共查询到20条相似文献,搜索用时 93 毫秒
1.
2.
3.
4.
不少学生学习了求导公式后 ,往往对导数定义不太重视。其实 ,导数的定义不仅是导数的原始基本概念 ,而且它在求极限、求导数的计算及证明中都有着重要的、甚至是不可替代的作用。本文仅就导数定义在导数计算中的地位与作用问题谈点粗浅的认识 ,以期学生对此问题引起重视。一、在分段函数求导计算中的情形对分段函数分段点的导数的计算 ,必须按定义求 ,不能套公式。例 1 设 f ( x) =e|x|,求 f′( x)。[错解 ] 因为 f ( x) =ex, x≥ 0e- x, x <0 ,所以 ,f′( x) =ex, x≥ 0-e- x, x <0[辨析 ] x=0是分段点 ,而对分段点的导数 … 相似文献
5.
6.
7.
数学是一种工具,数学教学的最终目标是利用数学这种工具去解决问题.导数就是一个很好的例证.导数作为高中数学新增内容,它为研究函数的性态提供了一般的方法,导数的几何意义又为研究平面几何的切线问题提供了更便捷的方法.在高考命题中,除了少数直接考查导数的有关知识外,更多是以导数为工具解决函数的性态问题、不等式的证明、平面几何的切线问题、应用题,甚至在求极限中都得到应用.一、解决函数问题借助导数的单调性进行更加透彻的研究,可以进一步研究极值、最值问题,把导数、函数、方程及不等式,有机地交融为一体.这也是高考考查重要方面… 相似文献
8.
本文讨论分段函数的求导问题,建立了求导时方法选取的一般程式。对于含绝对值的函数,给出了一个求导定理。一、分段函数的导数分段函数的求导,关键在于求分段点处的导数,常用方法有:①不连续则不可导;②导数或左右导数的定义;③导数单侧极限定理*:设f(x)在(a,b)内连续,x0∈(a,b),在(a,x0)及(x0,b)内可导且limf(x)、limf(x)都存在,则导数单侧极限定理用左右导数定义及微分中值定理可证,此处从略。下面仅作几点说明:1“定理中若厂十(X。)一片一(X。),则几X)在X。处可导,若不相等,则人X)在X。处不… 相似文献
9.
在新教材中,由于导数内容的加入,使得高中数学解题增添了新的活力,使很多题型有了新的解题思路,导数的应用更显活跃.导数除了解决切线的斜率,判断函数的单调性,求函数单调区间及求函数的极值与最值等问题外,也常用在求参数或参数范围,求不等式问题、解析几何问题以及数列、向量、三角等方面,下面举导数与其他知识综合应用的例题,以展示导数的工具作用.一、用导数求参数或参数范围例1已知函数f(x)=ex-ax+1是R上的单调增函数,求a的取值范围.分析:由于f′(x)=ex-a,又f(x)在R上是单调增函数,同f′(x)=ex-A>0恒成立,即a0,故a≤0… 相似文献
10.
11.
12.
ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
13.
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
14.
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows 相似文献
15.
Pankaj Mathur 《分析论及其应用》2006,22(2)
In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x). 相似文献
16.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
17.
18.
《高校应用数学学报(英文版)》2014,29(4)
正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with 相似文献
19.
《数学研究及应用》2014,(6)
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics. 相似文献
20.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6]. 相似文献