This is a short video about MATLAB trying 
to demonstrate its capabilities and how 
it can be used in this course, but also I 
think you'll find it useful beyond just 
the confines of this course, and actual 
practice as an engineer or in future 
courses. 
You can see I am running MATLAB because 
of what it says at the top of this title 
bar over here, on the right side. 
That's the command window for MATLAB. 
There is a public domain version of 
MATLAB, which is known as Octave. 
And, you can see the Octave can be 
obtained at the GNU website. 
You can download your own copy of Octave 
for free. 
It's, supports lots of different systems. 
I'm, I happen to be running on a 
Macintosh, and that's the one I would 
download if I were using it. 
The MATLAB command window is here over on 
the right side, the really interesting 
thing about MATLAB is I don't have to 
write a standalone program and then run 
it. 
I can do a lot just typing commands to 
MATLAB at the keyboard, and that's what 
I'm primarily showing today. 
Over on, here on the left side, is a 
figure window, a plot window, and that's 
where all my plots are going to show up. 
And I think you'll finally see why we're 
so enthusiastic about using MATLAB, 
especially for this course. 
So every variable In MATLAB, is a vector, 
or more generally a matrix. 
And this is extremely useful, as I want 
to show you. 
So let me define a, a vector named x, and 
I'm going to say that's equal to zero 
colon n. 
And so this says, it says, this command 
says, set the variable x equal to a row 
vector whose elements start at zero, 
increment by one, going from element to 
element in the vector and wind up with 
the value of ten. 
And if you just hit Return, you'll see 
that x has been defined to be that 
variable, and sure enough it's a vector 
of the 11 elements, consistent of the 
integer 0010. 
Well I can plot this against itself. 
It' snot a very interesting plot, but I 
can do it, and the plot command in that, 
in that tab is plot. 
This is what I would plot on the x-axis. 
You can see the little help window that 
pops up in Matlab. 
That won't pop up in Optic, but you 
really don't need it, eh, to do your 
work. 
And I'm going to plot that against 
itself. 
And you plot on the left side. 
It won't change much because that was 
what I was setting up for, and you can 
see that it's plotted a straight line as 
you would expect. 
Well, I can plot x to and instead I'll 
make the vertical scale 5 times x. 
So the usual syntax for doing 
multiplication, division, addition, and 
everything still apply to variables in 
MATLAB. 
So now I'm going to do something a bit 
fancier I'm going to plot x 5 times x 
plus 2. 
The reason that's fancy is what is going 
to happen when I add a, this is a vector, 
5 times x is a vector, but 2 is a scalar. 
And what does MATLAB do? 
Well it does the thing you want it to do. 
It's going to add 2 to every element of 5 
times x, and so when I finally, plot 
this. 
You see the plot changes, and there's an 
offset by two at the origin. 
So the vector plus a scalar is a vector 
with the scalar added to every element of 
the vector. 
Same for subtraction, etc. 
Now suppose I wanted to plot, Y = X^2. 
Well first of all, what is this mean? 
Well, you cannot multiply a vector times 
a vector. 
It doesn't work, and it's going to 
complain because it, basically it's 
assuming everything is in matrix 
multiplication. 
All the matrix multiplication rules 
apply. 
But MATLAB has a very special syntax for 
term by term multiplication. 
So, what this, see the dot in front of 
the star? 
What that means instead of thinking about 
x as a vector, and just doing vector 
times vector multiplication, this means 
to term by term multiplication. 
So, since x consists of the integers zero 
to ten, the y vector here should consist 
of the squares of every element, and 
that's exactly what they are. 
And so this dot star is what you need, if 
you want to apply the same, mathematical 
operation to every element of the vector. 
And now I can plot, y versus x, and I get 
a parabola, as you would expect. 
So let me label the axes. 
I always like to do that. 
You label the x axis with the command x 
label and you enclose strings in MATLAB 
with single quotes, not double quotes, it 
turns out, single quotes. 
And there will pop up a label over here 
in the plot window, and I'll do one for 
the y-axis. 
I'm not going to do anything fancy, just 
calling it y. 
And you can see it actually rotates it, 
counter-clockwise, so it looks pretty. 
Well, you've certainly, if you do 
something like what is sine of two time 
pi times x over 5. 
So pi is defined. 
It's already predefined for you and I 
think this makes perfect sense. 
But what does sign of a vector mean? 
All of the special functions in MATLAB 
are set up, so if you type this what this 
means is term by term application of this 
function to the factor x. 
And so what we get back is, you can see 
now the values are equal to sine of 2 pi 
times the integers here of the 10 divided 
by 5. 
It's not a very exciting result, but 
there it is. 
