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‫Welcome back.

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‫So let's see what it equals to this new state value that you computed at T plus tips using the third

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‫slope, it equals still your original state value, your very first original state value that you had

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‫because you are projecting this slope from this original point from which you started.

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‫So your original state, Disvalue, plus your third slope times, and now you're going to put here T.

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‫S and whites, well, that's because you're going from this point here till this point here and this

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‫entire interval here is your tips.

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‫So you start with your state and then you go through all the 12 states until you reach your state.

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‫So, again, this is your third slope.

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‫And then this state value was computed using the third slope like this.

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‫OK, and now I think you can already guess how to compute the fourth slope and the final slope, you

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‫take all these new state values that you have got from computing them, using the third slope, and

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‫again, you put them into these equations.

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‫All these state variables here will be replaced by all the state values here.

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‫And when you do that, then you get another 12 slope's another 12 time derivatives.

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‫And they will be your fourth slope's.

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‫And our fourth slope, we can name like this four P state, we can do it like this P, that sub K plus

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‫one, and in the sub index I'm going to put T plus.

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‫Yes, and that's it.

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‫And the reason why I put here T plus PTS was because this slope was computed using the state values

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‫that were obtained at time T plus PTS.

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‫And you use the same notation for all the other states as well, and this is where you stop because

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‫now you have your four slope's.