[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.11,0:00:05.52,Default,,0000,0000,0000,,Hi guys, I'm gonna give you a quick\Ncrash course tutorial on MathLab for
Dialogue: 0,0:00:05.52,0:00:08.07,Default,,0000,0000,0000,,first timers or\Napproximately first timers.
Dialogue: 0,0:00:08.07,0:00:11.68,Default,,0000,0000,0000,,When you first open MathLab you're\Ngonna see stuff like these,
Dialogue: 0,0:00:11.68,0:00:14.15,Default,,0000,0000,0000,,get rid of these as soon as you can,\Nthat's just getting in the way.
Dialogue: 0,0:00:14.15,0:00:18.05,Default,,0000,0000,0000,,You can still use them, they're\Nstill there, you just have to hover.
Dialogue: 0,0:00:19.94,0:00:21.82,Default,,0000,0000,0000,,This is the command window.
Dialogue: 0,0:00:21.82,0:00:23.79,Default,,0000,0000,0000,,You can use it like a calculator.
Dialogue: 0,0:00:23.79,0:00:27.42,Default,,0000,0000,0000,,Do all of your code immediately,\Nand get response back.
Dialogue: 0,0:00:27.42,0:00:31.95,Default,,0000,0000,0000,,I like to open up a script, and open\Nup the editor so I can write a script.
Dialogue: 0,0:00:31.95,0:00:33.22,Default,,0000,0000,0000,,And it's really clean in here.
Dialogue: 0,0:00:33.22,0:00:37.09,Default,,0000,0000,0000,,And then you can evaluate,\Nover in the command line.
Dialogue: 0,0:00:37.09,0:00:38.54,Default,,0000,0000,0000,,Notice, they're right next to each other.
Dialogue: 0,0:00:38.54,0:00:39.89,Default,,0000,0000,0000,,You can see.
Dialogue: 0,0:00:39.89,0:00:42.83,Default,,0000,0000,0000,,All the code heightwise.
Dialogue: 0,0:00:42.83,0:00:45.68,Default,,0000,0000,0000,,You can actually do this as well,\Nminimize the tool strip if you wanted to.
Dialogue: 0,0:00:45.68,0:00:54.41,Default,,0000,0000,0000,,I've already got a file here\Nthat we're gonna run through.
Dialogue: 0,0:00:55.76,0:00:58.37,Default,,0000,0000,0000,,And then go through all of\Nthis as quickly as possible.
Dialogue: 0,0:00:58.37,0:01:00.68,Default,,0000,0000,0000,,So just pause, rewind if you have to.
Dialogue: 0,0:01:02.79,0:01:06.41,Default,,0000,0000,0000,,When you start evaluating code in\Nthe editor, you can set these break points
Dialogue: 0,0:01:06.41,0:01:12.23,Default,,0000,0000,0000,,here to evaluate up to that point,\Nand then you can continue stepping.
Dialogue: 0,0:01:12.23,0:01:18.99,Default,,0000,0000,0000,,You can also set modify condition,\Nso this is a Boolean condition here.
Dialogue: 0,0:01:23.21,0:01:25.85,Default,,0000,0000,0000,,So to run, I like to use hotkeys.
Dialogue: 0,0:01:25.85,0:01:27.65,Default,,0000,0000,0000,,This is function F5, to run.
Dialogue: 0,0:01:29.14,0:01:32.81,Default,,0000,0000,0000,,Or you can just use one of the arrows,\Nup here, when there's a run arrow.
Dialogue: 0,0:01:34.12,0:01:37.81,Default,,0000,0000,0000,,Anyway, so\Nnow that it's running in debug mode,
Dialogue: 0,0:01:37.81,0:01:42.19,Default,,0000,0000,0000,,I can continue stepping by clicking\Nthis or just use the hotkey.
Dialogue: 0,0:01:44.25,0:01:51.37,Default,,0000,0000,0000,,So this first line, I stored a row vector,
Dialogue: 0,0:01:51.37,0:01:54.86,Default,,0000,0000,0000,,an array in a row into x1.
Dialogue: 0,0:01:56.02,0:01:57.94,Default,,0000,0000,0000,,And it goes from minus 2 pi to 2 pi.
Dialogue: 0,0:01:57.94,0:02:01.33,Default,,0000,0000,0000,,Or at least it's supposed to\Ngo from minus 2 pi to 2 pi.
