So if our inverse Laplace transform of that thing that I had written is this thing, an f of t, f of t is equal to e to the t cosine of t.

If this was just an F of s, what would f of t be?

So let's say my first parametrization, I have x of t is equal to t.

So this is going to be the integral from t equals a to t equals b, of p of p of x, really, instead of writing x, y, it's x of t, right? x as a function of t, y as a function of t.

Or we could just rewrite this as 2 times the unit step function starting at 2, where that's when it becomes non zero of t times f of t minus 2. f of t minus 2 is this with t being replaced by t minus 2.

I'll do it in another color, just to ease the monotony.

There is an initial state distribution for the time step 0.

So you get vb minus vc times time I'm just factoring out the time is equal to 300.

We started J, we went through, we could have said U, T, or S, but I will put T right over there.

Because each of those groups can make one to baby's T shirt.

He gets 3 for every ticket.

So I have another function. I think it's some sort of Jinja rendering thing.

We'll try to tempt the Rex now. Keep watching the fence.

It is defined as the ratio of the time derivative of the scale factor by the scale factor itself.

Well, this would just be shifting it to the right by 3.

This is the Laplace transform of f of t.

We're imaging that we're going be able to create a function T that is going to give us the answer to that.

I'm running out of space.

We'll get dr is equal to x prime of t dt times the unit vector i plus y prime of t times the differential dt times the unit vector j.

Let me do it on the side.

It's not impossible.

T statistic that we could derive from this, and you can view this T statistic as being a random sample from a

He leaves at the same time and he gets there 20 minutes early.

I want to put out a tracer on Eleanor Burnett.

It was the iPhone. The iPhone came out that day.

And then we'll call this f of t.

They're wearing rhinestone Tshirts.

The Laplace, which is equal to 0 to infinity e to the minus st f of t dt.

Let's see, so the Laplace transform of t is equal to uv. u is t, v is this right here.

And it's the integral of e to the minus s, but now instead of a t, we have the substitution.

The improper integral from 0 to infinity of e to the minus st times f of t so whatever's between the Laplace

So when you value this at 0, what happens?

Let's say that that is f of t.

t

T

...T.

I took out the constant terms there, and it's going to be a delta of t minus c dt.

Let's see if we can figure out the Laplace transform of t.

And it merges the stop sign and yield signs.

We saw, well, what if we took the Laplace transform of e to the I'll call it 1t.

So let's say that that's defined by r of t, which is just x of t times i plus y of t times our unit factor j.

Is it 2 times ab?

We have to be careful.

The word two, for example, needs its W in order to mark its connection to words like twice, twelve, twenty,

And this is almost superficially easy.