WEBVTT 00:00.780 --> 00:01.590 Hello. 00:01.800 --> 00:06.540 Welcome to my second lecture of distinction in this lecture. 00:06.540 --> 00:14.310 We'll talk about functions now functions are one of the most important part in commerce and metaphysics 00:14.730 --> 00:21.570 especially when you are doing advanced simulation where you need to input your own equations in your 00:21.570 --> 00:22.890 simulation. 00:22.890 --> 00:27.600 So I'll go one by one and explain what are these. 00:27.840 --> 00:33.810 So we have analytic function interpolation piece wise and we have more functions. 00:34.470 --> 00:40.980 So if we click on analytic we have an analytic function here. 00:40.980 --> 00:47.380 Now in the expression if I write X squared. 00:47.450 --> 00:53.450 Argument is X and if I choose to see a lower limit two minus one. 00:53.460 --> 01:01.430 And if I click on plot b c I get uh parabolic which is why equal to X squared. 01:02.040 --> 01:05.060 So this is a very basic example. 01:05.160 --> 01:11.790 Suppose you want to use a parabolic intuition inside your simulation somewhere in some form. 01:11.790 --> 01:18.480 You can use in one to call this parable inside your simulation. 01:18.480 --> 01:19.920 So this is the analytic function. 01:20.640 --> 01:22.590 Okay nice. 01:22.590 --> 01:26.560 Now let us check where this interpolation. 01:26.900 --> 01:28.800 Suppose a t equal to 1. 01:28.800 --> 01:38.980 I say that the function of value is 10 adequate to it is 20 a decoded 3 it is 50. 01:38.990 --> 01:40.610 Now if I plot. 01:40.680 --> 01:52.110 You see we get a plot where at t equal to one we have 10 uh equal to two we have 20 and be equal to 01:52.110 --> 01:57.420 three we have fifty which is equal to this value but basically this is why. 01:57.630 --> 02:01.460 And these are X values. 02:01.460 --> 02:10.140 So interpolation is used when you know the time and the functional value of your model what is peace 02:10.210 --> 02:11.120 price. 02:11.190 --> 02:12.200 Nobel Peace Prize. 02:12.210 --> 02:17.230 I think you have already understood that um. 02:17.310 --> 02:23.160 Suppose you have a function which is peace Y is continuous. 02:23.250 --> 02:25.400 So what does that mean. 02:25.410 --> 02:38.240 Now I define minus 1 to 1 and then to function the X now are defined from 1 to 3 as 7 times X if I click 02:38.250 --> 02:45.420 on plot what you see is from minus 1 to 1 02:48.410 --> 03:00.850 y equal to X is being plotted from 1 to t y equal to 7 x is plotted right. 03:01.000 --> 03:06.330 So this is a piece voice can heroes function. 03:06.710 --> 03:17.760 So in many kind of simulation for example if you are doing um let's say if you're working on my step 03:17.770 --> 03:19.110 index fiber. 03:19.180 --> 03:25.760 So basically if you're working on optical fiber whether refractive index very stepwise. 03:26.080 --> 03:34.960 So at the center we have the maximum effective index and then it's having stepwise effective index drop 03:35.680 --> 03:43.120 so you can define the effective index as a step function or as a piece rise and then carry on in your 03:43.180 --> 03:44.200 simulation. 03:44.200 --> 03:48.300 So the example I do not necessarily have to do that way. 03:48.310 --> 03:50.030 There are different other ways. 03:50.100 --> 03:57.410 First this is one scenario where you can use this option now in more option. 03:57.430 --> 04:00.060 You have a predefined function. 04:00.070 --> 04:02.190 For example you have a caution post. 04:02.200 --> 04:11.500 If you plot you get Al Gore's impulse for rectangle you have a rectangular way. 04:11.980 --> 04:19.000 So all these predefined functions are already built in form so so that we can use it in a simulation 04:19.420 --> 04:24.430 for whatever need you have to get your results. 04:24.430 --> 04:32.220 So I hope that I could explain um the properties of the function pan in my next video. 04:32.260 --> 04:37.400 I'll talk about um selection color and probe. 04:37.450 --> 04:38.890 Thank you for watching. 04:38.890 --> 04:39.900 See you around.