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Now Isaac Newton and/or Joseph Raphson figured out how to do this kind of thing for all differentiable functions.
既然牛顿和拉复生已经,指数了如何解这种可导函数,因此我们就不用太担心了。
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Successive approximation, Newton-Raphson was one nice example, but there's a whole class of things that get closer and closer, reducing your errors as you go along.
逐渐逼近,牛顿迭代是一个很好的例子,随着你不断的时行下去,你会不断的离结果越来越近，逐渐地减少误差。
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It's one thing to plug in all the numbers and say, "I know Newton's laws and I know how they work."
我们平时只是把数字代进公式,然后说,"我懂牛顿定律,也知道怎么使用"
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It's really amazing that what Newton did in the case of gravity was to find the expression for this.
这一点非常神奇,牛顿在引力方面的研究,只是为了找出这个的表达式
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There, Newton doesn't tell you what forces are going to be acting on a body in a given situation.
在式子里,牛顿没有告诉你,在给定条件下,有哪些力,作用在物体上
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Newton is not going to come and tell you what force the spring will exert when it's pulled by some amount.
牛顿不会过来告诉你,弹簧被拉伸一定量时会产生多大的力
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You divide and you find it's 9 and you say, "Okay, I know what to do with Newton's laws."
除一下,会得到 9,然后你说,"好了,我会用牛顿定律了"
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In fact, until we do electricity and magnetism the next semester, everything's going to be based on just the laws of Newton.
其实,在下学期学习电磁学之前,所有的内容都是基于牛顿定律的
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Suppose Newton comes to you and says, "I have this great law, but I don't want to publish it under my name.
假如牛顿对你说,"我发现了这个伟大的定律,但我不想以我的名义发表
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But we get tired of saying that long expression, so we're going to call that a Newton, right?
但我们不想说得这么复杂,所以把这个单位称为"牛顿",对吧
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So, Newton did not ever tell you what the expression for force is in a given context.
牛顿从来也没有告诉过你,在这种情况下力的表达式
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In fact, my program crashes because I end up trying to divide by zero, a really bad thing. Hint: if you implement Newton's method, do not make your first guess zero.
我下一步都没法开始,实际上，我的程序会崩溃，因为我试着去除0了，真糟糕,提示你：如果你想用牛顿的方法，第一个猜想数别设为0。
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The point of Newton is, two things in the Law of Inertia, which one may think is trivial.
牛顿的观点是,惯性定律分两部分,可能有人觉得这种分法无关紧要
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The great discovery that Galileo and Newton made is that you don't need a force for a body to move at constant velocity.
伽利略和牛顿的伟大发现就是,物体不需要力来维持匀速运动
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But Newton's law is-- You see, you've got to go back and wipe out everything you know.
但牛顿定律是,如你所知的,你必须回到过去,忘掉你所知道的一切
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You have to be careful that this first law of Newton is not valid for everybody.
大家需要注意的是,牛顿第一定律并非所有情况都适用
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Except for electromagnetism, the basics of mechanics, which is the motion of Billiard balls and trucks and marbles and whatnot, was set up by Newton.
除电磁学外,力学的基础,也就是台球,卡车,弹球以及其它小玩意儿的运动原理,都是由牛顿建立起来的
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It's the 10 Newtons acting on it, because I know the 10 Newton is pushing me and I'm going to feel it even if I'm here.
他们认为这 10 牛的力作用在了物体上,因为这个力在推着物体前进,物体能感觉到的,即使没有直接接触
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Your reaction may be that you've seen Newton's laws, you applied them in school.
你们的反应可能是,我已经见过牛顿定律了,以前在学校就学过
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