导函数

Finally numerical examples with three shape functions are analyzed in detail. The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.

最后，通过多个数值算例的计算比较了三种形函数的计算结果，结果显示本文提供的MGMLS方法关于函数值和各阶导数值都具有很高的精度。

Automatic differentiation and implicit function differentiation rule were used to calculate the precise absolute and relative sensitivity coefficients, with no truncation error introduced.

提出一种基于自动微分和隐函数求导法则的精馏塔优化计算灵敏度分析方法，可以求出精确的、无截断误差的灵敏度系数，以反映精馏塔模型中各种不确定因素变化所引起的改变和影响。

Keywords distillation column semi-open equation model;automatic differentiation;sensitivity analysis;implicit function differentiation rule

精馏塔半开放模型；自动微分；灵敏度分析；隐函数求导法则

Week 6 The derivative of implicit function.

第6周 隐函数的导数。

Calculus deals with the fundamental theories of calculus, including function, limit, continuation, derivative and differential, mean value theorem, the application of indefinite integral and definite integral, infinite series, as well as the practical instances applied in economic management.

微积分讲述微积分的基本知识，包括函数、极限、连续、导数与微分、中值定理、不定积分与定积分的应用、无穷级数等。以及这些知识在经济管理中的应用的实例与练习。

System is used VB6.0, MATLAB6.5 and MATLAB and Visual Basic OLE interface methods of production, use VB Visual Interface, the real object-oriented, event-driven approach using the structure of high-level programming language, the perfect tool Integrated production and friendly interface and features of MATLAB numerical terms, such as a strong graphic image processing function for the core to achieve the limit, derivative, differential, integral and indefinite integral, vector algebra and analytic geometry of space for the function will be Two aspects of the unique advantages of combining the strong points, to shorten the development cycle and reduce programming difficulty, the current rapidly changing information age is of high practical value.

在线等汉-英翻译，网上在线翻译的别回！！！！！系统是采用VB6.0、MATLAB6.5 和MATLAB与Visual Basic接口OLE方法制作的，利用VB界面的可视化、真正面向对象、采用事件驱动方式的结构化高级程序设计语言、工具的完美集成和友好性特点制作界面和MATLAB的数值计算、图形图像等强大的处理功能为内核来实现函数极限、导数、微分、定积分和不定积分、空间解析几何和向量代数的求解功能；将两方面具有的独特优势结合起来，取长补短，以缩短开发周期，降低编程难度，这对当前日新月异的信息时代是具有很高的实用价值。

Proves the calculus basic formula by the relation between function increment and differential,states briefly the intrinsic connection among indefinite integral, definite integral,derivativee and defferential.

利用函数增量与微分的关系证明了微积分基本公式，简洁地阐明了导数、微分、不定积分和定积分的内在联系。

Moreover, A very general optimization problems with a complementarity problem constraint, a inequality and a equality constraints, and an abstract constraint are studied.

最后，我们应用Mordukhovich广义导数方法，在较弱的约束规范性条件—静态条件下，研究当f，g，h，G，H为非光滑函数时，互补约束的优化问题的最优必要性条件。

In this paper, we present five sorts of methods for finding the particular solutions of the n-th-order inhomogeneous linear differential equation with constant coefficients.

本文给出了五种求n阶常系数线性非齐次微分方程待解的方法。这些方法只需计算特征函数A及其各阶导数在某点的值，方法简单，两种递推公式适合计算饥计算，本文还简化了文［1］中递推公式的证明

Limits provide the means of defining the derivative and integral of a function.

极限提供了定义函数的导数和积分的方法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。