And then there are variable names, things like X, and Y, and Z.

All of these are just constants, so this might as well just be 5.

Let me do that.

So it's going to be zero everywhere, and then at minus tau, we jump to this level, and then we stay constant at that level until we get to plus tau.

Sure.

And that was OK, because we had one set of initial conditions and we solved for our constants.

Let's do another ratio problem that's a bit of a classic.

It has to be an integer, he can't sell half of a ticket, so, and he definitely it has to be an integer.

It doesn't have to be.

The zoom level, measured in pixels per radian.

Or you could say that h of y is equal to some constant.

It's helpful for universality, but by itself it doesn't really provide us that.

And we start with the assertion that, again, testing the entire input should fail.

Now, let's multiply this times this and take all of the constants out.

The way we're going to show this is to go back to the definition of Big Theta.

languages don't is that it can also let you define functions that return multiple values or multiple arguments.

It's a whole class of functions.

Laplace transform of it's derivative, which is 3t squared.

Luckily for us, a JavaScript program is exactly the same thing, also a list of statements and function definitions.

Let's see if we can simplify it at ? all. ?

Since this is the only place where characters are being added, tag cannot be set.

As I scroll down, you can see the familiar init function, the position setting function, the set_noise function, and then we have two checking functions whether we have a collision with the world called grid, which I will show you in a minute. and we have a check_goal function to see if we reached a goal according to a certain distance threshold.

So this is a constant right here.

Irrational numbers.

So its formula will be y minus y1 is equal to some constant,

Both of those are numbers.

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So you could have just you have to have a constant, but it doesn't have to be on both sides of the equation, because they're arbitrary. cx minus cy, well, that's still just another constant.

There's nothing I can raise three three to the power of to get a negative number, so this is undefined.

Let me define a set, s, and it's equal to all of the vectors I can create, if I were to multiply v times some constant, so I multiply some constant, some scalar, times my vector v, and just to maybe be a little bit formal, I'll say such that c is a member of the real numbers.

I'll just show you some Python syntax that I've been using that is pretty helpful.

I'm going to add something later, when

So I can just rewrite that as A so now A is not a function anymore, it's just a number A times the second derivative of y, with respect to x, plus B times the first derivative, plus C times y.

So we'll take the derivative of the first expression with respect to x. mu of x is no longer a constant anymore, since we're taking the partial with respect to x.

So when you find these two distances, you sum of them up.

later videos, we'll take those algorithm and apply it specifically to the cost function J that we had to find for linear regression.

So you could also say that some constant times g of x plus some constant times h of x is also a solution.

So once again, maybe we'll subtract 3 from both sides, just to get rid of this constant term.

That's just a constant time operation there.

I could have written a plus c here, but then you have a plus c here.

So this is the same thing is 9 times x squared plus 9 times 6 is 54, 6x.

You, uh You gonna be in town long?

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So if you wanted to write it in the most general sense. you would write that 2X is the derivative of X 2 plus some constant.

That the original function, in order to not change it because if I just cancelled these two things out, the new function with these canceled would be defined when x is equal to negative 8.