Math 2250
Introduction to Matlab
Fall 2011
This document is an introduction to Matlab for Math 2250/2280 students. You will be
using Matlab in Math 2250/2280, in order to solve problems and do computer projects. You can
think of Matlab as an extremely powerful programmable calculator with many incredibly useful
features. Matlab will be used primarily to do numerical calculations as opposed to symbolic
calculations. You will use Matlab to solve problems where the answer is a number, vector, or
matrix, rather than a function. To solve symbolic problems, you will need to use a program
called Maple. While Maple can also solve numerical problems, Matlab is much more efficient
and well designed for this process. It is recommended that students understand how to use both
programs. Your specific assignments and requirements will depend on your particular Math
2250/2280 instructor.
Matlab is updated periodically, and the Mathematics Department is currently using
version 7.9.0. There are some backwards compatibility problems with Matlab, so documents
created with newer versions may not run as expected on older ones. However, this should not
be a problems considering the simple commands we will use in this course. Student computers
around campus (Engineering, Marriott, Math Department, Heritage Commons) have Matlab
software installed, and in most places you can find both the earlier and later versions. As an
enrolled student at the University of Utah, you are allowed to use Matlab on these computers for
free. You can also purchase a student version of Matlab 7.9.0 online for $99, directly from the
vendor, MathWorks. Any version of Matlab you use includes an extensive help menu with
detailed explanations about each command.
When you open Matlab you can find a series of demo videos by going to the "Help"
menu and selecting "Demos". It is recommended that you watch the first three videos in this list
to help you get started in Matlab. From then on, you will learn to use Matlab the same way you
learned to use Microsoft Word, i.e. by using it, using the help features, and asking friends, lab
assistants, TAs and teachers when you get stuck.
The Math 2250/2280 projects can usually be done using Maple, Matlab, Mathematica or
other math software. But, most Math Department support for these projects will assume you’re
using Maple.
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1)
Computer Labs on campus, and logging on/off:
There are many labs on campus, follow the link
http://www.it.utah.edu/services/connected/labs.html . Most of these labs have Matlab software,
and in most of these labs you log on using your University ID and password, i.e. the same way
you log on to register for courses, get transcripts, etc. For example, if you are using the MMC
labs this is the way you log on to your computer. It is generally true that when you log off a
student computer on campus, you should not turn off the computer.
One important exception to the universality of your UID/password for logging on to
campus computers is the Math Department computer system,
http://www.math.utah.edu/ugrad/lab.html. All students taking Math courses are assigned a Math
Department login name and initial password that are NOT the same as their UID and University
password. The undergraduate walk−in computer lab is located in the Rushing Math Student
Center, located underneath the plaza connecting JWB to LCB. There is also a computer
classroom in LCB 115, where some introductory tutorials are held. Useful information about
most aspects of the lab can be found by following links from the Math Department web pages
like the one above, or the precursor directory http://www.math.utah.edu/ugrad .
If you’re working on the Math Department system your login name will be of the form
c−azbc, where ‘az’ is first letter− last letter of your last name, and ‘b’,‘c’ are your first, and
middle initials, respectively. For example, if your name is Ulysses Attila Eratosthenes, your
login name will be c−esua. (Many people have the same initials, so to ensure your login name is
unique, a digit may be added after the initials, eg. c−esua1, c−esua2, ...). For people with more
complex (eg. hyphenated names) only the first character of each name is used.
Your initial password will be the letters as in the login name, followed by the last four
digits of your University ID number (e.g., if your UID is 123456789 and your login name is
c−esua, then your password is esua6789) or if the login name is c−esua2 the password is still
esua6789). You should change your password if it’s still the default one. To do so, log in, open a
terminal window using a mouse or icon selection (depending on the operating system you’ve
logged on with), then type ‘‘passwd’’ (followed by RETURN/ENTER). Ask a lab assistant how
to do this if you’re doing this tutorial on your own and are confused.
If you previously took a math class and used our system then your old account may still
be active, with the last password you used. If all your efforts to log on fail, ask a lab assistant for
help.
Don’t forget to log out when you’re done. Never turn off a Math Department computer.
