We want to integrate. So let's take the integral of both sides, going from the initial point to the final point.

分别从初态,到末态做积分，消去微分。

麻省理工公开课 - 热力学与动力学课程节选

so we're going to use this concept of the path to go from the initial point to the end point.

在处理状态函数时,路径的选取。

麻省理工公开课 - 热力学与动力学课程节选

You would have this initial response, now that initial response might be too slow to prevent you from getting chickenpox.

你对水痘病毒产生初始应答,这种初始应答可能,过于缓慢,无法预防水痘

耶鲁公开课 - 生物医学工程探索课程节选

Within 20 degrees of separation from you initial smile to the three people, the entire world will be smiling.

只需要20度的分隔,从你用笑容感染三个人开始，全世界就会笑起来。

哈佛公开课 - 幸福课课程节选

That's because they could have been released from different heights with different initial velocities.

那是因为它们可能是从不同的高度,以不同的初速度被抛出的

耶鲁公开课 - 基础物理课程节选

So then, going from the initial to final states with a red path, ou start with an isobaric processand then you end with an isothermal process.

因此沿着,这条红色路径，你从一个等压过程开始,以一个等温过程结束。

麻省理工公开课 - 热力学与动力学课程节选

get back to the initial point is going to require some input from outside, like heat or extra work or extra heat or something because you've done an irreversible process.

如果要逆转它,回到初始点，就需要外界的投入，比如额外的功，额外的热量等等,因为你进行了一个不可逆过程。

麻省理工公开课 - 热力学与动力学课程节选

p1 V1 Initial find -- there are many ways p2 V2 V1 I can get from one state to the other.

初态的氩气状态为,末态为。

麻省理工公开课 - 热力学与动力学课程节选

I released a piece of candy, threw it from my hand, and the initial conditions have to do with where did I release it and with what velocity.

我从我的手中抛出一颗糖,初始条件就是,我从什么位置抛出的,以多大速度抛出的

耶鲁公开课 - 基础物理课程节选

The answer is "Yes you would", the question is "Would that response, even though it's much faster, be fast enough to protect you from the initial exposure to tetanus that you got?"

是的,你的身体会马上做出应答,问题是 即便免疫应答十分迅速,但是否足够迅速,以保护你不被破伤风杆菌感染

耶鲁公开课 - 生物医学工程探索课程节选

So，the point is,every object falling under gravity is given by the same formula, but there are many, many objects that can have many histories, all falling under gravity, and what's different from one object and the other object is, when was it dropped, from what height, and with what initial speed.

关键是,每一个受重力作用下落的物体,都有同样的表达式,但是各个受重力作用下落的物体,都有不同的初始条件,所以它们的区别在于,下落时刻,下落高度和初始速度

耶鲁公开课 - 基础物理课程节选

How do you get from the initial state to the final state?

你是怎样,从初态过渡到末态的？

麻省理工公开课 - 热力学与动力学课程节选

Even at=0, and it has an initial velocity, so even without any acceleration, it will be moving from y0 to y0+vt.

即使at=0,它仍然有初速度,因此即使加速度为0,它也会从y0运动到y0+vt

耶鲁公开课 - 基础物理课程节选