Differentiation

We'll let R do the work.

Dispersion

Variance

We're almost at the correlation matrix.

You've already dealt with vectors.

Here we just use our implicit differentiation skills.

Eventually, this capital delta

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Dispersion samples

Field variance?

That's just dividing by N.

And now I have a variance co variance matrix.

Dispersion of the normal distribution

If psi is a function of x and y, and I would take not a partial derivative, I would take the full derivative of psi with respect to x, it's equal to the partial of psi with respect to x, plus the partial of psi with respect to y, times dy dx.

That's what a differential essentially is.

I expect you to see.

And we're done.

Plus the derivative of this with respect to x is easy, 2.

But this you could almost use differential notation. dy is a differential and dx is a differential.

It's pretty cool.

Because those correlations were based on samples that had a broader range of cognitive ability.

We gotta split them up!

That's what this playlist will deal with, ordinary differential equations.

So there's two big classifications.

Similarly, this is going to be the partial derivative of psi, with respect to y, but when we do the test, we take the partial of it with respect to x so we get that mixed derivative.

So plus f1 of x, that's just the first function, times the derivative of the second function.

So it's first order.

We took psi, up here, we treated the functions of x as a constant, and we just took the partial derivative with respect to y.

So those would be the high peaks of the density field.

But anyway, so this can also be written as the partial of y, with respect to x sorry, the partial of y, and then we took the partial of that with respect to x.

So, let's see what this, this equation will do.

So what is a linear second order differential equation?

Homogeneous differential equation.

So we'll just assume that that is our psi.

They say that y of 0 is equal to negative 1.

The mean is now a vector with 1 element for each of the variance.

So let's figure out what that is in terms of the derivatives of v.

The way you get that is divide the 6618 by 83. How about the variance?

The solvents in them do that very efficiently.

So if this is an exact equation, if this is the exact equation, if we were take the partial of this, with respect to y, right?

And then you have to multiply that times the derivative of y with respect x, which is just y prime.

We're going to use these throughout this entire course are standard deviation and variance.

Or if we use calculus terminology we would view it as the derivative.