柯西积分公式，高阶导数公式；
熟练掌握和运用柯西积公式与高阶导数公式；
Grip expertly and apply the Cauchy Integral Formula and derivatives of high order formula;
极值点和拐点是高阶导数应用中两个常见的概念。
The point of minima value and the point of inflexion are two common concepts of derivative.
研究了三个函数乘积的高阶导数，得到了一组相应的导数公式。
This paper studies derivatives of higher order about product of three functions, and obtains a group dependent derivative formulas.
将求两个函数的乘积的高阶导数的莱布尼兹公式作了多种形式的推广。
In this paper various forms for the Leibniz formula have been given.
在很多物理和力学的问题中常出现最高阶导数项带有小参数的微分方程。
In many problems of mechanics and physics there frequently appears the differential equation with the derivative term of the highest-order containing small parameters.
用函数的链式法则和乘积公式给出了参数函数和复合函数的高阶导数的计算公式。
The formulas calculating higher derivatives of parametric functions and composite functions are given by the chain rule and the product formula for derivatives.
求由参数方程所确定的函数的高阶导数，提出了一种较为直观、简便的逐次求导方法。
Author presented a concise gradual derivation about higher derivative whose function defined by parametric equation.
这种分解可以给出高阶张量协变导数的另一种定义。
This decomposition may give another definition of high order tensor's covariant derivative.
首先，简要介绍了三种主要的求和方法。然后，根据高阶等差数列通项的特性，利用新定义的形式导数列对其进行了有效的探讨。
We first introduce three methods of finding the sum of the first n terms for an arithmetic sequence of higher order, and then display another method by some formal derivatives of which are defined.
在一般的条件下，证明了解的存在性，而且得到解及其各导数的高阶一致有效渐近展开式。
Under the general conditions, we prove the existence of the solution and get the asymptotic expansions of the solution and its derivatives, which are uniformly valid for the higher orders.
最后给出了高阶相对导数的定义，并通过实例加以说明。
Finally, the definition of higher relative derivative is given. Further, we give an interpretation by an example.
通过把高阶张量写成若干逆变和协变矢量的乘积，直接从变换入手，给出了定义高阶张量协变导数的另一种方法。
This paper discusses another way, which is rewritten as product of a few contravariant vectors and covariant vectors, to define higher order tensors covariant derivative through transformations.
第三部分讨论最高阶偏导数项具有时滞的变分不等式的最优控制问题。
Finally in the third part, we study the optimal control problems for the variational inequality with delays in the highest order spatial derivatives.
在第四章里，引入集值映射的高阶广义相依导数和高阶广义邻接导数，同时讨论了它们的一些性质。
In Chapter 4, we introduce higher-order generalized contingent derivatives and higher-order generalized adjacent derivatives for set-valued maps, and discuss some of their properties.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
应用推荐