1 00:00:00,600 --> 00:00:01,380 ‫Welcome back. 2 00:00:02,130 --> 00:00:12,750 ‫So in the previous video, we computed our second slope for our wrong Akutan method, using the state 3 00:00:12,750 --> 00:00:18,870 ‫values that they themselves were computed using the first slope. 4 00:00:19,930 --> 00:00:27,580 ‫And now, since we have our second slope, let's see what we're going to do with it again, I'm going 5 00:00:27,580 --> 00:00:30,910 ‫to use P as our example, St.. 6 00:00:32,060 --> 00:00:38,720 ‫So now what we're going to do with the second slope, we're going to apply it, but we're going to apply 7 00:00:38,720 --> 00:00:46,160 ‫it here at the original point at time T. So the second slope, it will be no different from the first 8 00:00:46,160 --> 00:00:46,580 ‫slope. 9 00:00:47,420 --> 00:00:52,580 ‫So it won't be a tangential graph at this point. 10 00:00:52,860 --> 00:00:55,310 ‫It will be some kind of other slope. 11 00:00:55,490 --> 00:00:57,950 ‫So let's say that it's like this. 12 00:00:58,980 --> 00:01:06,960 ‫So this is the second slope here that you found here, but you're going to apply it still at your original 13 00:01:07,650 --> 00:01:16,080 ‫present state values, so that time equals T and then what you will do with this second slope. 14 00:01:16,680 --> 00:01:25,740 ‫Again, you're going to project it until time T plus T over to until here. 15 00:01:26,990 --> 00:01:37,070 ‫So this is your second slope and this point here will now be another state to value at T plus T. 16 00:01:37,070 --> 00:01:38,090 ‫S over to. 17 00:01:39,350 --> 00:01:51,380 ‫And we're going to call it piece of cake plus one at time, t plus tips over, too, but now we're going 18 00:01:51,380 --> 00:02:01,880 ‫to put here, too, in order to let you know that this new state value that you have here, this one, 19 00:02:02,450 --> 00:02:09,020 ‫it was computed using slope to not slope one, but slope to. 20 00:02:10,210 --> 00:02:19,270 ‫So this number here, it's not squared, it's to tell you that we use slope two to compute this new 21 00:02:19,270 --> 00:02:25,960 ‫state that is at time T plus it's over two in this point here. 22 00:02:27,100 --> 00:02:29,350 ‫And mathematically, it will look like this. 23 00:02:30,570 --> 00:02:38,520 ‫Piece of cake, plus one at a time t plus tips over to. 24 00:02:39,500 --> 00:02:48,650 ‫That is computed using the second slope equals P Sarp K and now be careful. 25 00:02:49,340 --> 00:02:54,920 ‫The important thing here is to note that you're still using the present state. 26 00:02:56,090 --> 00:03:06,560 ‫You are not using this data value that you computed using slope one, no, you are using the original 27 00:03:06,890 --> 00:03:08,560 ‫present state piece up. 28 00:03:09,080 --> 00:03:09,590 ‫Why? 29 00:03:09,980 --> 00:03:20,990 ‫Because you're taking this second slope, but you're applying it here at K at times Coastie at the original 30 00:03:21,470 --> 00:03:23,330 ‫place from which you started. 31 00:03:24,440 --> 00:03:31,700 ‫So now from this point, you are projecting your second slope and therefore here you will still have 32 00:03:31,700 --> 00:03:37,820 ‫your present state piece cake, the one that you had at the very beginning. 33 00:03:38,600 --> 00:03:39,830 ‫And then plus. 34 00:03:40,980 --> 00:03:45,320 ‫And this is your second slope now, right? 35 00:03:45,750 --> 00:03:52,710 ‫It's this one here, and then you multiply it by T. 36 00:03:52,800 --> 00:03:54,570 ‫S over to. 37 00:03:55,610 --> 00:04:07,580 ‫And why because you're projecting it until this point here and remember, this was teams over two, 38 00:04:08,630 --> 00:04:16,370 ‫and so that's how you compute the state value using the second slope and that's how you do it for all 39 00:04:16,370 --> 00:04:17,300 ‫the other states. 40 00:04:18,390 --> 00:04:28,740 ‫So just like you did a year, but now instead of this one here, you will have two and then you will 41 00:04:28,740 --> 00:04:30,510 ‫have your second slope here. 42 00:04:31,620 --> 00:04:41,310 ‫So you write down all your new states in this form, so all your new states that you compute using the 43 00:04:41,310 --> 00:04:44,190 ‫second slope, you will do it like this. 44 00:04:45,290 --> 00:04:53,870 ‫So you start with your use date and then you go all the way down until you reach your state, so the 45 00:04:53,880 --> 00:05:01,550 ‫same template, the same blueprint, the same format, and then guess what you're going to do next? 46 00:05:02,600 --> 00:05:11,600 ‫You're going to take your new states, your new state values that you computed using the second slope's 47 00:05:11,600 --> 00:05:12,440 ‫that you had. 48 00:05:13,500 --> 00:05:22,890 ‫And you're going to put all the state values into these equations, and when you do that, you get your 49 00:05:22,980 --> 00:05:34,440 ‫third slope's, your 12 new third slope's, and if we take our state as an example, then we're going 50 00:05:34,440 --> 00:05:45,900 ‫to call our third slope of this state like this P dot, sub K plus one. 51 00:05:47,050 --> 00:05:49,650 ‫Sup t plus T. 52 00:05:49,720 --> 00:05:52,120 ‫S over to. 53 00:05:53,110 --> 00:06:01,930 ‫Because even the third slope was computed using the state values that themselves were computed using 54 00:06:01,930 --> 00:06:10,600 ‫the second slope, but these state values, they were also positioned at time T plus T over two. 55 00:06:10,870 --> 00:06:17,440 ‫So that's why the sub index here is T plus two over two as well. 56 00:06:18,400 --> 00:06:23,780 ‫But we had this notation for our second slope, which was here. 57 00:06:24,580 --> 00:06:30,100 ‫So in order not to confuse them, I'm going to put an asterisk here. 58 00:06:31,330 --> 00:06:40,450 ‫So now you know that the slope with an asterisk and subindex deposits over to that's your third slope. 59 00:06:41,600 --> 00:06:47,480 ‫Our first slope was like this simply p dot k. 60 00:06:48,570 --> 00:06:57,750 ‫That was our second slope and that would be our third slope and that notation you can apply to all the 61 00:06:57,750 --> 00:06:58,930 ‫other states as well. 62 00:06:59,610 --> 00:07:04,890 ‫So in the next video, we're going to see what we are going to do with the third slope, and then we're 63 00:07:04,890 --> 00:07:12,080 ‫going to compute a fourth slope and then that will be it. 64 00:07:12,090 --> 00:07:20,550 ‫Then we compute the weighted average and apply it to compute our new state value. 65 00:07:21,460 --> 00:07:23,680 ‫At time equals T plus. 66 00:07:24,550 --> 00:07:30,340 ‫So here, but first we need to get our fourth slope and we'll do that in the next video. 67 00:07:30,790 --> 00:07:31,690 ‫Thank you very much.