Dialogue: 0,0:02:01.33,0:02:04.48,Default,,0000,0000,0000,,It defaults,\Nwhen it's just one colon there,
Dialogue: 0,0:02:04.48,0:02:07.14,Default,,0000,0000,0000,,it defaults to integer value increment.
Dialogue: 0,0:02:08.35,0:02:11.64,Default,,0000,0000,0000,,So you see over here it went\Nfrom -2 pi but it didn't quite
Dialogue: 0,0:02:11.64,0:02:16.29,Default,,0000,0000,0000,,hit positive 2 pi because\Nthe incrementation didn't allow it.
Dialogue: 0,0:02:17.67,0:02:22.36,Default,,0000,0000,0000,,So the next line here allows\Nit to do that because I
Dialogue: 0,0:02:22.36,0:02:27.48,Default,,0000,0000,0000,,enforced the conditions that it\Nreaches a total range of 4 pi.
Dialogue: 0,0:02:28.66,0:02:34.32,Default,,0000,0000,0000,,And it reaches that over 13 increments,\Nso there was a total of 14 points.
Dialogue: 0,0:02:35.53,0:02:39.00,Default,,0000,0000,0000,,And if you look at here, X2,\Nit goes from minus 2 pi to 2 pi.
Dialogue: 0,0:02:40.23,0:02:44.87,Default,,0000,0000,0000,,And he's our way to do this without\Nhaving to think about how to increment,
Dialogue: 0,0:02:44.87,0:02:47.18,Default,,0000,0000,0000,,is just to use the linspace command.
Dialogue: 0,0:02:48.61,0:02:51.40,Default,,0000,0000,0000,,And you just tell it how\Nmany points you want.
Dialogue: 0,0:02:51.40,0:02:55.56,Default,,0000,0000,0000,,This one, in this case, it's 14 points\Nthat it's identical to this, x2 and
Dialogue: 0,0:02:55.56,0:02:59.80,Default,,0000,0000,0000,,x3 are identical, if you look over here,\Nthey're identical.
Dialogue: 0,0:03:02.20,0:03:04.21,Default,,0000,0000,0000,,Just easier to use lens space sometimes.
Dialogue: 0,0:03:05.69,0:03:07.05,Default,,0000,0000,0000,,There's also log space.
Dialogue: 0,0:03:09.21,0:03:12.93,Default,,0000,0000,0000,,I created lens space again,\Nand using these for later.
Dialogue: 0,0:03:12.93,0:03:15.43,Default,,0000,0000,0000,,100 points for log spacing.
Dialogue: 0,0:03:16.48,0:03:23.19,Default,,0000,0000,0000,,This log space gives me ten to\Nthe zero to ten to the six.
Dialogue: 0,0:03:23.19,0:03:27.76,Default,,0000,0000,0000,,So it goes from one to a million\Nover a hundred points.
Dialogue: 0,0:03:31.12,0:03:35.11,Default,,0000,0000,0000,,So if you see, you look over here,
Dialogue: 0,0:03:35.11,0:03:38.96,Default,,0000,0000,0000,,this is the very largest number,
Dialogue: 0,0:03:38.96,0:03:45.02,Default,,0000,0000,0000,,it's a 1 times 10 to the sixth,\Nit's a million.
Dialogue: 0,0:03:45.02,0:03:46.93,Default,,0000,0000,0000,,Here's a matrix.
Dialogue: 0,0:03:46.93,0:03:51.17,Default,,0000,0000,0000,,It's a this is the first row,\Nsecond row, and they're separated,
Dialogue: 0,0:03:51.17,0:03:53.38,Default,,0000,0000,0000,,rows are separated by a semi colon.
Dialogue: 0,0:03:54.49,0:03:57.21,Default,,0000,0000,0000,,This a row vector B,\Nthis is a column vector C.
Dialogue: 0,0:03:59.37,0:04:02.31,Default,,0000,0000,0000,,The same values just one is\Na transpose of the other.
Dialogue: 0,0:04:03.57,0:04:10.00,Default,,0000,0000,0000,,It was three by four matrix of zeros,\Nthree rows, four columns.
Dialogue: 0,0:04:12.16,0:04:15.39,Default,,0000,0000,0000,,Matrix of ones,\Nthree by three identity matrix.
