导数

In the numerical differentiation matlab, useful midpoint formula, adaptive method, Richardson extrapolation methods such as France seek the derivative of the function, the algorithm of the program implementation in the document have been given.

详细说明： matlab中的数值微分，有用中点公式，自适应法，理查森外推算法等方法求函数的导数，算法的程序实现在文件中都已经给出了。

The first and second derivatives of the coordinates of a cam profile are calculated using numerical differentiation method,and substituted with curvature radius formulas in calculus,thus obtaining its curvature radius.

应用数值微分法计算凸轮廓线坐标的一、二阶导数，代入微积分学中曲率半径公式，即得凸轮廓线的曲率半径。

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

At present, many known results are obtained only on one dimensional functional space, and the research on high dimensional space is little, only the continuous solutions are discussed on RN, neither the differentiate solutions on RN nor the solutions on abstract space and manifold.

在一维情形下，所涉及的函数通常具有较好的性质比如单调性，逆映射导数的LipschitZ性(在研究光滑解时通常需考虑)等，而第il页摘要高维空间上函数则不具有这些好性质，因此，讨论高维空间上的迭代方程要求在方法上作一些改进和突破。

Which make it more expedient to study general character of function defined on open interval by means of derivative.

使得利用导数研究开区间上函数的整体性态更为方便。

Let be twice differentiable on the open interval. Then

如果函数在上连续，在内具有一阶和二阶导数，那么

Let be a function whose st derivative exists for each in an open interval containing.

如果函数在含有的某个开区间内具有直到阶导数，则对任意，有

Based on the analysis and summary of basic ideas and methods,this thesis proposes two new estimation of error of higher order approximation.

方法二是在等距分布的条件下，基于三次样条插值函数的三弯距算法，通过利用节点处弯距的加权和近似计算区间中点处的二阶导数。

In this project,we primarily investigated the growth of solutions of some types of differential equations,and the hyper order,the exponents of convergence of zeros and fixed points of solutions with infinite order, especially, expononts of convergence of fixed points of first, second order derivatives and differential polynomials of solutions.

中文摘要：在本项目中，重点研究了几种类型的微分方程解的增长性，及无穷级解的超级，零点收敛指数，不动点收敛指数，特别是解的一阶，二阶导数及微分多项式的不动点收敛指数。

In which denotes the th derivatives of with respect to is called an ordinary differential equation of order .

在一个方程中，如果未知量是一个函数，且方程中含有这个函数的导数，则称此方程为微分方程。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。