而且，由此自然地推导出单节点数值积分公式。
Therefore the generalized numerical quadrature formula with the single node is deduced naturally.
利用定积分换元公式，可推导出一些非常实用的积分公式。
Several applied integral formula can be deducted from the method.
提出了综合评价线性多步积分公式积分性能的两项新指标。
Put forward two new technical indices synthesize appraising property of a linear multistep methods for orbital integration.
根据一维无限深势阱的归一化条件推出了一个反常积分公式。
Based on the normalizing of one dimensional infinite potential well, an anomalous integral formula is deduced.
文章提出几个形如(方程序略)的重要的积分公式，并加以举例说明。
This article put forward some important integral formulas, such as baa (the equation is abbreviated), and performs to explain with examples.
同时建立了另一类上半平面解析函数在其分布边值意义下的积分公式。
And the distributed boundary value's integral formula of another set of analytic function in upper half-plane is established.
用微分算子级数法得到分部积分公式，使一类积分计算变得十分简单。
By using differentiator series method, the formula of partial integration is obtained.
不要求掌握分部积分公式，但还是希望，有些人能在单变量积分中记住它。
Well, I don't expect that you would need integration by parts, although I still hope that some of you remember it from single variable calculus.
本文对几类二阶非线性常微分方程，利用首次积分求得了其通积分公式。
This paper has found general integral formulas of some types of two - order nonlinear ordinary differential equations by first integral.
以半无限大平板导体为例，直接从麦克斯韦方程推导出涡流电流密度计算的积分公式。
Taking the example of a half-infinite conducting plane, a formula for computing eddy current density is derived directly from Maxwell's equation.
借助变量代换、迭代等方法，提出几类新的高阶常微分方程，给出其相应的通积分公式。
By means of variable substitution and iterative method, this paper puts forth some new higher-order differential equations, and gives their formula of reduction of integrals to common denominator.
通过对一个给定的数值积分公式进行加速、改进，得到了两类新的精度更高的数值积分公式。
Two new kinds of higher accurate numerical integration formulae is obtained by acceleration and improvement of the given formula.
给出圆盘上的一些双弦幂积分公式，并由此获得一些重要的性质及双弦幂积分的一些不等式。
In this paper, we calculate the double chord-power integrals on circular disk, and arrive at some important properties and inequalities of the double chord-power integrals.
利用一个特殊非协调矩形元导出了一个新的使用节点少而代数精度高的非常规数值积分公式。
In this paper, a new unconventional numerical quadrature with fewer node values is established based on a special nonconforming rectangular finite element.
使用基尔霍夫衍射积分公式和菲涅耳衍射积分公式对高斯光束通过方孔光阑的衍射进行了研究。
The diffraction of Gaussian beams at an square aperture is studied based on the Kirchhoff and Fresnel diffraction integrals.
常用求导公式和积分公式-这个系列的小抄囊括了微积分i级和II级课程常用的求导和积分公式。
Common derivatives and integrals - Here is a set of common derivatives and integrals that are used somewhat regularly in a Calculus I or Calculus II class.
文中导出了用初始裂纹长度的分布及马尔可夫转移概率密度函数计算给定时刻裂纹长度分布的积分公式。
The distribution function of crack length at given time can be calculated by integration of the initial crack length distribution and the transition function of Markoff process.
由原函数与反函数的关系、分部积分公式以及变量代换得出利用反函数法求不定积分的一系列积分公式。
This paper give a series Integration formula of indefinite integral by inverse function method, which use the relationship of a function and its inverse function and the Integration by parts.
从衍射积分公式出发，利用贝塞尔函数，求得夫琅禾费环孔衍射积分的精确解，并对衍射图样进行了分析。
Diffracton integral equations and Bessel Functions are used to get perfect solution of Fraunhofer ring aperture diffraction, and the diffraction pattern is analysed.
基于瑞利衍射积分公式，推导出非傍轴离轴高斯光束相干合成和非相干合成在自由空间中传输的解析公式。
Starting from the Collins formula, the properties of the off-axis Gaussian beam (OAGB) propagating through a paraxial ABCD optical system with an aperture are studied in detail.
以椭圆的离心角为积分变量，得到椭圆柔性铰链的转角计算的积分公式，推导出椭圆柔性铰链的刚度表达式。
In this paper, an integral formula for elliptical flexure hinge is deduced by introducing centrifugal Angle as the integral variable.
本文从衍射积分公式出发，利用贝塞尔函数，求得夫琅禾费环孔衍射积分的精确解，并对衍射图样进行分析讨论。
In this paper, diffraction integral equations and Bessel Functions are used to getting perfect solution of Fraunhofer ring aperture diffraction, and the diffraction pattern is analysed.
我们用从负无穷到正无穷的积分公式F(x)*x*dx,你看到的，这是相同的事，因为积分是类似的求和过程。
We have the integral from minus infinity to plus infinity of F(x)*x*dx, and that's really--you see it's the same thing because an integral is analogous to a summation.
利用惠更斯-菲涅尔衍射积分公式导出了部分相干平顶高斯光束（PCFGB）通过ABCD光学系统的传输公式。
The propagation formula of the cross-spectral density of partially coherent flattened Gaussian Beam(PCFGB) through ABCD optical system was derived using Huygens-Fresnel diffraction integral formula.
为了解决非均匀介质中的光传输问题，利用光学相位共轭波的时间反演特性，实现了对克斯林衍射积分公式的改进。
In order to study laser propagation in inhomogeneous medium, Collins formula was improved by using time inversion characteristic of optic phase conjugation wave.
在此本构模型基础上，利用隐式积分方法，推导出新的应力和背应力积分公式以及整体迭代所需的一致切线刚度矩阵。
Then we establish the constitutive model for simulating the non-massing behavior. Based on radial method and back Euler integration, new stress and back stress integration algorithm are proposed.
高余维子流形是仿射微分几何中难于处理的问题，鉴此，主要研究在余维数为2的情况下，中心仿射微分几何的积分公式。
Multi-condimensional submanifold is a difficultly problem in the study, and this paper investigates the integration formula of centroaffine differential geometry of codimension 2.
采用矩阵分解的方法，从柯林斯衍射积分公式出发，对高斯光束通过失调空间滤波器的传输特性进行了分析，得到了相应的解析式。
Based on the method of matrix decomposition, and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through misaligned spatial filter are studied.
采用矩阵分解的方法，从柯林斯衍射积分公式出发，对高斯光束通过失调空间滤波器的传输特性进行了分析，得到了相应的解析式。
Based on the method of matrix decomposition, and the Collins diffraction integral formulae, the propagation characteristics of a Gaussian beams passing through misaligned spatial filter are studied.
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