-
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。
-
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。
-
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。
-
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
-
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。
-
So you can see that we're starting to have a very complicated equation, and it turns out that it's mathematically impossible to even solve the exact Schrodinger equation as we move up to higher numbers of electrons.
所有你们可以看到我们得到了,一个非常复杂的方程，结果是它在数学上是,不可能解出确定的,薛定谔方程,当我们考虑更高的电子数目的时候。
-
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？
-
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。
-
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
-
Final topic is laughter and this is a true mystery.
最后要讲的是笑,这是一个真正的未解之谜。
-
It operates in a similar fashion to DNA polymerase in that it denatures locally or opens up the double stranded DNA, but it's different in that it creates a new polymer from the DNA template in the language of RNA, using RNA nucleotides and not DNA nucleotides.
它的作用机制类似于DNA聚合酶,在局部使DNA双链变性,解旋,但不同的是,它合成了一个基于DNA模板的,使用RNA编码语言的新聚合物,即使用核糖核苷而非脱氧核糖核苷
-
The power of linearity is F=k1+k2 if I come across f of x, y, z equals k1 plus k2, if it is a linear equation, I don't have to go and solve it all over again.
线性的威力是,一个方程，如果它是个线性方程，那么我就不用再去解他了。
-
You also need to bring a calculator, we'll be solving problems that involve calculations.
你还需要带一个计算器，因为我们会需要解一些涉及计算的题目。
-
So, laughter is kind of a puzzle.
所以笑是一个难解之谜。
-
Just one strategy for each player and that strategy was given by this equation.
每个参与人只有一个策略,而那个策略是这个方程的解
-
But the question is, is this the most general answer, or is it just one answer, and I think you all know that this is not the most general answer.
但问题在于,这是不是通解,或者说这是否只是一个特解,我想你们都知道,它不是通解
-
I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
-
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
-
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
-
We don't always want to go and solve the Schrodinger equation, and in fact, once we start talking about molecules, I can imagine none of you, as much as you love math or physics, want to be trying to solve this Schrodinger equation in that case either. So, what Lewis structures allow us to do is over 90% of the time be correct in terms of figuring out what the electron configuration is.
我们并不想每次都去解薛定谔方程，而且实际上，一旦我们开始讨论分子，我可以想象,你们中没有一个人，不管你有多么热爱数学或物理，会想去解这种情况下的薛定谔方程,总之，路易斯结构能让我们,有超过，90%，的概率判断出正确的,电子排布。
-
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
-
If you do that, you will find there is one unknown, which is v0, and we can solve for v0.
这样就只剩下一个未知量了,也就是 v0,我们就能解出 v0
-
It's a particle of mass m and momentum p has this energy so you solve for the energy, you get two answers.
一个质量为m,动量为p的粒子,有这么大的能量,你解出能量,得到两个解
-
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。
-
psi The solution of the Schr?dinger equation is psi, a wavefunction.
那薛定谔方程的解是什么，是，一个波函数。
应用推荐