数图象，我希望大多数读者对这些要求没有问题。
There is some mathematics in most chapters, but it's usually just elementary algebra and plots of functions, which I expect most readers will be okay with.
从初等数学到高等数学，我们经常研究函数的最值问题。
From elementary mathematics to advanced mathematics, we have been studying the issue of the maximum and minimum of the function.
这个初等逼近是从常值函数开始的，并且是可行的和有效的。
This elementary approximation starts off with constant function, and is feasible and efficient.
在初等分析中，从本质上来说，要么是指数函数的变种，要么是。
In essence, all functions studied in elementary analysis are either variations of the exponential function or they are.
文章阐述了求有理函数曲线的渐近线，不仅可用常规的通过求极限值的方法来确定，还可用初等方法来确定。
This article elaborates the solution of asymptote of rational function curve, pointing out both the common way of finding limit value and the elementary way.
微积分研究的对象是函数，研究工具是极限，微积分概念的定义方式与以往学习的初等数学概念有本质的区别。
Functions are research objects of the calculus and limit is its research tool. The way to define the calculus concept differs distinctly from that of elementary mathematics.
用初等几何方法给出线性函数在无穷远点的保角性证明。
The use of elementary geometry method can give conformal demonstration of lineal function in infinite eigenvector.
运用拟齐次函数的性质，给出了一类解析函数正规型的一个简单的初等的证明方法。
The normal form of a kind of analysis function is proved with a simple and elementary method by using the properties of semiquasihomogeneous functions.
对“抢渡长江”问题进行了分析，建立了一种函数极值的数学模型，分析了解题思路和初等求解方法。
In this paper, the problem of Crossing Speedily the Changjiang River is analysed, and a type of functional extreme value model is built, then its analysis and elementary solution is illustrated.
采用初等方法，对二进制数字之和函数的八次均值的计算进行了猜想、归纳，得出了精确的计算公式。
Using elementary method, digital function sum and its 8-th power means value formula was supposed and induced, an exact calculation formula was obtained.
本文的主要目的是利用初等方法给出l—函数的一个均值估计。
The main purpose of this paper is to give a mean value estimate of L-function by an elementary method.
本文完全用初等的方法证明了完全集上连续可微函数都有可微开拓。
By very elementary method, it is proved that every continuous differentiable function defined in a perfect set has differentiable extension.
利用初等方法及拉盖尔多项式的生成函数给出一类包含拉盖尔多项式的恒等式。
The main purpose of this paper is using the element ary method and the generating function of Laguerre's Polynomials to give some id entities involving Laguerre's Polynomials.
通过讨论初等多值函数的单值解析分枝问题，重点研究了初等多值函数在复变函数中的具体应用。
The multi-valued problems of elementary complex functions are discussed, and then the applications of general multi-valued functions in complex functions are discussed mainly.
主要讨论一类能表示成最大值函数、最小值函数的分段函数的初等性。
The elementary properties of a sort of separate function which can be described maximum function or minimal function are researched.
主要讨论一类能表示成最大值函数、最小值函数的分段函数的初等性。
The elementary properties of a sort of separate function which can be described maximum function or minimal function are researched.
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