Angličtina pro matematiky II
COURSE MATERIALS WEEK IV.
Listening 3
http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring-2006/VideoLectures/detail/embed01.htm
Listen to the part of the lecture and answer the following Qs.
1) What is the lecturer assuming?
a]……………………………………………………………….
b]……………………………………………………………….
2) Where can you study differential equations or modeling in case you need some explanations?
3) Which acronyms is the lecturer going to use?
4) What is the difference between those two equations?
5) What does the blue color indicate?
Transcript - Lecture 1 – 18.03
Listen for the second time and try to fill in the missing words.
OK, let's get started. I'm assuming that, A, you went recitation yesterday, B, that even if you didn't, you know how to 1) _____ variables, and you know how to 2) _____ simple models, solve physical problems with differential equations, and possibly even solve them. So, you should have learned that either in high school, or 18.01 here, or, yeah. So, I'm going to start from that point, assume you know that. I'm not going to tell you what differential equations are, or what modeling is. If you still are uncertain about those things, the book has a very long and good explanation of it. Just read that 3)______. So, we are talking about first order ODEs.
ODE: I'll only use two acronyms. ODE is ordinary differential equations. I think all of MIT knows that, whether they've been taking the course or not. So, we are talking about first-order ODEs, which in standard form, are written, you 4) _____ the derivative of y with respect to, x, let's say, on the left-hand side, and on the right-hand side you write everything else. You can't always do this very well, but for today, I'm going to assume that it has been done and it's 5)_______. So, for example, some of the ones that will be considered either today or in the problem set are things like y' = x / y.
That's pretty simple. The problem set has y' = x - y^2. And, it also has y' = y - x^2. There are others, too. Now, when you look at this, this, of course, you can solve by separating variables. So, this is solvable. This one is-- and neither of these can you separate variables. And they look extremely similar. But they are extremely dissimilar. The most dissimilar about them is that this one is 6)_________ solvable. And you will learn, if you don't know already, next time next Friday how to solve this one
This one, which looks almost the same, is unsolvable in a certain sense. Namely, there are no elementary functions which you can write down, which will give a solution of that differential equation. So, right away, one 7)_________ the most significant fact that even for the simplest possible differential equations, those which only involve the first derivative, it's possible to write down extremely looking simple 8) ________.
I'll put this one up in blue to indicate that it's bad. Whoops, sorry, I mean, not really bad, but 9) _________. It's not solvable in the ordinary sense in which you think of an equation is solvable. And, since those equations are the rule rather than the exception, I'm going about this first day to not solving a single differential equation, but indicating to you what you do when you meet a blue equation like that.
What do you do with it? So, this first day is going to be 10) _________ to geometric ways of looking at differential equations and numerical. At the very end, I'll talk a little bit about numerical ways. And you'll work on both of those for the first problem set.
Have a look at the underlined expressions and try to replace them with the expressions of the same or similar meaning.
Transcript - Lecture 1 – 18.03
Listen for the second time and try to fill in the missing words.
OK, let's get started. I'm assuming that, A, you went recitation yesterday, B, that even if you didn't, you know how to separate variables, and you know how to construct simple models, solve physical problems with differential equations, and possibly even solve them. So, you should have learned that either in high school, or 18.01 here, or, yeah. So, I'm going to start from that point, assume you know that. I'm not going to tell you what differential equations are, or what modeling is. If you still are uncertain about those things, the book has a very long and good explanation of it. Just read that stuff. So, we are talking about first order ODEs.
ODE: I'll only use two acronyms. ODE is ordinary differential equations. I think all of MIT knows that, whether they've been taking the course or not. So, we are talking about first-order ODEs, which in standard form, are written, you isolate the derivative of y with respect to, x, let's say, on the left-hand side, and on the right-hand side you write everything else. You can't always do this very well, but for today, I'm going to assume that it has been done and it's doable. So, for example, some of the ones that will be considered either today or in the problem set are things like y' = x / y.
That's pretty simple. The problem set has y' = x - y^2. And, it also has y' = y - x^2. There are others, too. Now, when you look at this, this, of course, you can solve by separating variables. So, this is solvable. This one is-- and neither of these can you separate variables. And they look extremely similar. But they are extremely dissimilar. The most dissimilar about them is that this one is easily solvable. And you will learn, if you don't know already, next time next Friday how to solve this one
This one, which looks almost the same, is unsolvable in a certain sense. Namely, there are no elementary functions which you can write down, which will give a solution of that differential equation. So, right away, one confronts the most significant fact that even for the simplest possible differential equations, those which only involve the first derivative, it's possible to write down extremely looking simple guys.
I'll put this one up in blue to indicate that it's bad. Whoops, sorry, I mean, not really bad, but recalcitrant. It's not solvable in the ordinary sense in which you think of an equation is solvable. And, since those equations are the rule rather than the exception, I'm going about this first day to not solving a single differential equation, but indicating to you what you do when you meet a blue equation like that.
What do you do with it? So, this first day is going to be devoted to geometric ways of looking at differential equations and numerical. At the very end, I'll talk a little bit about numerical ways. And you'll work on both of those for the first problem set.