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I think you can tell by analogy with what I did in one dimension that the position of that object at any time t is going to be the initial position plus velocity times t plus one half a t square.
你们可以类比一下我在一维情况下的结论,这个物体在任意时刻 t 的位移,等于初始位移,加上 v ? t + 1/2 ? a ? t^2
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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。
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In which I said, you know, I didn't like the fact that things like plus are overloaded, because you can use plus to add strings, you can use plus to add numbers, you can use plus to add floats.
那个玩笑是这样的，你们懂得，我并不喜欢,加法被重载这样的事情，但是你可以用加法，来对字符串进行合并，你可以用加法来加数字。
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So he curses existence, curses God at having made him so impotent that he can't change the fact that two plus two equals four.
所以他诅咒生存，诅咒上帝让他如此无能,无能到无法改变二加二等于四的事实。
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pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
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If I'm using algorithm that I'm now calling merge sort, T the running time involved in sorting N elements, T of N, you know, is just the same as running the algorithm for the right half, plus what's this plus N come from?
如果我用归并排序算法，对N个元素其运行时间，就等于此算法一半元素的运行时间,另一半的运行时间，再加上N，这个N是什么呢？
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if I say a particle's location is i times t^2 plus j times 9t^3, for every value of time, you can put the numbers in and you can find the velocity by just taking derivatives.
一个质点的位置,i ? t^2 + j ? 9t^3,在每一个时间点,你可以把数值代入,并通过求导得到速度
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I don't want to go through this in detail because I assume that you know it, plus I think it's a little bit easier to read and have some time to digest, but this process of translation or conversion of messenger RNA into a protein is a complicated biological process that's occurring all the time.
我不想在这些上讲太多的细节,因为我猜你们之前都有所了解了,你们花上一点时间,就能消化这些内容,但mRNA翻译,或者说转译成蛋白质的过程,是个极其复杂的生物过程,而且每时每刻都在发生
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And you can use mnemonics to try to keep these straight I see the T as sort of a plus sign.
你可以使用记忆术来记清它们,我将T看成是加号。
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*t t of n minus 1 is 3 plus 2 t of n minus 2.
加上。
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They start glomming together, but they don't stop with one plus one.
它们开始相互吸引，但是并不以1个吸引1个的形式结束。
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du external dV minus T surroundings dS is less than zero.
加上压强p，du，plus，p,乘以dV减去环境温度T乘以dS小于零。
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If I reduce that it would be 3 plus t of b minus 3, so in general 3*k+t this is 3 k plus t of b minus k. OK.
把b减去一个,在外面加个3就可以了,因此也就是。
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V So it's minus T dV/dT at constant p, plus V.
负的T乘以恒定压强下dV/dT，再加上。
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It says, in either case in general, t of b-- and this is where I'm going to abuse notation a little bit but I can basically bound it by t, 12 steps plus t of b over 2.
我可以用一个,比12+t的数代表,这里有点不准确的地方,具体的步数依赖于奇数偶数，但是你们可以看到在两个case中。
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So this is 3, plus 2 times 3, plus 4 t minus 2.
也就是3+2*3+4t，好。
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And so redefining then the temperature scale to the Kelvin scale, where t in degrees Kelvin is equal to t in degree Celsius, plus 273.15.
以K为单位的温度,是以℃为单位的温度,加上273。15度。
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This is 3 plus 3 plus t of b minus 2. Right?
+3+t对不对？
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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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Normally I couldn't do that Vdp because this term would have p dV plus V dp, but we've specified the pressure is constant, so the dp part is zero.
一般情况下我不能这么写,因为这一项会包含pdV和，但是我们已经假定压强为常数，所以包含dp的部分等于零。
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Delta u is q plus w. Delta u isn't zero.
U是q+w，△U不是零。
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And if I pull it out one more level, 12k it's 12 plus 12 plus t of b over 8, 12 k because I'll have 12 of those to add up, plus t of b over 2 to the k.
总结一下也就是说，在k步以后，总步数应该是，那这种情况什么时候才能停止呢？,才能到达最基本的情况呢？
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We all do believe something makes it true that two plus one equals three, but it's not the fact that empirical objects-- We don't do empirical experiments to see whether two plus one equals three.
我们都相信有些东西,使2加1等于3是正确的,但这不是说现实的东西,我们不会在现实中做实验,去看看二加一是不是等于三
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10 Even if your content subtotal was negative ten, that doesn't mean you're not better off alive, because negative ten plus the extra hundred points for the mere fact that you're alive is still going to give you a positive total, 90 plus 90.
就算你的生活内容部分总和是，那也不意味着你活得不够好，因为-10加上额外的100分说明了,你活着得到的总和仍然是正数，超过。
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q Work is zero. Delta u is w plus q, work plus heat. This is zero, this isn't.
功是零，△U是w加，功加上热量，这个是零。
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On the next step though, this, we get substituted by that. Right, on the next step, I'm back in the even case, it's going to take six more steps, plus t of b minus 1. Oops, sorry about that, over 2.
这一步就是偶数了，这一步会让我们得到，6+t这样的结果，因为b-1现在是偶数了,别忽略这里的细节。
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