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ANNOUNCER 1: 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 mitopencourseware@ocw.mit.edu. PROFESSOR: Hi. Today we're going to study something called the hyperbolic functions. And in a sense, we're going to show that in a very major way, the study of the hyperbolic functions mimics the study of the circular functions. And so in a sense, what we will do is parrot much of what we did for circular functions to wind up with our hyperbolic functions. Since the basic difference between a hyperbola and a circle is a sign, namely 'x squared' plus 'y squared' equals 1 versus, say, 'x squared' minus 'y squared' equals 1, I've entitled today's lesson, 'What a difference a sign makes'. Now, by way of brief review, recal...

GUEST SPEAKER 1: So hi, everyone. My name's Nicole. I'm here with Elaine. And both of us are part of the Society of Women Engineers. So we both just wanted to give you a little bit of background on ourselves, and then talk about some of the opportunities that SWE has. So I actually didn't know anything about SWE when I was in high school, either. I learned about it during my senior year. So SWE has multiple scholarships. We give away thousands and thousands of dollars to support girls who are excited about STEM and about engineering and getting involved in those fields. So when I [AUDIO OUT] had no idea what I wanted to do. I really liked doing the engineering side of things. So I'd worked in a lab for a couple summers at UCLA in a bioengineering lab. But I also really liked the business side. So I was part of a floral arrangement business, actually, that was run by my school. And so we did everything from marketing to sales to actually putting the flower ...

SPEAKER 1: 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 view additional materials from hundreds of MIT courses, visit MIT mitopencourseware@ocw.mit.edu. PROFESSOR: In this demonstration, we're going to explore a very curious phenomena in two beam interference, which is, where does the light go when we have destructive interference or a dark field? And we'll use our normal Michelson Interferometer to study this phenomena. Here it is. We have the laser here. It is the beam from the laser being reflected by mirror here, and then we go through this lens, then from the lens onto this Mirror and then from this mirror, then we enter the Michelson Interferometer. Here is one arm of interferometer, and here is the other arm. And then the beams leaving the interferometer will go onto this mirror, through this lens, and then on...

GUEST SPEAKER 1: My name is My name is Abraham, this is Jason. Jason, Kevin, [INAUDIBLE] And our team was called Speed Racers, and that now it's called the "Cat's Cradle." That's the name of the game. The change of the name was like a learning experience, at least the way I see it. And I'm sure my teammates will expand on this. So last week, when we did the little two-day project, one of the, I guess, the pitch we took was to make a racing game. And we had this plan that we were going to use the roll ball physics simulation mechanic to make it two simple wheels for an object. And in trying to solve... it ended up being a little harder than that. And next week we decided which is going to expand on that same project and try to finish the racing [INAUDIBLE] And the components that we tried to figure out and that we came up with making a game is something like a fail state, things that change speed, ramps, and [INAUDIBLE] But of the big debate and t...

SPEAKER 1: 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 view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Good morning everybody. Today we're going to continue our journey in looking at the 10 sort of basic types of reactions that you will encounter when studying basic metabolism. And they're all found on your vitamin bottle. So here are the Flintstones vitamins. I like Flintstones vitamins because you don't have to swallow them. You can chew them. And today what I'm going to start talking about is redox chemistry. What are the two redox active cofactors? And what we will focus on today is vitamin B2, which is riboflavin, and vitamin B3 which is niacin. So we're going to talk about oxidation and reduction. And what the cofactors are that involved i...

SPEAKER 1: 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 view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today what I want to do within the lexicon is tell you about nature's most spectacularly beautiful cofactors. And these are formed from vitamin B-12, which you find in your vitamin bottle. OK. So what is the structure of vitamin B-12, and why do I say they are spectacularly beautiful? So it's very hard to see, but if you look at the structure of this, where have you seen a molecule this complicated with five membered rings, each of which has a nitrogen in this? You've seen this when you studied hemoglobin, and you think about heme and proto protoporphyrin IX. If you look at the biosynthetic pathway of heme, a branchpoint of that pathway is to make this...

PROFESSOR 1: About yourselves, so raise your hand, I guess, if you're from Wellesley. Nobody at Wellesley wants to fly. OK. Harvard? OK. Everybody else can boo. Who has no MIT affiliation? All right. Awesome. Well, welcome. Raise your hand if you've never been in a light aircraft, if you have no experience in a little airplane. OK. PROFESSOR 2: That's good. That's a good number. For the MIT folks, how many of you are undergrads? OK. That's a good number. How many of you are graduate students? It's an even larger number, and how many of you are neither? You're just like an MIT alumni or staff. Just a few, OK, great. Well, welcome, all of you. PROFESSOR 1: And let's just go through the goals. Let's see who's in the room. Who wants to eventually fly an airplane? Whoa. How about a helicopter? Good. I'm happy to see that. What about drones? PROFESSOR 2: All right. That's a larger number than last year. That's great. PROFESSOR...