我们还学过微分的链式法则，也就是用其他量来代替这些偏导数。
So, we've learned about differentials and chain rules, which are a way of repackaging these partial derivatives.
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.
采用了压缩性的坐标变换后，推导得到了五个一阶导数的微分方程组。
Using a compressibility coordinate transformation, a set of the first derivative differential equations has been derived.
讨论了一般微分单项式的导数的值分布，提出一个新的定理，并进行较为详细的证明。
The paper discusses the value distributions of the derivative of differential monomials, presents a new theorem and proves it in more details.
在很多物理和力学的问题中常出现最高阶导数项带有小参数的微分方程。
In many problems of mechanics and physics there frequently appears the differential equation with the derivative term of the highest-order containing small parameters.
针对对称导数、对称偏导数，给出了一些新形式的微分中值定理。
In this paper, symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
本文旨在研究求解非凸约束优化问题的基于二阶导数的微分方程方法。
The aim of the dissertation is to study second order derivatives based differential equation approaches to nonconvex constrained optimization problems.
其中关于均方全微分和均方方向导数的定理是多指标随机过程所特有的结论。
Four of them, i. e. the theorems on the mean-square total differential and mean-square directional derivative are special conclusions of the multiple parameter stochastic processes.
利用能量范数的导数的性质，将超越特征值问题转化为常微分方程的初值问题。
And by using the property of derivatives of energy norms, the eigenproblem is transformed safely into a specific initial value problem of an ordinary differential equation.
科学计算及其应用常常需要多变量函数的有关偏导数问题的计算，通常使用的计算方法是符号微分或差分近似。
Evaluation relevant to the partial derivatives of the multivariable functions is often done in scientific computation, usually by means of the symbolic differentiation or the divided difference.
具体求解方法可归结为求导数、求解微分方程或求积分。
The concrete solving process can be reduced to finding derivative, differential equation or integral.
根据端淬实验数据和实验曲线导数变化规律，用线性试探法建立了端淬曲线微分方程，然后解得硬度分布函数。
A differential equation of the Jominy curves has been constructed according to the Jominy experimental data and the change of derivative of the Jominy curve.
偏微分方程就是，跟函数各个偏导数有关的方程。
A partial differential equation is an equation that involves the partial derivatives of a function.
所提出的插补方法采用五次样条和四次曲线多项式微分法近似求取导数，能够更好的满足精确加工的需要。
The applied interpolation method adopts quintic spline and derivatives generation approach for discrete points by using quartic polynomial, which can better meet the needs of high-accuracy machining.
自动微分技术能以较低的成本精确计算中大规模问题函数的导数，在科学计算、工程计算及其应用领域中有着广泛的应用。
Automatic differentiation, by which the derivatives of the function can be evaluated both exactly and economically, is applied to the field of scientific and engineering computation extensively.
微分方程简单说是含有导数的方程。
A differential equation is simply an equation that contains a derivate.
对多元有限离散函数引入了偏导数及微分新概念，并讨论了其性质。
The partial differentiations and derivatives are introduced for multivariate finite discrete functions, and the properties of which are discussed.
利用类似微分几何理论的方法，通过引入微分代数系统的m导数，利用微分代数系统无源性定义以及kvp特性的等价定理。
Similar to methods of differential geometry theory, equivalent theorem between differential algebraic systems passivation and KVP property was used by introducing m derivative.
根据有理函数及其导数性质，用微分法把有理函数分解为部分分式的和，给出了一次因式所对应的部分分式各系数和二次质因式前两对系数的计算公式。
Raised the differential method of resolving rational function into fractions, and formulas were suggested of the coefficients which correspond to liner factor and quadratic prime factor.
有了边界变量偏导数的终端值以及它们适合的微分方程，就可以由终端反向积分这些微分方程求解出这些变量来。
With the terminal value of the partial derivative for boundary variates and their differetial equation, the variates can be solved by backward derivation of the differetial equation.
研究了一类和广义微分算式(在弱导数的意义下)相联系的最小算子和最大算子。
It is shown that the minimal operators are symmetric and the adjoint operators of the minimal operators are exactly the corresponding maximal operators.
该方法采用微分电路和三采样值运算法，以电流的二阶导数深度抑制非周期分量并提高对采样值的甄别。
The approach utilizes 2-level derivation of secondary current and a 3-sample fitting calculation for decaying DC component depress as well as the sample data identifying.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
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