基态波函数可以表示为沿这条确定轨迹的一系列积分，而能量则可以用位势极小值处的一系列微分表示。
The ground state wave function can be expressed as a series of integrations along the trajectory and the energy as a series of differentials at the minimum of the potential.
现在可以看到，全微分里面的这些偏导数系数，都可以用一个变量表示出来。
Now you see how the total differential accounts for, somehow, all the partial derivatives that come as coefficients of the individual variables in these expressions.
利用微分法我们可以，表示出这种情况下的df和dz的关系。
Using differentials means that we will try to express df in terms of dz in this particular situation.
因为，如果这些收入或效用的增加可以化为无穷小，那我们既能使用符号表示，也能利用微分学强大的操作了。
For if these increases of income or utility are reduced to being infinitesimal, one can use both the symbolism and the powerful manipulations of the differential calculus.
然后，可以用微分关系,或受约束的偏微分来表示,曲线的切向量，就是这样了。
Then actually there are ways you can use basically differentials and constrained partials to figure out what the tangent vector to the curve is and so on.
研究完整力学系统准坐标表示的运动微分方程在群的无限小变换下的形式不变性。
The paper studies the form invariance of differential equations of motion for holonomic systems in terms of quasi coordinates, under the infinitesimal transformations of groups.
微分动作(字母d表示)测量并对过程信号变化率进行反应，调整控制器的输出以达到最小的突出峰。
Derivative action (referred to by the letter d) measures and responds to the rate of change of process signal, and adjusts the output of the controller to minimise overshoot.
在此参数表示下，模糊数可直接视为二维度量空间r 2中的有界连续曲线，这给分析模糊微分方程带来了便利。
By the parametric representation, fuzzy number means a bounded continuous curve in the two-dimensional metric space R2, so that it is easy to analyze fuzzy differential equations.
比方说，如果已知一块金属板边界上的温度，那么整块金属板的温度就可由一个偏微分方程表示，这称为边值问题。
For example, the temperature of a metal plate can be expressed as a partial differential equation if the temperature on the boundaries is known. This is called a boundary value problem.
麦克斯韦电磁理论和爱因斯坦的广义相对论也表示的语言微分。
Maxwell's theory of electromagnetism and Einstein's theory of general relativity are also expressed in the language of differential calculus.
利用直接求微分的方法，给出了右伸长张量率的不变性表示公式。
An invariant formula for the right stretch tensor rate is given by a differential method directly.
在柱坐标下从微分波动方程出发，推导柱面光波的场分布，并利用远场近似条件导出当线光源与光轴成任意角度时，在垂直光轴方向的参考面上的复振幅表示。
The expression of complex amplitude is given in reference plane vertical to the optical axis by far-field approximation when the line source and the principal axis are at any Angle.
速率定律可以用微分形式或积分形式来表示。
Rate laws may be expressed in differential form or integrated form.
许多环境数学模型是用常微分方程表示的，它只考虑了时间对种群密度的影响。
Many environment mathematical models are ordinary differential equations where time is considered only as its effect on population density.
用求解常微分方程及其初值问题的方法得到由函数方程表示的基本初等函数。
The basic elementary functions represented by functional equations were obtained by using the methods of solving ordinary differential equations and initial value probe.
在柱坐标下从微分波动方程出发，推导柱面光波的场分布，并利用远场近似条件导出当线光源与光轴成任意角度时，在垂直光轴方向的参考面上的复振幅表示。
Starting from the wave differential equation, a method is deduced to express the complex amplitude of light wave fields in the reference plane which is vertical to the optical axis.
为模拟自然界中既包含竞争关系又包含捕食-被捕食关系的生态系统，建立用常微分方程组表示的环状模型。
An annular model for chemostat was depicted by a group of ODE(ordinary differential equation) to imitate the ecosystem which included competition and predator-prey relations in nature.
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.
用代数动力学方法求得了用泰勒级数表示的局域收敛的常微分方程的精确解。
By algebraic dynamical method, the exact analytical solutions of the ordinary differential equations are obtained in terms of Taylor series with local convergent radius.
在两端简支的边界条件下采用分离变量法求解偏微分方程，得到用级数表示的应力解，然后根据剪力滞系数的定义即可得到组合箱梁翼板的剪力滞系数。
Separation of variables is employed to solve the differential equation under the boundary condition of two ends of the girder being simply supported, and the solution of stress is…
图像的微分结构信息是图像结构的一种重要表示方法，可用微分不变量进行描述。
The image differential structure information, which can be described by using the differential invariants, is an important method to characterize the image structure information.
恒电量微扰下的过渡过程可用一组线性微分方程组表示，求解的关键是确定其初始条件值。
Under coulostatic perturbation, the transition process may be described by a group of linear differential equations, the key of deriving the equations is to determine the value of start condition.
研究完整力学系统准坐标表示的运动微分方程在群的无限小变换下的形式不变性 。
On the form invariance of differential equations of motion for generalized mechanical system in terms of quasi-coordinates;
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equation…
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exa...
在两端简支的边界条件下采用分离变量法求解偏微分方程 ，得到用级数表示的应力解 ，然后根据剪力滞系数的定义即可得到组合箱梁翼板的剪力滞系数。
On the basis of mathematical statistic, using the method of multiple regression analysis, the practical calculating formula of the shear lag coefficient in thin-walled curved box girders is derived.
在两端简支的边界条件下采用分离变量法求解偏微分方程 ，得到用级数表示的应力解 ，然后根据剪力滞系数的定义即可得到组合箱梁翼板的剪力滞系数。
On the basis of mathematical statistic, using the method of multiple regression analysis, the practical calculating formula of the shear lag coefficient in thin-walled curved box girders is derived.
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