积分微分的

On the one hand, Lagrange hit upon the new idea to redefine the complete integral when he was inspired by his study on the first-order partial differential equation with the method of variation of constants.

在分析、比较欧拉和拉格朗日完全积分定义的基础上，依据原始文献，重点考究了拉格朗日重新定义偏微分方程完全积分的原因和动机。

In section 2, the integral expression, continuity and twice continuous differentiability and integro-differential equation satisfied by the expected discounted penalty at ruin Ф〓 are derived.

在第二节，我们得到了Ф〓的积分表达，连续性及二次连续可微性和积分-微分方程。

Therefore, it is significant to study the existence and controllability of multivalued functional differential equations and integrodifferential equations.

因此，对多值泛函微分方程和积分微分方程存在性和可控性的研究具有重要意义。

Then the integral-differential equations were reduced to the form with degenerate core by expanding Green＇ s function as series of characteristic function.

再使用展开法求出格林函数，即将格林函数展开为特征函数的级数形式，积分微分方程就成为具有退化核的形式，从而容易得到关于时间的非线性常微分方程组。

The numerical method for fractional integral presented in this dissertation isapplied to solve the equations.

然后利用分数积分的计算方法对这类非线性积分-微分方程组进行求解。

Applying the Hermite polynomial expansion, this integral-differential equation is creatively transformed into deterministic differential equation.

创造性地使用Hermite多项式展开，将确定性的积分——微分方程转换为确定性的微分方程。

Then the explicit expression of it under exponential claims and the differential equation are obtained.Thus we discuss the effects of credit and debit interests on it through data analysis. Through the research of the mean,the moment generating function and the higher moments of discounted aggregate dividend payments,we discuss the optimal dividend payments problems.

而对于Gerber-Shiu函数的研究，则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题，然后得到了它在指数索赔下的明确表达式以及Erlang(2)索赔下满足的微分方程，并通过数值分析得到贷款利息及存款利息对它的影响。

By adapting the existed numerical methods for ordinary and delay differential equations, and matching certain suitable numerical quadrature formulas, Rosenbrock methods are constructed for delay integro-differential equations, the stability criteria of the methods are derived.

通过改造现有常及离散型延迟微分方程的数值方法，并匹配以适当数值求积公式，构造了求解时滞积分微分方程的Rosenbrock方法，导出了其稳定性准则。

The discretisation of the velocity space in the kinetic theory of gases allowsus to replace an integro-partial-differential equation,the Boltzmann equation,by a system of hyperbolic semi-linear partial differential equations.

在气体运动论中将速度空间离散化处理，使得我们可以用一个双曲型的半线性偏微分方程组来取代Boltzmann方程这个积分微分方程。

Multivalued functional differential equations and integrodifferential equations are an important branch in the theory of nonlinear analysis, which have wide applications in many fields such as engineering, economics, optimal control and optimization theory.

多值泛函微分方程和积分微分方程是非线性分析理论的一个重要分支，它在工程、经济、最优控制及最优化理论等领域有着广泛的应用。

Life. But the intrinsic way of the Internet by wire confines accessing and using of the network information.

然而，Internet固有的有线连接方式大大限制了人们对网络信息的访问和使用。

I have a strong persuasion that this is true .

我坚信这是正确的。