So this is what differential calculus is all about.

And especially in a first year calculus or differential course, we're probably going to be dealing with continuous functions in soon. our domain.

This dy is differential. dx is a differential.

What's a differential?

Homogeneous differential equation.

Math, differential equations.

I took calculus and philosophy.

You know, calculus is wonderful.

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

Instantaneous rates of change differential calculus and Newton's term for differential calculus was the method of flexions which actually sound something fancier but its all about what's happening in this instant in this instant and to think about that why it not a super easy problem to address with the traditional algebra, lets draw a little graph here.

learning about the techniques of calculus,

The best known is situation calculus.

No calculus, I'll cut out that.

So the differential equations.

Here's differential productivity rates.

But this is actually a really useful technique later on when you get to calculus, and actually, differential equations, because a lot of times it's much easier and

Learning calculus requires a lot of practice.

Norvig The final problem involves situation calculus.

But you eventually end up in calculus.

It is called the differential,

What does a differential mean?

Differential equations are something different.

least the solvable differential equations.

We're solving a differential equation.

What is a differential equation?

Let's do one more homogeneous differential equation, or first order homogeneous differential equation, to differentiate it from the homogeneous linear differential equations we'll do later.

I'll pay you back with my calculus notes.

And at top of that pyramid, it's calculus.

I swallowed my pride, and I learned calculus.

So calculus has traditionally been taught very late.

You could do it with calculus, if you had, if you had calculus at your, at your, at your fingertips.

That's what a differential essentially is.

So what is a differential equation?

So, they have this differential ? derivative. ?

We have solved this differential equation.

This was the original differential equation.

And even within differential equations, we'll learn later there's a different type of homogeneous differential equation.

If Isaac Newton had done YouTube videos on calculus,

So I have students who are learning calculus already.

If Isaac Newton had done YouTube videos on calculus,

What does a homogeneous differential equation mean?

How does this relate to word differential ?

making math matter differential equations in action.

Partial differential equations we'll get into later.

Let's say this is my differential equation.