I talked about life is not like a mathematic problem ? with you or in my other class ?
我说过生活不是个数学难题,是跟你们说过?,还是在我另外的课上?
We don't have requirements. We don't have to take math, that's the reason I applied to Brown,
我们没有什么硬性要求。我们不用上数学课,这是我选择布朗大学的原因,
So, what we are going to study now is a non-living object and we're going to pick it to be a mathematical point.
我们现在所要研究的的,是一个没有生命的物体,我们要把它看作一个数学上的点
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。
All the words mean things mathematically.
都可以从数学上描述。
In that autistic people show no impairments dealing with the physical world, they show no impairments on-- they don't necessarily show any impairments on mathematical skills or spatial skills, but they have a lot of problems with people.
因为孤独症患者并未表现出生理上的缺陷,所以他们并不会在数学技能或空间技能上,表现出什么缺陷,但他们却在人际交往方面存在很多问题
The so called binary system, 1 these zeros and ones that you'd probably have some vague sense underlie all computers today actually reduced to the exact same grade school kind of math and system except with computers, 1 because it's a lot easier to use just two digits, zero and one.
所谓的二进制就是,你觉得模糊的0与,在电脑上计算,事实上可以简化为跟小学数学一样,只是在电脑上计算而已,因为它更容易,仅仅使用两个数字,0与。
So in my first year, I took math, I took English, I took architecture.
所以在第一年里,我上了数学、英语、建筑方面的课。
But I know today in my math class, we were learning about the guys who created RSA Public Key Cryptography.
但是今天的数学课上,我们在学习RSA公钥加密算法的创始人。
And now I'm putting math on the board.
现在我将会在黑板上写一些数学运算
He was trying to describe electrons, but the theory said there are two roots in the quadratic equation and the second root is mathematically as interesting as the first one.
他当时只是想去描述电子,但是数学理论告诉我们,二次方程有两个根,而第二个根在数学上和第一个根一样有趣
Mathematically, it's done by taking the expression for R and differentiating everything in sight that can be differentiated as vector t.
从数学上看是这样的,写出 R 的表达式,并对所有可以进行矢量微分的部分,对时间 t 求微商
It is true mathematically, you can add two numbers, but you've got to ask yourself,"What am I doing as a physicist when I add these two numbers?"
在数学上它是正确的,你可以引入这两个常数,但是你需要问问自己,当我引入这两个常数时,这么做有什么物理意义
Mathematically, we can make it 0.
在数学上讲,我们把它变成零
- And in fact, mathematically if it's-- don't really have room for this.
事实上,从数学上来说-,这儿没有空间了。
So I don't know your mathematical background, but the textbook has an appendix, which is a reasonable measure of how much math you should know.
我不太清楚你们的数学功底,但教材上有附录,它能清楚地告诉你,你应该掌握多少数学
So, that's sort of the mathematically how we get to a, but we can also just look at the graph here, because every time we go one wavelength we can see that we're back in a maximum.
这是就我们得到a的数学,办法,但我们可以直接,从图上看,因为每次我们,经过一个波长,都回到一个最大值。
So if you're going to turn the crank v on the math correctly, you're going Cv to have to change this p into a V somehow.
所以如果哟啊正确地推导,我们需要把这个p变成,因为从数学上说这不是。
But mathematically, we've mentioned this before, log N or really to be precise, log base 2 of N, is the way you express this mathematically.
但从数学上说,之前我们已经提到过了,准确地说是log,N,以2为底N的对数,这就是它在数学上的表示。
So the object is a mathematical point.
这个物体就是一个数学意义上的点
Mathematically, you don't have to.
从数学上来讲没这个必要
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