Let's say you have to go through three or four operations to get a final number, well, do it algebraically.
让我们说,你不得不通过3-4个操作,才能得到最终的数,好吧,用代数方法求解。
I mean, you may not understand it with algebra before but some of these sorts of pictures have you seen before?
我是说可能代数部分你没看懂,但你们以前见过类似的图像吧
I want to show you how easy it is to change the code. But, notice, once I've added this I actually have a problem. This is now an under-constrained problem. I have more unknowns than I have equations.
我加上这个条件后,我马上面临一个问题了,这就是现在是一个非约束性问题了,我的未知数比方程数多,你从代数中可以知道。
I am going to do it first pictorially and then I will write the algebra. What happens here?
下来我会做绘画工作,并写下一些代数,这儿怎么了?
You add them all up algebraically, keeping track of their sign, and that's the total force.
你再对这些力做代数加法,注意符号,就求出合力了
Now, unlike high school math or in algebra Z where you call things X and Y and Z, in programming, in computer science, you're actually dealing with humans where it's useful to have a variable name that's more descriptive than X and Y and Z.
不像高中数学或者代数中,称为X和Y和,在程序设计和计算机科学里,你实际上是在和人打交道,在这里有个描述性比xyz更强的,变量名称是很重要的。
All right, again this is straightforward kind of algebraic manipulations to get here.
好,必须再提一次这已经是,直截了当的代数运算了。
All I did was, I did a little bit of calculus, a little bit of algebra, and then I drew the thing.
我只不过是稍微用了点微积分,做了点代数运算,然后就画出来了
If you don't know how to measure anything, you are doing algebra and trigonometry.
如果你不知道如何进行测量,你就是在研究代数或者三角函数了
This is a matter of simple algebra, of taking this and putting it here.
本质上讲,这是简单的代数运算,把这个式子代入上面的式子
We did something very nerdy, namely, we just played with calculus and algebra.
我们使用了些死板的,微积分和代数
I mean the algebra doesn't really help the intuition here.
这里代数并没有真的有助于猜测
Now, we get to draw some lessons out of this thing, so everybody who's feeling a little bit shell shocked from having been doing algebra and calculus and drawing pictures and feeling like they've been cheated into taking a class that looks far too much like economics, calm down we're going to actually talk right now.
下面我们从中总结点经验出来,那些因为代数和微积分计算还有绘图,而感到十分不爽的同学,你们是不是感觉被我忽悠了,才会选这门一点都不像经济学的课啊,稍安勿躁,我们马上切入正题
My algebra, which is often wrong, suggests that the solution is S1* equals S2* equals 1 over .
我代数总是算错,最后解是S1*=S2*=1/
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