查询词典 integral calculus

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational functions.

不定积分概念，，不定积分性质，基本积分公式，不定积分证明方法，不定积分换元积分法，分部积分法，不定积分有理函数积分。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

The results show that mechanical heterogeneity has great influence on the J-integral of welded joint containing transverse crack. The J-integral on the path cross the interface between welded joint and base metal is higher than the J-integral on the paths in the weld metal for undermatched joint,while the J-integral on the path cross the interface between weld metal and base metal is lower than the J-integral on the paths in the weld metal for overmatched joint. Moreover,the difference of J-integral values increases with the increasing of the load and strength mismatching difference and the path-enclosed length of interface between weld metal and base metal.

计算结果表明：力学不均匀性对含横向裂纹焊接接头的J积分有重要影响，低匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值高于积分路径在焊缝内的J积分值，高匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值低于积分路径在焊缝内的J积分值；载荷越大，焊缝与母材的强度差别越大；积分路径中包含的焊缝与母材界面长度越大，J积分的差值越大。

Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, of fractal dimension calculus and fractal measure are given.

摘 要：探讨了宇宙分维构造的形式，给出了分维微积分及分形测度的数学基础，包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。

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。

This paper discusses the integrability of Riemann integral systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann integral and then gets integrable functions.

摘要本文较为系统地讨论了积分的可积性：通过分析诸多积分概念的共性，抽象定义了积分并详细讨论了其可积性，得出了可积函数类。

This paper discusses the integrability of Riemann's integral theory systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann's integral theory and then gets integrable functions.

摘要本文较为系统地讨论了积分可积性理论：通过分析诸多积分概念的共性，抽象定义了积分，详细讨论了其可积性理论，得出了可积函数类。

With the publication of the Dai Wei Ji Shi Ji, a translation of Loomis' textbook Elements of Analytical Geometry and of the Differential and Integral Calculus (1851), in 1859, the differential and integral calculus was introduced into China.

19世纪后期是中国数学由传统向近现代转化的一个重要时期，微积分是近代数学乃至大部分自然科学的最基础的理论，这个理论是从1859年出版的译著《代微积拾级》中介绍到中国来的。

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。

He became prime minister in 1997 and won international acclaim for his role in the Northern Ireland peace process.

他在1997年成为总理，并且因为在北爱尔兰的和平进程中发挥的作用受到国际社会的赞许。

Mixed Page Sorting Method Using the cuttable user model, this thesis proposes a mixed page sorting method by using cutted user model in server-side and complete user model in client-side.

隐私分级利用的混合式页面排序方法针对个性化搜索中搜索结果排序的问题，本文利用隐私可控开放的用户偏好模型，提出一个在客户端和服务器端分步进行的隐私分级利用的混合式页面排序方法。