‫Welcome back.
‫So in the previous video, we computed our second slope for our wrong Akutan method, using the state
‫values that they themselves were computed using the first slope.
‫And now, since we have our second slope, let's see what we're going to do with it again, I'm going
‫to use P as our example, St..
‫So now what we're going to do with the second slope, we're going to apply it, but we're going to apply
‫it here at the original point at time T. So the second slope, it will be no different from the first
‫slope.
‫So it won't be a tangential graph at this point.
‫It will be some kind of other slope.
‫So let's say that it's like this.
‫So this is the second slope here that you found here, but you're going to apply it still at your original
‫present state values, so that time equals T and then what you will do with this second slope.
‫Again, you're going to project it until time T plus T over to until here.
‫So this is your second slope and this point here will now be another state to value at T plus T.
‫S over to.
‫And we're going to call it piece of cake plus one at time, t plus tips over, too, but now we're going
‫to put here, too, in order to let you know that this new state value that you have here, this one,
‫it was computed using slope to not slope one, but slope to.
‫So this number here, it's not squared, it's to tell you that we use slope two to compute this new
‫state that is at time T plus it's over two in this point here.
‫And mathematically, it will look like this.
‫Piece of cake, plus one at a time t plus tips over to.
‫That is computed using the second slope equals P Sarp K and now be careful.
‫The important thing here is to note that you're still using the present state.
‫You are not using this data value that you computed using slope one, no, you are using the original
‫present state piece up.
‫Why?
‫Because you're taking this second slope, but you're applying it here at K at times Coastie at the original
‫place from which you started.
‫So now from this point, you are projecting your second slope and therefore here you will still have
‫your present state piece cake, the one that you had at the very beginning.
‫And then plus.
‫And this is your second slope now, right?
‫It's this one here, and then you multiply it by T.
‫S over to.
‫And why because you're projecting it until this point here and remember, this was teams over two,
‫and so that's how you compute the state value using the second slope and that's how you do it for all
‫the other states.
‫So just like you did a year, but now instead of this one here, you will have two and then you will
‫have your second slope here.
‫So you write down all your new states in this form, so all your new states that you compute using the
‫second slope, you will do it like this.
‫So you start with your use date and then you go all the way down until you reach your state, so the
‫same template, the same blueprint, the same format, and then guess what you're going to do next?
‫You're going to take your new states, your new state values that you computed using the second slope's
‫that you had.
‫And you're going to put all the state values into these equations, and when you do that, you get your
‫third slope's, your 12 new third slope's, and if we take our state as an example, then we're going
‫to call our third slope of this state like this P dot, sub K plus one.
‫Sup t plus T.
‫S over to.
‫Because even the third slope was computed using the state values that themselves were computed using
‫the second slope, but these state values, they were also positioned at time T plus T over two.
‫So that's why the sub index here is T plus two over two as well.
‫But we had this notation for our second slope, which was here.
‫So in order not to confuse them, I'm going to put an asterisk here.
‫So now you know that the slope with an asterisk and subindex deposits over to that's your third slope.
‫Our first slope was like this simply p dot k.
‫That was our second slope and that would be our third slope and that notation you can apply to all the
‫other states as well.
‫So in the next video, we're going to see what we are going to do with the third slope, and then we're
‫going to compute a fourth slope and then that will be it.
‫Then we compute the weighted average and apply it to compute our new state value.
‫At time equals T plus.
‫So here, but first we need to get our fourth slope and we'll do that in the next video.
‫Thank you very much.