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And that's follow-- so this is, let me say this is a keyword-- that is followed immediately by a name.
接下来就是关键词，紧跟着名字的是一个等式-,在这个例子中。
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This is just an equality. I have a constant pressure dH process. This term here is equal to zero.
这是一个等式，这是个恒压过程,这项等于零，这意味着。
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What this equation merely says is that the present value of your remaining payments is always equal to the mortgage balance.
这个等式说明了,剩余偿还额的现值,就等于抵押贷款的余额
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That's what the optimist thinks-- not just for themselves individually, but for everybody, the total is always positive.
那是乐观主义者的想法-,而且不但是对他们自己，而是对所有人，等式结果总是正数。
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I think the main reason is that there are no equations that involve the third derivative explicitly.
我想主要原因是因为还没有等式,明显涉及三阶导数
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I've set these two things equal to each other: I've got one equation and one unknown.
我让两个方程相等,只剩下了一个等式和一个未知数
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That's certainly one way to do it, but for computers that's not necessarily the easiest way. So another way of solving it is to do something we already saw last time, which is basically, why not simply enumerate all possible examples and check them?
将一个等式代入另一个等式，这当然是一种办法,但是对电脑来说这绝对不是一件简单的事,所以解决这个问题的办法，正如我们上一次看过的,非常基本？
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He speaks in a language of math and it is very important for students to be able to have hot copies so that they can take notes on the paper rather than be working very hard to copy down the equations that he used in these lectures.
他以数学语言授课,所以发给学生教学材料,是非常重要的,这样就可在纸上做笔记,而不用拼命,抄下他在课上,用到的等式。
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So in fact this is indeed a positive number so we didn't make a mistake in our signs.
因此等式的右边也是正数,两边符号吻合。
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I'm sorry, I don't understand since the left hand side of your equation does not equal the right hand side, isn't that discount, not price?
对不起,我不太理解,这里等式左边和等式右边,并不相等,这里应该是折扣率而非价格
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System of linear equations. What are the equations here? Well, I could say, you know, the number of pigs plus the number of 20 chickens equals 20, right? Because we've got 20 heads. And then what else do I have?
如何解决这个问题呢？,用线性方程式的办法来解决，等式是什么呢？你应该知道,猪的数量加鸡的数量等于,对吧？因为我们有20个头？
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Now, what do those totals come to?
那么等式得出来的结果是什么？
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Let's multiply both sides by 2, I'll get 2q1* is equal to a - c over b - q1*.
等式两边同时乘以2,得到,2q1*=/b-q1
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dV OK, so we've got dT here dV here.
等式的左边是dT，右边是。
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By the way, that's a very remarkable property of the gravitational force-- the cancellation of the two ms.
顺便说一下,这是重力的一个重要属性,即可以消去等式两边的 m
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You might say that optimists are people who think that for everybody in every case, in every circumstance, the total is always positive.
乐观主义者认为,任何人在任何情况下，在任何环境里，等式结果永远是正数。
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This is the equation that relates the expected return on an asset.
这个等式是关于某一资产的预期收益。
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You might ask, well is this an approximate formula?
你们可能会问,这是一个约等式吗
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There's one more equation that I wanted to write down ... and I'm going to not-- I'm not going to spend a lot of time explaining this because it's going to take awhile.
这里我想再写一个等式,当然我不会-,我不会花太多的时间解释这个,因为要花太长时间。
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RT/V this expression becomes Cv dT over T is equal to CvdT/T=-RdV/V minus R dV over V.
这样，or，RT，over，V，bar。，So，now，这个等式就,可以化成。
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For example, if t* is the time you hit the ground, then t* satisfies the equation h - 1/2 g ^2 = 0.
例如,如果在 t* 时刻落地,那 t* 就满足等式 h - 1/2 g ? ^2 = 0
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So taking advantage of the fact that we know S1 is equal to S2 I can simplify things by making S1* equal to S2*.
我们利用S1=S2这个等式,这样用S1*=S2*可以化简了
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Solve this equation for t*, put it there and that's where you land.
从这个等式里解出 t*,代入那个式子就知道落点了
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What we do is we take the interest rate, which I'll call r, and plug it into a formula, which I didn't actually do the arithmetic to their number.
我们只需将利率r,代入等式中,虽然我没有代入数字验证过...
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And so, we can immediately write this du and then we can write du for the universe, which is system plus surroundings is equal to zero.
因此，我们可以立刻写出这个等式,然后可以写出总的的，也就是系统加环境的du，等于零。
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Let me just solve this for--let's solve x1 for r.
现在我们先解出用r表示x1的关系等式。
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I know this is the right answer, because if I now find the acceleration, I find it's mg divided by m and I get -g as the answer for all bodies.
我知道这个等式是正确的,因为现在如果我要求物体的加速度,用 mg 除以 m,我就得到 -g,这个结果对所有物体都成立
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So this guy here gets rid of this, and I have my answer as V1 over V2 to =p2/p1 the gamma power is equal to p2 over p1.
这两项抵消掉了，于是等式,变成了^γ
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One peculiar property of this--incidentally, at every point of time this thing holds, this is time to maturity.
顺便说一下这个公式一个特别的性质,这个等式在任何时候都成立,这是贷款剩余期限
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And, of course, see that either way we do that we'll have an equality.
利用两种不同的顺序求二阶导数,就可以得到一个等式。
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