Now Isaac Newton and/or Joseph Raphson figured out how to do this kind of thing for all differentiable functions.

既然牛顿和拉复生已经,指数了如何解这种可导函数,因此我们就不用太担心了。

麻省理工公开课 - 计算机科学及编程导论课程节选

Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.

假设我的方程是这样，然后给出了一个解。

麻省理工公开课 - 固态化学导论课程节选

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, we'll pick up with that, with some of the solutions and starting to talk about energies on Friday.

会去解薛定谔方程的某个方面，我们在周五,将从一些薛定谔方程的解开始。

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're going to work out what firm's demands are going to look like for each possible price they could set.

你们要解出,公司针对每一个其可能设定的价格,它的需求是什么

耶鲁公开课 - 博弈论课程节选

Seems like, as far as I can tell, it's still a possibility that although there're a lot of puzzles here.

在我看来，这种可能性是存在的,尽管还有很多未解的疑团。

耶鲁公开课 - 死亡课程节选

This was no Saint Francis with enough time to knock out a few canticles or to preach to the birds or do any of the other endearing things so close to Franny Glass's heart.

圣人弗朗西斯没有足够的时间去,来唱颂歌或者向鸟儿告解或者做任何,其他讨喜的事情，正合弗兰尼的心意。

耶鲁公开课 - 1945年后的美国小说课程节选

So you know from algebra I can't actually solve this. There may be multiple solutions to this. What would I have to do to change my code? And the answer is fortunately not a lot.

我解不出来方程,可能会有多组答案,我需要怎样修改我的代码呢？,很幸运的,答案是不用修改很多。

麻省理工公开课 - 计算机科学及编程导论课程节选

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

But you might have to,also, refer to a Psalm over here or to another passage over here. And it's too difficult if you're unraveling scrolls and everything.

但你也许还要查阅，诗篇或者另一段文字,而解卷展轴太麻烦了。

耶鲁公开课 - 新约课程节选

Now just working with the four-note motive here-- A strange little dissonant chord there resolving to consonance.

现在四音符的动机出现,这有一段有点不和谐的和弦,解构成和谐音

耶鲁公开课 - 聆听音乐课程节选

I'm going to shift and spend the rest of this class on a couple of mysteries.

本节课接下来的时间,我们来讲几个心理学未解之谜。

耶鲁公开课 - 心理学导论课程节选

How could such a debauched character possibly understand the mysterious truths about chastity?

这样一个行为不检点的人物,怎么可能明白关于贞节的难解的事实呢？

耶鲁公开课 - 弥尔顿课程节选

I have to tell you the path, if you're going to solve a problem.

我得告诉你，如果你要解一个问题。

麻省理工公开课 - 热力学与动力学课程节选

Now, dereferencing works on y and because the pointers are sharing 13 that one pointee, they both see the 13.

现在，解引用在y上起作用了,因为指针共享,同一个指针数据，它们两个都看到了。

哈佛公开课 - 计算机科学课程节选

But when you solve the Schrodingerequation, you don't get just a set of solutions that are dependent upon one number.

但当你解薛定谔的方程式时，你没得到有一个统一答案的,一系列解决方法。

麻省理工公开课 - 固态化学导论课程节选

And, if we do so, we can actually get a handle on that Born exponent by solving the equation.

如果我们这样做，我们实际上能够得到波恩指数,通过解这个方程得到。

麻省理工公开课 - 固态化学导论课程节选

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

And when you solved the relativistic form of the Schrodinger equation, what you end up with is that you can have two possible values for the magnetic spin quantum number.

当你们解相对论形式的,薛定谔方程，你们最后会得到两个,可能的自旋磁量子数的值。

麻省理工公开课 - 化学原理课程节选

We're going to be looking at the solutions to the Schrodinger equation for a hydrogen atom, and specifically we'll be looking at the binding energy of the electron to the nucleus.

我们将研究下氢原子薛定谔方程的解,特别是电子和核子的结合能,我们将研究这部分。

麻省理工公开课 - 化学原理课程节选

The perspective is tricky-- and so we're trying to find the roots.

从视图上来看可能比较困难,因此我们来试试找到这个问题的解。

麻省理工公开课 - 计算机科学及编程导论课程节选

So, so far, we've been working pretty hard and we haven't, I guess, learned a lot, we've just kind of solved the thing out.

到目前为止我们的计算真的很繁琐,但是我觉得我们没学到什么东西呢,我们只是解出了一道题罢了

耶鲁公开课 - 博弈论课程节选

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

Somebody who's not a math major, tell me how I solve out for the maybe the math majors can't do it actually, it's too simple.

谁不是数学专业的,告诉我们怎么解呀,数学专业的觉得它太简单而不屑去解

耶鲁公开课 - 博弈论课程节选

The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.

解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件

耶鲁公开课 - 基础物理课程节选

It's a bit of a mystery right now.

现在这仍是个未解之谜

耶鲁公开课 - 死亡课程节选

So the game is not just to somehow or other get the solution to the problem set but to fully understand how it's done, and the TAs will be there to help you.

所以,这个过程不仅仅是,通过某种方式解出题目,还要全面理解解题的过程,助教会帮你们的

耶鲁公开课 - 基础物理课程节选

So, laughter is kind of a puzzle.

所以笑是一个难解之谜。

耶鲁公开课 - 心理学导论课程节选

You get a set of solutions that are dependent upon -These quantum states fall out of the solution to this equation.

你得到一系列的解,这些解依赖于量子状态,和方程解不相干的解。

麻省理工公开课 - 固态化学导论课程节选