Well you can see that what MATLAB does is 
that after a calculation, like the sine, 
it gives you an answer. 
And it's going to tell you that, well you 
may not want to see every detail of every 
calculation. 
So what you can do is you type it in. 
If you end the last line with a 
semicolon, nothing gets typed actually, 
but the calculations are still performed. 
Notice it just performs the calculation, 
but it did not type them out for you. 
So, I'm going to, from now on, use the 
semicolon, because I don't want to see 
all the intermediate, calculations. 
Now, there's another very cool thing that 
saves typing. 
Remember, use MATLAB a lot at the command 
line, not necessarily to, to write a 
program for. 
I'm going to type s i n, and I you can't 
see it but I'm going to type an up arrow 
on my key board and it's going to bring 
up the previous command that began with s 
i b. 
I'm going to go over here and say y 
equals and hit return, and now the 
variable y if I just type it I can see 
it's values. 
You can see it has stored all the values 
of this previous calculation that I did 
before, and I can plot it. 
So I'm going to bring up the plot 
command, I type pl up-arrow and there it 
is, and it doesn't look much like a sine 
wave, but I can fix that. 
So, I'm going to redefine x, I may say X 
and I am going, just going to go up 
arrow. 
There is X label, hit up arrow again, and 
there is my definition for X. 
I am going to add an argument here. 
0.01 colon, so if you have an 
intermediate value in the colon notation 
here, now the increment, instead of being 
1 between the elements of the vector, now 
it's going to be 0.01. 
And I don't really want to show you all 
of those, so I'm going to type a 
semicolon out there and there's x. 
I'm going to recalculate the sine 
function. 
[SOUND] So, I'm going to be over the same 
interval, but now much more finely 
represented in the plot command, gives me 
something that looks very much like a 
sine. 
So, now you can see that you can really 
do some very simple calculations or 
complicated calculations, at the 
keyboard, getting plots and seeing what 
they look like. 
Now I want to show you something else 
that's very, going to be very important. 
suppose I want to plot 1 over x. 
So let's define y equals to 1 slash x. 
Do you think this is going to work? 
And one is a scalar, don't forget that x 
is a vector, and a scalar divided by a 
vector doesn't work very well, and you 
get that same command again, guess what 
you type to fix this? 
If I just hit an up arrow now, it's just 
going to bring up the previous line. 
And I'm going to go over, type my dot, 
like I should have. 
And I'm going to put a semi-colon out 
here because I certainly don't want to 
see all these values of y here. 
Let's see, there's .01 times 10, so 
there's 1000 elements there. 
And I don't really want to see them all. 
So I'll do that, and now I'll bring up my 
plot command, and there it is. 
It looks like a hyperbola. 
Well, those of you who know what I've 
follow what I just did, know that y of 
one is 1 over 0, and guess what math lab 
says it is, it is indeed infinity. 
So the way to access any element of a 
vector is you give the name of the 
vector, and in parenthesis you put the 
element you want to extract. 
If I wanted to extract the first 10 
elements, guess what I use. 
I use the colon notation again, this time 
always, since it's trying to index y, it 
always starts, the increments should be 
1. 
So 1 colon 10 over 5 and in that lab, all 
indexes for arrays start at 1, not 0 like 
they do in C. 
So this gives me the first 10 elements 
and it should be one over X, going on a 
very, fine way, a detailed way, and see 
it has explicitly knows infinity, and 1 
over 0.01 is 100, etc. 
So the plot command is smart enough, and 
if it sees infinity it doesn't plot it at 
all. 
So that's why this plot, the vertical 
scale here, starts at 100. 
And by the way all plots are auto-scaled, 
it's going to find the scale that makes 
things fit. 
and you can change those if you look at 
the details of how the Plot command 
works. 
So, the getting help is easy for a given 
command like plot. 
How do I change the axes, things like 
that. 
You type like plot. 
And you will get something, that's, that 
you can see. 
It's got lots and lots of detail here. 
which you should go through when you're. 
First getting started with MATLAB. 
Now, suppose I want to try something I 
want to calculate something that looks 
like oh, let's say, x squared divided by 
sin of x. 
So y equals x dot up arrow two. 
I think you now know what the dot means, 
that means I'm going to take the vector 
x, and, turn by turn, compute the square. 
I'm going to divide that by sine of x, 
which is about the same thing, but I'm 
going to do it anyway. 
And notice I have to do the dot again, so 
it's dot slash, and I don't want to have 
it all typed out at me. 
And so let's see what y is in first ten 
elements, and you can see that x equals 
0, we get 0 divided by 0, and MATLAB has 
said that's not a number. 
