We said this could be any constant and this could be any constant.

It could be 1 2, it could be 10.

We can keep doing that.

I mean, we don't know what they are.

We could say, plus c, but just so that we can simplify it a

I hope that doesn't confuse you.

Let's say I have this bizarre looking function.

And you could see that even this holds.

Repeated Any Number of Times

What's the definition of the Laplace transform?

This right here is e to the minus st times f of t.

Before we said when f of x is equal to x squared that x is just any real number.

2 is just one little point in R.

Actually let's do something else just to clean it up a

So we first want to evaluate 1 to the 1st power, and anything to the first power is just that anything.

In this case 2, 3, and 5 are the prime factors of 30.

let's call them k's.

And you can just subtract them from both sides.

But once again, c is an arbitrary constant.

You get the point

And, you know, we could have some base a.

But imagine if it was, you know, an n by n by n cube.

It's pretty simple code.

Well, and you could look at this visually

To be clear, imagine the universe of all numbers and ignore the primes.

Matches an arbitrary amount of whitespace.

And this is a much faster way of evaluating the Laplace

Let's ignore c for a little bit.

This is our box.

Now.

Any

And you could look up e other places.

You must have these parentheses.

If we want to say there's no dirt in any location, it's a little bit more complicated.

When t is equal to infinity, what is x?

Well, we could put any value in for x.

Random engine

Random colors

Random Lamp Style

Any files

Any kind of value

Jeeves, Mr. Bickersteth is still up the pole.

Any raccoon.

So, non zero number.

This goes there. This matches that part.