无穷级数

This article is mainly discussed the relation between some important concepts and conclusions about the Limit of Sequence, the Limit, Continuity ,Differentiability, Integrability of Function, the Infinite Series , and the Limit, Continuity, Derivativeness,Differentiability of Multivariable Function ,as well as the Multiple Integral, and Integral with parameter .

本文对数列极限，一元函数的极限、连续性、可微性、可积性，无穷级数，多元函数的极限、连续性、可导性、可微性以及重积分，参变量积分中的一些重要概念和结论之间的关系进行了一些探讨，每一个问题都作了适当说明或举出反例，并对一些相关的内容进行了讨论，得到若干结果。

In 3D scalar Helmholtz equation computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by The GMT.

首次从理论上证明，在三维静电场分析中，存在一种无穷级数收敛，且有一定普遍性的解析解；推导出三维静电场分析的多极理论通解及其使用规则，证明或解释广义多极技术不能证明或解释的若干使用规则，用多极理论求解工程实际中的三维静电场边值问题。

In 2D eddy current field computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by the GMT, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁场分析中存在一种无穷级数收敛，且有一定普遍性的解析解。

Mathematical analysis is largely taken up with studying the conditions under which a given function will result in a convergent infinite series.

数学的分析常被当作研究形成收敛无穷级数的和的给定函数的条件。

Mathematical analysis is largely taken up with studying the conditions under which a given function will result in a convergent in finite series.

数学的分析常被当作研究形成收敛无穷级数的和的给定函数的条件。

This curriculum primary coverage includes: Function and limit, a circular function derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral, definite integral application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral, curvilinear integral and surface integral, infinite series, differential equation.

该课程的主要内容有：函数与极限，一元函数的导数与微分，中值定理与导数的应用，不定积分，定积分，定积分的应用，空间解析几何和向量代数，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，微分方程。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

The higher mathematics curriculum is a college engineering course undergraduate course each specialized student's compulsory important basic theory class, through this curriculum study, causes the student to obtain: Circular function calculus study, the space analytic geometry and the vector algebra, the function of many variables calculus study, the infinite series, aspect and so on ordinary differential equation basic concepts, the elementary theory and the fundamental operation skill, and further obtain mathematics knowledge for the study successor curriculum to lay the essential mathematics foundation,During instruction knowledge, must train the student through each teaching link to have the abstract thinking ability, logic reasoning ability, spatial imagination ability gradually and studies independently ability, but also must pay attention specially trains the student to have the quite skilled operational capability and the synthesis utilization studies the knowledge to analyze the question and to solve the question ability.

高等数学课程是高等学校工科本科各专业学生的一门必修的重要基础理论课，通过本课程的学习，使学生获得：一元函数微积分学，空间解析几何与向量代数，多元函数微积分学，无穷级数，常微分方程等方面的基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础，在传授知识的同时，要通过各个教学环节逐步培养学生具有抽象思维能力、逻辑推理能力、空间想象能力和自学能力，还要特别注意培养学生具有比较熟练的运算能力和综合运用所学知识去分析问题和解决问题的能力。主要是其中的一些专有名词查不到，比如一元函数等

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。

Hilbet-type inequality is important in analysis and its applications. In recent years, by improving the way of weight coefficient, some research on the extensions and applications of this type of inequalities are developed. In this paper, we give a Hilbert infinite series inequality with the best constant factor whose kernel is a negative quadratic form by applying the method of weight coefficients. And an equivalent form is considered.

Hilbert型不等式在分析中有重要作用，近年来，由于改进权系数的方法，发展了这类不等式，并进一步推广应用和研究，应用权系数方法给出的一个带有最佳常数的核为负二次型齐次的Hibert型无穷级数不等式，同时考虑了它的等价形式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。