积分公式

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

In this paper, we consider the properties of so_called N_analytic functions , integral formula of Cauchy type and the problem of Riemann boundary value.

研究了N 解析函数的性质、Cauchy型积分公式及相应的Riemann边值问题，然后将其结果应用到一类奇异微分—积分复方程的可解性理论中，建立了其特征方程解的积分表示式。

In this paper, find Euler's formula using double integral , power series convergence and uniform convergence in the convergence region.

本文利用二重积分公式，幂级数在收敛区间内的收敛性质、一致收敛性质及可逐项积分的性质来证明Euler公式

A new concept of convex set and its some characteristic properties This paper give a new definition, the support direction of a boundary point of convex set.

2复杂网格的Buffon概率在积分几何中，运动公式是一些定义在定区域与动区域交集上的几何函数的积分公式。

Under the higher-dimensional situation, it introduces mainly the multiple integrals formulas on some standard areas, the multiple integrals formula by the methods of sampling, the reduction of dimensions and the boundary type cubature with a certain algebraic precision, and calculate multiple integrals with the methods of number theoretical net and so on.

在高维情形下，主要介绍了一些标准区域上的多重积分公式，用抽样法来求多重积分，具有代数精度的降维展开式和边界型求积公式，以及用数论网格的方法来计算高维积分等。

A variable-step modified Euler time integration method is proposed and analyzed. Four major factors that affect the efficiency of the variable-step modified Euler time integration method are discussed. These include stability and accuracy analysis for the damped fix-step modified Euler integration formula, adjustment method of the fix-step basic integration formula to accommodate step-size changes, suitable range of the step-size selection strategy based on truncation error concept and development of the step-size selection strategy based on apparent frequency concept to satisfied the specified error bound and stability condition.

提出了变步长修正Euler时间积分法，详细讨论了影响变步长修正Euler时间积分算法效率的四个主要因素，它们包括：有阻尼问题的修正Euler法的稳定性和精度分析，调整固定步长的基本积分公式使之容纳步长大小变化的研究，基于截断误差概念的步长大小选择策略适用范围的讨论，同时满足规定误差界和稳定性条件的、基于表观频率概念的步长大小选择策略的建立。

The traditional virtual boundary integral expression is based on the extension of single layer potential, for the integral formulas related to single layer potential for parabolic problem, the numerical computation of the exponential integral function is unavoidable.

通常的虚边界积分公式是利用单层位势的延拓来建立虚边界元积分方程，但对带时间变量的单层位势，要涉及到指数积分函数的计算。

The characteristic of this method lies in transforming improper integral into the usual one. Thus various kinds of usual approximate integrals can be used, and the observed data may be calculated directly and conveniently to obtain necessary numerical accuracy.

该方法的特点是把Abel变换的广义积分变化成通常的积分，这样就能够使用各种通常的近似积分公式直接从实验数据计算到所要求的数据精度。

The indefinite integral formula of rational proper fraction function is worked out by utilizing the relation between derivation and indefinite integral, and indefinite integral is calculated by using derivative.

本文利用求导与不定积分的关系，得出了有理真分式函数不定积分公式，并利用导数计算其不定积分。

On Buffon's problem for the complicated lattice Kinematic formulas in integral geometry are integral formulas that represent integrals of geometric functions on the intersection of fixed and moving domains.

2复杂网格的Buffon概率在积分几何中，运动公式是一些定义在定区域与动区域交集上的几何函数的积分公式。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。