Open course ware

PROFESSOR: We have to ask what happens here? This series for h of u doesn't seem to stop. You go a 0, a 2, a 4. Well, it could go on forever. And what would happen if it goes on forever? So if it goes on forever, let's calculate what this aj plus 2 over aj as j goes to infinity. Let's see how the coefficients vary as you go higher and higher up in the polynomial. That should be an interesting thing. So I pass the aj that is on the right side and divide it, and now on the right-hand side there's just this product of factors. And as j goes to infinity, it's much larger than 1 or e, whatever it is, and the 2 and the 1 in the denominator. So this goes like 2j over j squared. And this goes roughly like 2 over j. So as you go higher and higher up, by the time j is a billion, the next term is 2 divided by a billion. And they are decaying, which is good, but they're not decaying fast enough. That's a problem. So let's try to figure out if we know o...

So, one question to ask ourselves is, what is engineering? How do we define, what is engineering? Well, the definition I like to use is one put forth by Steve Senturia, one of our professors who is now retired. He defined engineering to be the purposeful use of science. All right, so what is 6.002 about? So, 6.002 is a first course in engineering. And I like to view 6.002 as the gainful employment of Maxwell's equations. Many of you have seen Maxwell's equations before. Most of you should have. And they are hard stuff. 6.002 is all about teaching you how to simplify our lives, make things simple. So, if you can gainfully employ Maxwell's equations, gainfully employ the facts of nature to build very interesting systems. So let me show you how the transition is made. So, there's a world around us, nature, so we made some observations in nature. We make measurements, and we can write down large tables of measurements. So, for example, we can take objects and ...