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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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So, it's Newtonian mechanics, and the reason for this is because Newtonian mechanics does not work on this very, very small size scale.
牛顿力学，因为牛顿力学,在这种很小的尺度下不适用,我们说过，牛顿力学。
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And this is just a Newtonian expression of momentum, the product of the mass of the electron times its instant velocity.
这只是牛顿学上关于动量的表达，用电子质量,乘以瞬时速度。
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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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We use the adjective "Newtonian" but we don't speak of certain writers who are still interested in quantum mechanics as "Newtonian writers."
虽然我们用牛顿主义者这个词“,但是我们不会把那些,对量子力学有兴趣的人称作牛顿主义作家“
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Much more than biological instincts, much more than neurosis, much more than the person who exists in a Newtonian reality like a billiard ball.
不仅仅是生理本能，不仅仅是神经症，不仅仅是牛顿学说世界里的台球。
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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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In fact, I'll give an example in your own life where you will find that this law doesn't work.
其实,我可以举一个你们现实生活中的例子,它就不满足牛顿第一定律
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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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And so, you know from your Newtonian mechanics, as you were learning in 8.01, the dynamic force here mv^2/r is mv squared over r.
在8。01节对牛顿动力学系统的学习中，我们可以知道这里的运动受力,就是。
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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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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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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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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 is a Newtonian system from the mechanical standpoint.
这就好比是谈,牛顿的力学系统。
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And they had this feeling because there had just been this huge boon of discovery, of scientific advances that included Newtonian mechanics, it included Dalton's atomic theory of matter, also thermodynamics and classical electromagnetism.
他们会有这样的感觉,是因为他们刚，经历科学上的,大繁荣期，包括牛顿力学,道尔顿物质原子理论，热力学和电磁学,都取得了巨大进展。
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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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We'll come back to that, but you have to understand the structure of Newtonian mechanics.
我们等下回头再讲,不过你们要理解牛顿力学的体系框架
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The first law, if you want to say, "What's the summary of all of this?"
关于牛顿第一定律,如果你要问,"它该如何概括呢"
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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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So we are going to be studying in the beginning what's called Newtonian mechanics.
我们首先学习的是,牛顿力学
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By the way, Mr. Newton did not have math guys he could go to.
顺便说一下,牛顿先生可没有数学外援
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