Let's say I have this bizarre looking function.

What's the definition of the Laplace transform?

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

2 is just one little point in R.

Well, and you could look at this visually

And this is a much faster way of evaluating the Laplace

This is our box.

Now.

Prev

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.

I could draw it like that as well, but let's just say this is set R.

We could make the ddmin even more generic by also passing the test function as a parameter.

So I don't know, it could be x squared times cosine of y or something.

Let me do the same idea.

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

And I'm going to shift it and multiply it times some arbitrary function f of t.

And at some point, we get tired and stop writing in elements.

I hope that doesn't confuse you.

And you could see that even this holds.

And actually, as you'll see later, it turns integration to divisions by s.

Repeated Any Number of Times

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

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.

Prev

let's call them k's.

And you can just subtract them from both sides.

But once again, c is an arbitrary constant.

But that's a good way to help you, hopefully, remember how to do these.

You get the point

So you could imagine, you can make an arbitrarily complicated function of things jumping up and down to different levels based on different essentially linear combinations of these unit step functions.

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

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

Second, not only should your approach take a minimum of tests for these 5 inputs but also for other arbitrary inputs.

It's pretty simple code.

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

Matches an arbitrary amount of whitespace.

Let's ignore c for a little bit.

Any

And you could look up e other places.

You must have these parentheses.