You've already dealt with vectors.

And I think this whole notion of these skills should be taught.

You know, calculus is wonderful.

It makes sense, because normally when we're doing antiderivatives, you just take you know, when you

Or the slope of the tangent line at that point of the curve.

Newton and Leibniz, independently without knowing each other, invented calculus.

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

I had science projects and tons of astronomy books.

In algebra you probably won't.

So what's the derivative of psi with respect to x?

This is called the PlD controller.

So if I had a little cube here in the volume under consideration, that's a little cube you consider that dv.

I'll pay you back with my calculus notes.

In summary, instead of our students

Well, it's going to be the density function, x squared yz times the volume differential, but we're integrating with respect to z first.

So in the next video, we're now going to use this integrating factor.

Khan Academy is most known for what's now is about thousand videos on YouTube.

(Applause)

It's one of the great products of the human mind.

Let me just give you a few examples. So here's a baby.

That's true with regular equations or differential equations.

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

Have you used the videos yourself?

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.

Differentiation

The y integration.

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

In the next video, we're going to go into the details of the derivative term, which I wrote out but didn't really define.

Integral

And that's what the vertex is, is the minimum point of, or the maximum point of the parabola.

So for example, this is telling us 10 pi radians per second

In this video I want to familiarize you with the idea of a limit, which is a super important idea.

And my best sense of that is ... ... once you start doing calculus, ... ... you start using d for something very different ... ... you use it for the derivative operator.

And these are just a few.

These are just a few.

So that's just the area of the curve.

They didn't teach it before then.

It's saying, let's take a step down the hill and use that as our new equation our new position. Sorry.

Integral step

That's going to equal our old location, yi, and then this gradient, and the gradient here is just going to be the derivative with respect to yi.

And it should be obvious to you that now this is no longer calculus.

And I think what you'll find is that we're not learning really anything new.

Here we just use our implicit differentiation skills.

Eventually, this capital delta

And then that's how we know that that the derivative of psi with respect x is equal to 0, because our original differential equation was equal to 0.