Dialogue: 0,0:04:17.05,0:04:24.31,Default,,0000,0000,0000,,Now, when we started\Ndoing matrix operations,
Dialogue: 0,0:04:24.31,0:04:29.72,Default,,0000,0000,0000,,let's take a look at how to solve this,\NA times Y is equal to B.
Dialogue: 0,0:04:31.13,0:04:35.21,Default,,0000,0000,0000,,If we know A and we know B,\Nhow do we solve for Y?
Dialogue: 0,0:04:37.46,0:04:42.98,Default,,0000,0000,0000,,So we invert A, so\NI'm gonna grab this and put it down here.
Dialogue: 0,0:04:44.23,0:04:47.62,Default,,0000,0000,0000,,This operator says,\Ninvert A and operate on B.
Dialogue: 0,0:04:48.67,0:04:52.62,Default,,0000,0000,0000,,This is going to give me an error because\Nthe matrix dimensions must agree,
Dialogue: 0,0:04:52.62,0:04:59.38,Default,,0000,0000,0000,,which means MathLab doesn't know how\Nto operate a matrix on a row vector.
Dialogue: 0,0:05:00.72,0:05:05.51,Default,,0000,0000,0000,,So this row vector for the least,
Dialogue: 0,0:05:05.51,0:05:10.04,Default,,0000,0000,0000,,the less obscure mathematical operation,\Nwhich is just matrix
Dialogue: 0,0:05:10.04,0:05:13.13,Default,,0000,0000,0000,,multiplication that has to be a column\Nvector, it has to be a column vector.
Dialogue: 0,0:05:14.14,0:05:18.66,Default,,0000,0000,0000,,There's also a way to do a row\Nvector here but it's a more
Dialogue: 0,0:05:18.66,0:05:23.02,Default,,0000,0000,0000,,obscure operation,\Nout of product of some sort.
Dialogue: 0,0:05:23.02,0:05:26.66,Default,,0000,0000,0000,,MathLab doesn't know how to\Ndo it unless you massage it.
Dialogue: 0,0:05:28.84,0:05:33.68,Default,,0000,0000,0000,,So you come over here and you put this\Ntranspose operator, this tick mark, and
Dialogue: 0,0:05:33.68,0:05:36.20,Default,,0000,0000,0000,,that'll allow it to do\Nthe correct operation.
Dialogue: 0,0:05:37.39,0:05:39.34,Default,,0000,0000,0000,,So that gives me a solution.
Dialogue: 0,0:05:39.34,0:05:43.12,Default,,0000,0000,0000,,My solution Y for this linear system.
Dialogue: 0,0:05:44.41,0:05:48.51,Default,,0000,0000,0000,,And then YY is gonna be the same thing\Nbecause C is already the transpose of B.
Dialogue: 0,0:05:48.51,0:05:52.62,Default,,0000,0000,0000,,[COUGH]\NThis is to check to make sure that I get
Dialogue: 0,0:05:52.62,0:05:55.19,Default,,0000,0000,0000,,B back, so there's B back.
Dialogue: 0,0:05:57.05,0:05:59.13,Default,,0000,0000,0000,,When I got my solution Y.
Dialogue: 0,0:06:00.79,0:06:06.40,Default,,0000,0000,0000,,Now here if I have an array of\Ninput values into this function,
Dialogue: 0,0:06:06.40,0:06:10.05,Default,,0000,0000,0000,,then this function automatically\Nloops through all those values, so
Dialogue: 0,0:06:10.05,0:06:12.00,Default,,0000,0000,0000,,you don't have to write\Nyour own four loop.
Dialogue: 0,0:06:14.36,0:06:18.53,Default,,0000,0000,0000,,So that's the output here is the sign\Nof every one of those individually.
Dialogue: 0,0:06:18.53,0:06:23.53,Default,,0000,0000,0000,,Now I'm gonna use these down below here.
Dialogue: 0,0:06:23.53,0:06:28.58,Default,,0000,0000,0000,,So this dot here
Dialogue: 0,0:06:28.58,0:06:33.02,Default,,0000,0000,0000,,doesn't mean dot product it means\Nelement wise multiplication or
Dialogue: 0,0:06:33.02,0:06:38.50,Default,,0000,0000,0000,,in this case element wise multiplication,\Ndown here it's element wise division.
Dialogue: 0,0:06:39.79,0:06:45.56,Default,,0000,0000,0000,,So it just takes the first element here\Nmultiply it with the first element here.