NAN means not a number. 
And so Matlab can take care of these 
calculations, it doesn't care if the 
things goes to infinity, if you divide 0 
by 0, we're still going to return an 
answer. 
And that's one of the very interesting 
things about MATLAB. 
So plot, I can plot these two things, and 
it looks kind of screwy at the places 
where the sine function is going to zero. 
You can see it's going to start to blow 
up, but the plot is still there. 
Okay. 
So this is how you divide a vector by 
another vector. 
You use the dot slash notation. 
Now the other interesting thing about 
MATLAB is that it loves complex numbers. 
It doesn't care. 
So if you type square root of minus 2, 
it's going to tell you that that is 0 
plus 1.4142 times i. 
They use i for the square root of minus 
1. 
I can't change it to j. 
However, what's also very interesting 
about MATLAB is that the variable i is 
predefined, in this case to be 28 because 
I've written a program before. 
If I say i equals the square root of 
minus 1, that turns out to be the 
default. 
When you first run MATLAB, that's 
going to be the default that I use. 
There's a special symbol that they use, 
but you see what happened to me. 
I ran a program before where I used i as 
an index and I, being the square root of 
minus 1, got redefined by my program. 
There's a special symbol, 1i, Which is an 
illegal variable name that is reserved in 
Mat lab to be the square root of -1. 
And also we want j as defined, which is 
also the square root of -1. 
So I would tend to use 1j. 
So I'm going to define y to be equal to 
the exponent of 1j times 2 times pi times 
a vector, f, which I'm going to say runs 
from 0 to point, in terms of steps, of 
101 to, 2. 
Let's see, I notice I didn't have to 
define a immediate variable. 
I can just type this vector inside, and 
everything's going to work fine, so I do 
that and if I did plot y. 
Y is complex and what its going to do is 
plot the imaginary part versus the real 
part. 
And that's a circle. 
So I can also plot, the real part of y, 
which is a cosine. 
And notice I did not give it an x 
argument. 
What it's doing, it's just plotting it 
against the index into the vector. 
And this is a way of getting plots going 
very quickly, not worrying about the 
details of a plot when you're trying to 
debug or get something just to work. 
And of course you can do the imaginary 
part. 
And there's the sine wave that's coming 
out of the complex exponential. 
But notice, it, the thing I want to 
emphasize is it did calculations with 
complex numbers just like they were real 
numbers. 
It really doesn't care. 
So, this is very handy for us, because 
here's our complex exponential signal, we 
use that a lot in this course, and it's 
very easy to type it in and use it just 
like It was a, a real variable that you 
would, in most other programming 
languages. 
So I think you can see why MATLAB is so 
useful. 
Learn, play with it, learn its commands, 
and one other thing before I leave, is I 
want to show you how to write, a loop. 
So the For command exists in MATLAB, and 
I'm just going to say i equals one colon 
ten. 
And I think, I forgot the equals, equals 
one colon ten. 
And I think you know what it's going to 
do. 
It's a loop. 
It's going to start with i equal to one, 
and wind up at a value of ten, 
incrementing by one every time. 
And I'm going to say that Z and I is 
equal to I up arrow T. 
So I'm going to put in the squares, just 
kind of a silly program, and I've been, 
the way that the for loop is terminated 
is with the end statement. 
And it has set up a vector z, which is 
going to have 10 elements equal in it, 
equal to the squares. 
I could have done this much more simply. 
Let's say, for x equals 1 colon 10. 
Does exactly the same thing, except I 
didn't square it, and now if I do x.up 
there 2, now I get the same thing as z, 
and I, could've either written a loop or 
I could've used, used the special 
notation in Matlab. 
And I think it's pretty clear that 
writing the loop is not that great a 
deal. 
Now, suppose I wanted to find this, the 
average of the x's. 
Okay. 
There's a special command that will do 
that called, sum, and that will sum it 
all up. 
And you can divide by the length of x, 
and I think it's pretty clear what the 
length is going to do. 
And that's the average of the squares of 
the first 10 integers. 
You can also do some other very important 
things like this that are matrix-like 
things. 
There's a mean function which will be 
exactly the same thing as what I just 
typed, and of course it gives exactly the 
same answer. 
There are many, many built in functions 
ready for you to use, and you just have 
to go in there and explore MATLAB and 
find out, to find out what they are. 
There's many many tutorials on lab, 
online, for helping you on getting into 
MATLAB and get started, but I think you 
can see why we use it a lot. 
And you are, will be asked to use it to 
work some of the homework problems. 
because. 
I need some numeric answers 
occassionally. 
Hope you enjoy using matlab in this 
course and later on.