Separable equations.

So that's separable.

Are these data linearly separable?

Uranium will be chemically separable from Thorium, and we can go make a bomb out of it. Right?

Then I can make a variable substitution that makes it separable.

That turned it into a separable equation in terms of v.

This is a separable equation in terms of v and x.

And this is actually a separable differential equation in and of itself.

And that variable substitution allows this equation to turn into a separable one.

little bit to see if it's separable, because that's always the most straightforward way.

That makes sense, because the separable differential equations are really just implicit derivatives backwards.

But anyway, hopefully at this point you have a pretty good sense of separable equations.

And this first class of differential equations I'll introduce you to, they're called separable equations.

And also do fine and do reasonable things even if your data is not linearly separable.

And let's say we try to do this, and it's not separable, and it's not exact.

I think it's reasonable to do one more separable differential equations problem, so let's do it.

Using just your first year calculus derivative and integrating skills, you can solve a separable equation.

But if you look here, you actually could have figured out that this is actually a separable equation.

So we get mu over x, this is just a separable equation now, is equal to d mu dx.

And let's see, we want it to be separable, so let's put all the v's on the left hand side.

So the first separable differential equation is dy over dx is equal to x squared over 1 minus y squared.

If it's not separable, but you can still put it in this form, you say, hey, is it an exact equation?

And you can, if you'd like, you can try to make this a separable, but it's not that trivial to solve.

This is where we just get our algebra hat on, and try to simplify until it's a separable equation in v.

Or another way to think about it is whenever you took an implicit derivative, the end product was a separable differential equation.

And I know we did a couple already, but another way to think about separable differential equations is really, all you're doing is implicit differentiation in reverse.

Now, as I said, perceptron only converges if the data is linearly separable, and then it converges to a linear separation of the data, which is quite amazing.

And the reason why they're called separable is because you can actually separate the x and y terms, and integrate them separately to get the solution of the differential equation.

So once we solve this differential equation, and this is a separable differential equation, then we can use this initial condition, when x is 0, y is 1, to figure out the constant.

This is well, I don't know if it's an exact equation yet, but if you saw something of this form, your first impulse should be, oh well, actually, your very first impulse is, is this separable?

And of course if the data were not linearly separable so if you had some positive examples in here, or if you had some negative examples in here then the SVM will also do the right thing.

This was a homework problem or they were a closely related homework problem where you can take a graph and try to work out whether it is separable into two sets of nodes with edges only going between the sets.

Well, we collect data from satellites, from airplanes, from ground vehicles, from people.

It's from Decatur. From where?

Not from what, from whom.

I could come from here, from here, or from above.

like this with positive and negative examples, this data is linearly separable and by that, I mean that there exists, you know, a straight line, altough there is many a different straight lines, they can separate the positive and negative examples perfectly.

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