Dialogue: 0,0:06:45.56,0:06:49.48,Default,,0000,0000,0000,,Second element here, multiply it by\Nthe second element here, and so forth.
Dialogue: 0,0:06:49.48,0:06:52.62,Default,,0000,0000,0000,,And stores it in W.
Dialogue: 0,0:06:52.62,0:06:56.82,Default,,0000,0000,0000,,So if you look at the size of w, compare\Nit with the size of either Y1 or Y2,
Dialogue: 0,0:06:56.82,0:07:00.99,Default,,0000,0000,0000,,it doesn't matter,\Nthey're both the same size.
Dialogue: 0,0:07:00.99,0:07:03.34,Default,,0000,0000,0000,,And size returns all dimensions.
Dialogue: 0,0:07:04.61,0:07:08.44,Default,,0000,0000,0000,,As compared to length which I\Nhave suppressed the output so
Dialogue: 0,0:07:08.44,0:07:09.76,Default,,0000,0000,0000,,I have to actually bring it over.
Dialogue: 0,0:07:11.79,0:07:16.72,Default,,0000,0000,0000,,Let's say for example, length of B,\NB if you look up here,
Dialogue: 0,0:07:16.72,0:07:21.97,Default,,0000,0000,0000,,B is 3 by 4 and C is 4 by 3.
Dialogue: 0,0:07:21.97,0:07:26.10,Default,,0000,0000,0000,,So the length of either of these
Dialogue: 0,0:07:26.10,0:07:29.61,Default,,0000,0000,0000,,is the same because length\Nfinds the longest dimension.
Dialogue: 0,0:07:31.98,0:07:36.60,Default,,0000,0000,0000,,So going into the plotting,
Dialogue: 0,0:07:38.55,0:07:43.44,Default,,0000,0000,0000,,you can just call up the plot function and\Nit brings up a figure.
Dialogue: 0,0:07:43.44,0:07:48.15,Default,,0000,0000,0000,,Applies to that figure, you can come in\Nhere and insert labels, title, legend and
Dialogue: 0,0:07:48.15,0:07:50.90,Default,,0000,0000,0000,,all the stuff right here\Nif you wanted to but
Dialogue: 0,0:07:50.90,0:07:55.44,Default,,0000,0000,0000,,I suggest since we're gonna be coding\Na lot just get used to writing your code
Dialogue: 0,0:07:55.44,0:07:58.52,Default,,0000,0000,0000,,to do everything for\Nyou at least as much as possible.
Dialogue: 0,0:07:58.52,0:08:02.12,Default,,0000,0000,0000,,So there we added a title to it,\Nwe added a label.
Dialogue: 0,0:08:02.12,0:08:05.74,Default,,0000,0000,0000,,Now if I wanna add another\Nplot to the same figure
Dialogue: 0,0:08:05.74,0:08:07.19,Default,,0000,0000,0000,,I have to hold on to the figure.
Dialogue: 0,0:08:07.19,0:08:12.56,Default,,0000,0000,0000,,[COUGH] So then I can throw in another\Nplot under that same set of axis,
Dialogue: 0,0:08:12.56,0:08:14.55,Default,,0000,0000,0000,,let go the figure.
Dialogue: 0,0:08:15.85,0:08:20.72,Default,,0000,0000,0000,,Just because I've let go of it,\Nyou might assume that you can now
Dialogue: 0,0:08:20.72,0:08:25.43,Default,,0000,0000,0000,,start another plot and it'll create a new\Nfigure for that plot, but it doesn't.
Dialogue: 0,0:08:25.43,0:08:28.45,Default,,0000,0000,0000,,It overwrites on top of this,\Nit writes to the same figure.
Dialogue: 0,0:08:30.54,0:08:35.57,Default,,0000,0000,0000,,So that's an obvious problem,\Nthe way to get over that is by explicitly
Dialogue: 0,0:08:35.57,0:08:40.74,Default,,0000,0000,0000,,calling the figure,\Nthis is just a quirkyness with MathLab,
Dialogue: 0,0:08:40.74,0:08:43.71,Default,,0000,0000,0000,,there's probably a way around it,\NI just, I'm not aware of it.
Dialogue: 0,0:08:43.71,0:08:47.74,Default,,0000,0000,0000,,So create a whole new figure,\Nand then plot to that.
Dialogue: 0,0:08:49.73,0:08:51.67,Default,,0000,0000,0000,,So it's the same thing with subplot.
