And a quick note.

What it really is doing is, it's kind of saying, x k plus 1 is

nothing but x times k plus 1 times delta t.

Right? And xk is nothing but

x at time k delta t.

So it's, by incrementing k, what we are doing is we are finding out at

the next time instant, discrete dimension where should

I be, depending on my previous time instant.

That's all this equation is really doing.

A good thing to note here, though, is that we will be using just the first

two terms of the Taylor expansion, which is

what you guys did in the lectures as well.

This expansion

is really an approximation, because you see these dot

dot dot here it just goes on and on.

You keep taking derivatives, and you keep going on, so obviously the more

terms you use, the better your approximation of x of t will be.

But as of now, we're just going to use the first two terms of the expansion.

So let's see.

Here we have x of t is 2x, delta t is 0.5, we know this, t is k

delta t, and now let's put this entire thing

into this equation of ours, the discrete time equation.

And we get this guy here, x k plus 1 is equal to 2xk.

You guys should do this yourselves. It's really simple.

But just, you know, plug in values. You get this one equation.

And this is now our discrete time update equation.

And how do we use this?

Well, we are simply going to say okay, so at k is equal to 0, x of 0 is 0, and now

xk plus 1, which is x1, will be 2 times x of 0, which is actually 20, right?

So we saw that at k is equal to 1, which

is actually time point 0.5, I jumped from here to here.