无穷积分

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

其主要内容有：函数与极限，导数与微分，中值定理与导数应用，不定积分，定积分及其应用，空间解析几何与矢量代数，多元函数的微分法及其应用，重积分与曲线积分，无穷级数，微分方程等。

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。

The former is a theoretical foundation of the "probability language" compared with the Daniell Integral; and the later, as will be seen in the following chapter, offered the main methods for Daniell Integral.

并且介绍Daniell积分在定义无穷维空间积分中的应用。第四章我们首先按照Wiener 1923年文章中的方法考察Brown运动的数学描述，说明Daniell积分，特别是Daniell[5]中的方法，在Wiener工作中的重要

However, for exterior problem, in order to ensure the uniqueness of the solution, the behavior of the solution at infinity must be specified, thus the modification for the expression of the solution and the constraint for the solution of boundary integral equation are needed.

对外边值问题，考虑到二维Dirichlet问题的解应当在无穷远处有界，故解的边界积分表达式要做修正，对积分方程的解要有约束，这样去解边界积分方程得出的解才等同于原问题的解。

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。

Infinite integral is a type of improper integral in calculi, and it is also a difficult point in integral.

无穷限积分是微积分学中广义积分的一种类型，是积分知识的一个难点内容。

Infinite integral is a type of improper integral in calculi,and it is also a difficult point in integral.

无穷限积分是指函数在无限区间上的积分，例如+∫∞afdx型，它属于广义积分的一种。

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

Limits, Continuity, Derivatives, and Integration of Single Variable, Integration Techniques, Applications of Derivatives and Integrals, Infinite Sequences and Series, Multivariable Function and Their Derivative, Multiple Integrals, Integration in Vector Fields.

课程内容：单变数函数之极限、连续、微分、积分，积分技巧，微分与积分的应用，无穷数列与级数，多变数函数之偏微分、可微性，多重积分，极值问题，向量场积分。

The subjects include :(1) Limits and continuity,(2) The derivative,(3) The applications of derivative,(4) Partial derivative,(5) Infinite series,(6) Integration,(7) The technique of integral,(8) The applications of integration,(9) Multiple integrals.

主要课程包含有：(1)极限与连续，(2)导函数，(3)导函数的应用，(4)偏导函数，(5)无穷级数，(6)积分，(7)积分的技巧，(8)积分的应用，(9)重积分。

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。