So, that was more like solving chess puzzles, and I couldn't have seen a career on that.

所以这一切更像是解一个棋局，我原来从不认为哲学可以成为一种职业。

普林斯顿公开课 - 人性课程节选

So, what we can do instead of talking about the ionization energy, z because that's one of our known quantities, so that we can find z effective.

我们做的事可以代替讨论电离能,因为那是我们知道的量子数之一，那是我们可以解出有效的，如果我们重新排列这个方程。

麻省理工公开课 - 化学原理课程节选

If the time you are interested in is not zero, you're allowed to cancel it and get the time from here.

如果你们关注的解不是零时刻,那么就可以忽略它,然后从这里解出时间

耶鲁公开课 - 基础物理课程节选

You then denature again, each one of these strands gets separated, primers bind, turn on the polymerase, a new strand is made.

然后你可以再次使产物链变性,使各链解旋,再结合引物,激活聚合酶,再生成新链

耶鲁公开课 - 生物医学工程探索课程节选

You'd pull out your pencil and paper, you can do it as a matrix inversion if you know how to do that, or you can just simply do substitution of one equation into another to solve it.

你知道你在小学的时候是怎么做的对吧？,你拿出你的笔和纸,如果你会的话,你可以解一个方程组,或者你可以单纯地。

麻省理工公开课 - 计算机科学及编程导论课程节选

I am going to show the equation, but I don't expect you to solve it.

我将给出这个方程式，但我不期望你可以得出解。

麻省理工公开课 - 固态化学导论课程节选

Prozac makes serotonin more prevalent and so in some extent might help alleviate depression.

百忧解能够增加血清素的含量,因此可以在某种程度上缓解抑郁症的症状

耶鲁公开课 - 心理学导论课程节选

Set the intersection points equal, the equations equal to each other and solve.

令交点处的两个方程相等,然后就可以解出来了

耶鲁公开课 - 博弈论课程节选

psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time,

我说过我们也可以解,波函数，我们讲的稍微有点慢，

麻省理工公开课 - 化学原理课程节选

So, we just want to appreciate that what we'll be using in this class is, in fact, the solutions to the Schrodinger equation, and just so you can be fully thankful for not having to necessarily solve these as we jump into the solutions and just knowing that they're out there and you'll get to solve it at some point, hopefully, in your careers.

所以，我们仅仅想要鉴别,将会在这门课中用到的，事实上就是薛定谔方程的解，而且你们可以非常欣慰,因为你们没有必要去,解这些方程而是直接用它们的解,并且知道这些解出自那里,希望你们在学习生涯中。

麻省理工公开课 - 化学原理课程节选

Do you realize that this is a pair of simultaneous equations in which you can solve for these two unknowns, if you like, in terms of these two knowns and these coefficients, which are like these numbers, 3, 2, 4, and 6?

你们是否发现这其实就是一个方程组,你可以用它来解出这两个未知量,你愿意的话,可以用这两个已知量,和这些系数,比如这些数字,3,2,4和6

耶鲁公开课 - 基础物理课程节选

You won't have to solve it in this class, you can wait till you get to 18.03 to start solving these types of differential equations, and hopefully, you'll all want the pleasure of actually solving the Schrodinger equation at some point. So, just keep taking chemistry, 18 03 you'll already have had 18.03 by that point and you'll have the opportunity to do that.

你们不用在课堂上就解它，你们可以等到得到18，03之后,再开始解这些类型的微分方程，希望你们都想得到,实际解薛定谔方程的乐趣,所以，保持来上化学课，你们在那个点将会得到,你们有机会做到的。

麻省理工公开课 - 化学原理课程节选

So always amazing to us how we go into the problem, our eye or mind can see one class of solutions, but the math will tell you sometimes there are new solutions and you've got to respect it and understand and interpret the unwanted solutions, and this is a simple example where you can follow what the meaning of the second solution is.

解决问题的方式总能让人惊喜不已,我们的眼睛或思想可以看见一类解,但数学有时会告诉你还有新的解,你不能忽视它,而是解释这些不期而至的解,这只是一个简单的例子,由此你可以理解第二个解的意义

耶鲁公开课 - 基础物理课程节选

You can do that by gently adding heat and making it basic, but you make the two DNA strands separate.

你可以通过逐渐加温并使之碱化的方法,使双链DNA解旋

耶鲁公开课 - 生物医学工程探索课程节选

So we know that we can relate to z effective to the actual energy level of each of those orbitals, and we can do that using this equation here where it's negative z effective squared r h over n squared, we're going to see that again and again.

我们知道我们可以将有效电荷量与,每个轨道的实际能级联系起来，我们可以使用方程去解它,乘以RH除以n的平方,它等于负的有效电荷量的平方,我们将会一次又一次的看到它。

麻省理工公开课 - 化学原理课程节选

So, let's say we start off at the distance being ten angstroms. We can plug that into this differential equation that we'll have and solve it and what we find out is that r actually goes to zero at a time that's equal to 10 to the negative 10 seconds.

也就大约是这么多,所以我们取初始值10埃,我们把它代入到,这个微分方程解它,可以发现，r在10的,负10次方秒内就衰减到零了。

麻省理工公开课 - 化学原理课程节选

In the early days when there are four or five formulas, you could memorize all of them and you can try each one of them until something works, but after a couple of weeks you will have a hundred formulas and you cannot memorize all of them.

刚开始我们只会涉及到四,五个公式,你可以全部记下来,你可以一个一个试,直到解出答案,但过了几个星期,你就已经学了一百多个公式了,你没法全部记下来

耶鲁公开课 - 基础物理课程节选

But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.

但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。

麻省理工公开课 - 化学原理课程节选