所以你要做的第一件事是你写下，你的微分方程。
So the first thing you do is your write down your differential equations.
因此可以马上写下，这个微分方程的，解法。
So you can write down immediately the solution to this differential equation.
只是在用微分的语言表达，来看先前提到的例子。
Just in the language of differentials. The example that I promised.
这个微分方程的，解法是什么呢？
得到一个微分方程。
这是一个我们先前不了解的精密复杂的微分信号系统。
This is a sophisticated differential signaling system that we haven't previously known about.
顺便说一下，也可以从微分的角度来考虑。
By the way, we can also think of it in terms of differentials.
这是个微分方程。
我们不再讨论微分方程序。
我们已经讲了微分。
我们来看g的微分。
这是一个，由电场e确定的偏微分方程。
It is a partial differential equation satisfied by the electric field e.
为什么我们偏爱偏微分呢？
好，注意到这里面有两个不准确微分量，和一个准确微分量，这是结论。
OK, notice we have two inexact differentials and exact differentials. This is a condition.
现在要进行微分，对除以温度之后的吉布斯自由能。
OK, now I have this derivative of the Gibbs free energy divided by the temperature.
有其它的方式来得到的，从这里开始求微分。
But we have another way to find it, which is starting from this and differentiating.
当对下面做微分的时候，这里的负号就消失了。
The minus sign here disappears when you take the derivative on the bottom.
下面我会就这三者稍微分别谈论一下。
所以我们就消掉了G的微分。
我只需要取它的对数，对温度微分。
I just need to take log of it, take its derivative with respect to temperature.
例如，这个解决方案的微分方程是一个功能。
For example, the solution of a differential equation is a function.
最后，给出了上述问题在偏微分方程方面的一个应用。
At last, an application of this problem in partial differential equation is also discussed.
让我们首先，对分母做温度的微分。
So let's take the derivative with respect to the temperature on the bottom first.
类似的方法还可以用在其它类型的偏微分方程数值解中。
Similar method may be applied in other types of partial differential equations.
这些量不是全微分。
常微分方程是大自然的语言。
The Ordinary differential equation is the language of the nature.
中心焦点判定是微分方程定性理论的重要组成部分之一。
The center focus decision problem is an important part of the differential equation theory.
本文给出了在复杂运动条件下，单摆的运动微分方程。
This paper give differential equations of the motion of the complex pendulum.
该控制微分方程求解简便。
The solution of the governing differential equations is very easy.
该控制微分方程求解简便。
The solution of the governing differential equations is very easy.
应用推荐