# 积分的

integral

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

Based the new definition of double chord-power intergral which the pair of lines intersect the convex body in integral geometry, this paper studies the relationship of double chord-power intergral and chord-power intergral.

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.

The nonsingular integrals are popularly calculated by the Gauss numerical integral, and they are low in precision when the source points approach the element, and the singular integrals are complex.

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.

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.

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

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.

This paper presents an alternative way to transform the double integral in elasticity problem on 3-d into the linear integrals on the boundary of each subdomain, so that all the singular integrals and nonsingular integrals are calculated by analytical method.

Conditions of integral chain can be closed.

antiderivative：不定积分的

anticommutator 反换位子 | antiderivative 不定积分的 | antiholomorphic 反全纯的

indefinite integral：不定积分的

indefinite form 不定形式 | indefinite integral 不定积分的 | indefinite operator 不定算子

integrable：可积分的

176. infinitesimal 无穷小 | 177. integrable 可积分的 | 178. integral 积分

Integrating factor：积分因子Btu中国学习动力网

integrate 积;积分;......的积分Btu中国学习动力网 | integrating factor 积分因子Btu中国学习动力网 | integration 积分法Btu中国学习动力网

upper limit of integration：积分的上限

upper limit 上极限 | upper limit of integration 积分的上限 | upper pure value 上纯值

lower limit of integration：积分的下极限

lower limit 下限 | lower limit of integration 积分的下极限 | lower measure 内测度

principal value of integral：积分的值

principal value of argument 辐角的值 | principal value of integral 积分的值 | principal value of power 幂的值

unintegrated：未积分的

Definite integrations by parts：定积分的分部积分法

Newton-Leibniz's formula 牛顿-莱布尼兹公式 | Definite integrations by parts定积分的分部积分法 | Definite integrations by substitution 定积分的换元法

Definite integrations by substitution：定积分的换元法

Definite integrations by parts定积分的分部积分法 | Definite integrations by substitution 定积分的换元法 | Calculating definite integrals by using elementary定积分的元素法