18-01F07-L24 - MIT OpenCourseWare http:/ocw.mit.edu 18.01...

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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus, Fall 2007 Please use the following citation format: David Jerison, 18.01 Single Variable Calculus, Fall 2007 . (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms
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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus, Fall 2007 Transcript – Lecture 24 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today I want to get started by correcting a mistake that I made last time. And this was mistaken terminology. I said that what we were computing, when we computed in this candy bar example was energy and not heat. But it's both. They're the same thing. And in fact, energy, heat and work are all the same thing in physics. I was foolishly considering the much more, what am I trying to say, the intuitive feeling of heat is just being the same as temperature. But in physics, usually heat is measured in calories and energy can be in lots of things. Maybe kilowatt-hours or ergs, these are various of the units. And work would be in things like foot-pounds. That is, lifting some weight some distance. And the amount of force you have to apply. And these all have conversions between them. They're all the same quantity, in different units. OK, so these are the same quantity. Different units. So that's about as much physics as we'll do for today. And sorry about that. Now, the example that I was starting to discuss last time and then I'm going to carry out today was this dartboard example. We have a dartboard, which is some kind of target. And we have a person, your little brother, who's standing over there. And somebody is throwing darts. And the question is, how likely is he to be hit. So I want to describe to you how we're going to make this problem into a math problem. Yep. STUDENT: [INAUDIBLE] PROFESSOR: What topic is this that we're going over. We're going over an example. Which is a dartboard example. And it has to do with probability. OK. So what is the probability that this guy, your little brother, gets hit by a dart. Now, we have to put some assumptions into this problem in order to make it a math problem. And I'm really going to try to make them pretty realistic assumptions. So the first assumption is that the number of hits is proportional to ce ^ - r ^2. So that's actually a kind of a normal distribution. That's the bell curve. But as a function of the radius. So this is the assumption that I'm going to make in this problem. And a problem in probability
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This note was uploaded on 01/18/2012 for the course MATH 18.01 taught by Professor Brubaker during the Fall '08 term at MIT.

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18-01F07-L24 - MIT OpenCourseWare http:/ocw.mit.edu 18.01...

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