‫Welcome back.
‫So let's see what it equals to this new state value that you computed at T plus tips using the third
‫slope, it equals still your original state value, your very first original state value that you had
‫because you are projecting this slope from this original point from which you started.
‫So your original state, Disvalue, plus your third slope times, and now you're going to put here T.
‫S and whites, well, that's because you're going from this point here till this point here and this
‫entire interval here is your tips.
‫So you start with your state and then you go through all the 12 states until you reach your state.
‫So, again, this is your third slope.
‫And then this state value was computed using the third slope like this.
‫OK, and now I think you can already guess how to compute the fourth slope and the final slope, you
‫take all these new state values that you have got from computing them, using the third slope, and
‫again, you put them into these equations.
‫All these state variables here will be replaced by all the state values here.
‫And when you do that, then you get another 12 slope's another 12 time derivatives.
‫And they will be your fourth slope's.
‫And our fourth slope, we can name like this four P state, we can do it like this P, that sub K plus
‫one, and in the sub index I'm going to put T plus.
‫Yes, and that's it.
‫And the reason why I put here T plus PTS was because this slope was computed using the state values
‫that were obtained at time T plus PTS.
‫And you use the same notation for all the other states as well, and this is where you stop because
‫now you have your four slope's.