Dialogue: 0,0:08:51.67,0:08:55.61,Default,,0000,0000,0000,,If I just start subplotting, it's gonna\Nwrite over the top of this figure.
Dialogue: 0,0:08:56.89,0:09:04.28,Default,,0000,0000,0000,,Then it's gonna create a subplot axis or\Nset of axis and
Dialogue: 0,0:09:04.28,0:09:09.50,Default,,0000,0000,0000,,then it's gonna plot to that set of axis\Nand it's gonna tie it all to that axis.
Dialogue: 0,0:09:10.80,0:09:15.66,Default,,0000,0000,0000,,Now this X label, notice how I've\Ndone this, it's a carrot for
Dialogue: 0,0:09:15.66,0:09:19.84,Default,,0000,0000,0000,,a super script and\Nthen an underscore for a subscript.
Dialogue: 0,0:09:21.58,0:09:26.76,Default,,0000,0000,0000,,And the curly braces are if you have\Nmultiple characters that you need to
Dialogue: 0,0:09:26.76,0:09:30.94,Default,,0000,0000,0000,,include in the scripts,\Nin the subscripts, super script.
Dialogue: 0,0:09:30.94,0:09:37.44,Default,,0000,0000,0000,,So then the subplot it says\Nmake me a 2 by 1 region
Dialogue: 0,0:09:38.47,0:09:42.58,Default,,0000,0000,0000,,and here is populate in\Nthe first region and
Dialogue: 0,0:09:42.58,0:09:46.34,Default,,0000,0000,0000,,now it's populating in the second region,\Nthese plots.
Dialogue: 0,0:09:48.20,0:09:53.00,Default,,0000,0000,0000,,So there's the second region of the plot,\Ntitle, label, okay?
Dialogue: 0,0:09:53.00,0:09:56.38,Default,,0000,0000,0000,,So if I continue going now since\NI have called figure again,
Dialogue: 0,0:09:56.38,0:10:01.26,Default,,0000,0000,0000,,this is going to override this and that's\Nfine because I'm done looking at all this.
Dialogue: 0,0:10:03.32,0:10:07.41,Default,,0000,0000,0000,,Well okay, so notice that it\Ndidn't override the whole thing,
Dialogue: 0,0:10:07.41,0:10:09.84,Default,,0000,0000,0000,,it just overwrites the current axis.
Dialogue: 0,0:10:11.42,0:10:12.70,Default,,0000,0000,0000,,So this is an exponential.
Dialogue: 0,0:10:14.03,0:10:17.64,Default,,0000,0000,0000,,We have a linear set of\Npoints on the input and
Dialogue: 0,0:10:17.64,0:10:19.48,Default,,0000,0000,0000,,then we have the exponential\Nset of the output.
Dialogue: 0,0:10:21.37,0:10:24.62,Default,,0000,0000,0000,,I want to get rid of,\NI want to look at this on,
Dialogue: 0,0:10:24.62,0:10:28.80,Default,,0000,0000,0000,,let's call our new figure, whoops.
Dialogue: 0,0:10:31.43,0:10:36.61,Default,,0000,0000,0000,,So now I can look at both of these\Nif I choose to at the same time.
Dialogue: 0,0:10:38.42,0:10:39.39,Default,,0000,0000,0000,,So notice how I have.
Dialogue: 0,0:10:41.29,0:10:43.95,Default,,0000,0000,0000,,Just gone from plot to send their log Y.
Dialogue: 0,0:10:43.95,0:10:48.83,Default,,0000,0000,0000,,So it suppress the exponential\Ngrowth in the Y direction by scaling
Dialogue: 0,0:10:48.83,0:10:50.49,Default,,0000,0000,0000,,it logarithmically.
Dialogue: 0,0:10:52.16,0:10:58.17,Default,,0000,0000,0000,,Now, if I give inputs that\Nare growing exponential and
Dialogue: 0,0:10:58.17,0:11:04.59,Default,,0000,0000,0000,,then the output is exponential\Nof the exponential input.
Dialogue: 0,0:11:06.23,0:11:08.70,Default,,0000,0000,0000,,It wants to be a double\Nexponential growth.
Dialogue: 0,0:11:09.71,0:11:10.92,Default,,0000,0000,0000,,So let's see what that looks like.
