极限定理

Course Content:The main part of this course is about infinitesimal calculus and ordinary differential equations,including :functions and limits,derivative and differential integral and their application,differential methods of function of several variables and its application,heavy integral,curve integral,camber integral,infinite progression and differential equations.

课程内容：学科教学法与CAI研究与实践是师范计算机专业教学系统的重要组成部分，学科教学法与CAI研究与实践课程是计算机科学教育的主要内容。通过本课程的学习使学生掌握现代学科教学法与CAI研究与实践的基本概念，基本原理和基本方法；能设计并使用所学的教学理论进行中学信息技术课程的教学设计，试讲，试教。课程内容：以微积分学和常微分方程为主干，介绍函数与极限，导数与微分，中值定理。不定积分，定积分及其应用，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数及微分方程等。

We introduce the uniform Hausdorff metric H on the space 〓 offuzzy complex numbers and investigate the topological structure of 〓.We show the completeness of 〓 and study on 〓 limits of thesequence of fuzzy complex numbers,metrical and leverwise convergence,and relation between metrical convergence and leverwise convergence.Weprove the equivalence theorem of metrical convergence and leverwiseconvergence on 〓.

在模糊复数空间〓上引进一致Hausdorff度量H，讨论了模糊复数空间的拓扑结构，证明了的完备性，并在完备的模糊复数度量空间上研究了模糊复数列的极限、度量收敛和水平收敛，讨论了度量收敛与水平收敛之间的关系，在上证明了度量收敛与水平收敛的等价性定理。

The third chapter discusses and proves Il"yashenko"s Theorem, that is, if every vertex on the polycycle of an analytic vector field in the real plane is hyperbolic, then limit cycles cannot accumulate on this polycycle.

第三章详细讨论和证明了Il'yashenko定理，即平面解析向量场的多边环上每一顶均为双曲奇点，则此多边环附近不能结集无限多个极限环。

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。

By the analysis of dive and horizontal plane nonlinear model, the catastrophe model on de dive plane is deduced, and catastrophe stability is analysized. In the horizontal plane, simplified equation is gained by center manifold theory, then draws the conclusion that the stability of limit circle arises from critical point is relate to small difference of move point and critical point.

通过对潜艇垂直面和水平面非线性运动模型进行分析，导出垂直面运动的突变控制模型，并进行了突变稳定性分析；在水平面运动的非线性分析中，通过中心流形定理简化方程，得出临界点处极限环的稳定性与微差占的符号有关的结论，这样在无法或很难得到李亚普诺夫函数的情况下，可以通过这种方法判别临界点的稳定性。

Theorem 1 (Uniqueness of Limit of Function) If exists, then its limit is unique.

定理 1 如果存在，那么这极限唯一。

According to superior limit theorem of ultimate analysis ,the power equation of entire structure will be transformed into the power equation of subdmain by using the concept of plastic hinge line.

根据极限分析的上限定理，利用塑性铰线的概念，将整体结构的功率方程转化为子域的功率方程，利用王洪生提出的分配系数法，进而得出子域的平衡方程。

On the basis of introducing the fixed point of Banach theorem, this paper firstly elaborates the important application of the existence of the solution of the linear algebraic equation and the ordinary differential equation, then it narrates the important application of obtaining the leading Newton repetitive process and the natural number the inferior square root and the equation root in the approximate calculation.

本文在介绍Banach不动点定理的基础上，首先阐述了其在线形代数方程、常微分方程解的存在性中的重要应用；然后讲述了其在求导Newton迭代法、求自然数的次平方根、求方程根的近似计算中的重要应用；最后，介绍了其在求一类递推数列极限中的应用。

Through studying the singular points of the plane differential systems, the sufficient conditions of the nonexistence of limit cycle for the system are obtained by means of comparing theorem, analyzing divergence and change of variable.

通过对微分系统的奇点进行研究，借助比较定理，将该方程与其对称的方程进行比较，并通过分析散度和变量代换的定性分析，得到了其极限环不存在的充分条件。

A new formula is established which provided a simple and practical theoretical method for deriving speed at different points of the slide bar mechanism.

利用三心定理、几何和极限理论首次证明导杆机构的滑块绕机架与滑块的绝对瞬心的角速度等于导杆转动的角速度，并建立了新公式。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。