Dialogue: 0,0:11:12.38,0:11:19.03,Default,,0000,0000,0000,,Well, the problem here, you won't be\Nable to see it, unless we plot it.
Dialogue: 0,0:11:25.85,0:11:30.90,Default,,0000,0000,0000,,That's a straight line,\Nnotice the X-axis here
Dialogue: 0,0:11:30.90,0:11:37.40,Default,,0000,0000,0000,,doesn't come any where near\Nthe largest X values of X log.
Dialogue: 0,0:11:37.40,0:11:41.17,Default,,0000,0000,0000,,Remember this is,\None million is the largest value.
Dialogue: 0,0:11:41.17,0:11:45.71,Default,,0000,0000,0000,,So what's happened is it's gone to\Nthe maximum that this can possibly go to,
Dialogue: 0,0:11:45.71,0:11:46.64,Default,,0000,0000,0000,,on the Y value.
Dialogue: 0,0:11:46.64,0:11:50.50,Default,,0000,0000,0000,,That's the maximum it can go to, before it\Nthinks that all the numbers are infinity.
Dialogue: 0,0:11:51.73,0:11:55.89,Default,,0000,0000,0000,,So this actually goes infinitely higher,\Nand this goes much further to the right.
Dialogue: 0,0:11:55.89,0:12:00.07,Default,,0000,0000,0000,,So this is a totally garbage,\Na total garbage plot here.
Dialogue: 0,0:12:00.07,0:12:01.06,Default,,0000,0000,0000,,It doesn't, it's meaningless.
Dialogue: 0,0:12:02.40,0:12:07.48,Default,,0000,0000,0000,,So I'm gonna rescale, I'm gonna create
Dialogue: 0,0:12:07.48,0:12:12.82,Default,,0000,0000,0000,,X log small enough that it'll\Nactually plot those values.
Dialogue: 0,0:12:15.84,0:12:20.57,Default,,0000,0000,0000,,So now you can see,\NI should probably get rid of these dots.
Dialogue: 0,0:12:22.45,0:12:26.23,Default,,0000,0000,0000,,Let's replot this new set of points.
Dialogue: 0,0:12:26.23,0:12:28.38,Default,,0000,0000,0000,,Just a default solid line.
Dialogue: 0,0:12:29.49,0:12:33.53,Default,,0000,0000,0000,,So this is,\Nthis actually is the exponential growth
Dialogue: 0,0:12:35.42,0:12:39.24,Default,,0000,0000,0000,,of the inputs and it goes over all\Npossible values of the inputs.
Dialogue: 0,0:12:40.86,0:12:45.54,Default,,0000,0000,0000,,So that's still not very\Nappealing to look at so
Dialogue: 0,0:12:45.54,0:12:51.02,Default,,0000,0000,0000,,let's create a new figure and\Nsuppress the logarithmic or
Dialogue: 0,0:12:51.02,0:12:54.65,Default,,0000,0000,0000,,the exponential growth in the X-axis now.
Dialogue: 0,0:12:54.65,0:13:00.03,Default,,0000,0000,0000,,So we we semi log X and\Nnotice that I don't have
Dialogue: 0,0:13:00.03,0:13:05.84,Default,,0000,0000,0000,,to repause a million times,\Nbut let's do this.
Dialogue: 0,0:13:11.29,0:13:16.53,Default,,0000,0000,0000,,So it is an exponential growth, it's\Ndoubled the exponential because the input
Dialogue: 0,0:13:16.53,0:13:22.09,Default,,0000,0000,0000,,is, the inputs are growing exponentially\Nand the output is growing exponentially.
Dialogue: 0,0:13:23.58,0:13:28.29,Default,,0000,0000,0000,,It's tough to see it's exponential because\Nthere, it's doubled the exponential.
Dialogue: 0,0:13:28.29,0:13:32.30,Default,,0000,0000,0000,,So if you have a doubly\Nexponential growth,
Dialogue: 0,0:13:33.83,0:13:36.81,Default,,0000,0000,0000,,the input and the output then do log log.
Dialogue: 0,0:13:39.70,0:13:42.09,Default,,0000,0000,0000,,And that shows you\Nthe exponential characteristic.
Dialogue: 0,0:13:42.09,0:13:47.01,Default,,0000,0000,0000,,All right, that's about it for this video.
Dialogue: 0,0:13:47.01,0:13:48.83,Default,,0000,0000,0000,,The next one will go into more depth.