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2)
Opening Matlab
Matlab may appear as icons on your computer desktop and perhaps the icon will contain
a picture of the "MathWorks" logo. Alternately, you may open Matlab with a terminal window
command or by searching directories. If you’re not sure how to find and open Matlab, ask a lab
assistant. In Marriott if you can’t find a class software or applications directory with Matlab in it,
ask at the help desk.
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3) Using Matlab
If you are starting the tutorial at this point, we assume you have already opened Matlab.
Matlab is partly just a very fancy calculator; it can do practically any undergraduate
mathematics computation. Additionally, in Matlab you can write programs, create plots, save
large amounts of data, customize how you want the program output to appear on your screen,
and much more.
Demo Videos for New Users
When you open Matlab you can find a series of demo videos by going to the "Help"
menu and selecting "Demos". It is recommended that you watch the first three videos in this list
to help you get started in Matlab. This is a good way to learn generally about what Matlab can
do. If you wish you can explore now, or you can continue with the Math 2250 notes below and
come back to the demo videos later.
Matlab Window
On opening Matlab, you will notice that the window is broken up into several sections.
On the left column, there is a Directory Section titled "Current Folder" which displays all the
files and folders in the current directory, and just below that is a Description Section which gives
further details about the file that is selected in the Directory Section. For the time being, we will
ignore these two sections on the left hand side of the window.
In the center of the window is the largest section titled "Command Window". This is the
only section that we will be concerned with during this introductory tutorial. You will notice
that in this window there may (or may not) be some text written at the top which gives some
details about the version of Matlab you are using. Below this text is the command prompt, ">>",
which is where you will type in the Matlab Commands described below. You should see your
cursor blinking next to the command prompt.
On the right column, there is a section titled "Workspace" which shows a list of all the
variables that have been defined in the current Matlab session and gives some basic details about
them. The section directly below this one is entitled "Command History" which shows, in
reverse order, all previous commands entered into Matlab at the command prompt. For the time
being, we will ignore these two sections on the right hand side of the window.
Entering Matlab commands
Focusing on the "Command Window", make sure that your cursor is blinking in front of
the first command prompt, which is denoted with a ">>" symbol. After typing a command and
pressing "Enter" on your keyboard, you should see the output of the command and then a new
command prompt below, again denoted by the symbol ">>". If you wish to suppress the output
after any command, simply make sure to type a semicolon after at the end of the command
before pressing Enter. If you want to enter multiple commands at the same command prompt,
hold down the "Shift" key and press "Enter" to change lines without executing any command.
When you have finished entering all commands, press "Enter" to execute them all
simultaneously.
If you incorrectly align parentheses or brackets, or do something else which makes your
command unexecutable you will get a ‘‘syntax error’’ message and Matlab will try to point out
your mistake with the cursor and cryptic diagnostic phrases. These syntax error messages are
always presented in text that is colored red. If everything was executed properly, any output
from the command will be in text that is colored black. After a while you will become good at
fixing mistakes but they can be annoying at first. Spaces are generally ignored in Matlab, so you
may use them to make input easier to read. You can enter explanatory comments in a command
line by inserting a ‘‘%’’ to the left of the comments; Matlab ignores any text after the % on a
command line. You will also notice that any text after the "%" is colored green, to indicate that
Matlab will ignore it. Inserting these comments may help you better understand what your
Matlab code is doing so it is easier to find mistakes or make changes.
Now, let’s try entering some commands. (You may try just the math commands, the
comments were only added to explain what the particular commands are illustrating ! ) Check
that you understand what each command is doing.
>> 3 + 1
%
%
%
%
%
%
%
Matlab will add 3 and 1. The output, "ans = 4",
is displayed below the command prompt. Notice how
the output is broken up into different lines, this
is done to make larger data structures, such as
vectors and matrices, more readable. For individual
numbers it seems a little weird but it is easy to
understand and get used to.
>> 4 * 2
% Matlab will multiply 4 and 2.
>> 10 / 5 % Matlab will divide 10 by 5.
>> 2^3
Output is "ans = 2".
% Matlab will raise 2 to the power of 3.
% "ans = 8".
>> (3+1)*(2-5)^4
>> pi
Output is "ans = 8".
%
%
%
%
%
%
%
%
%
%
%
Output is
Matlab will compute this expression using
the order of operations, interpreting
parenthesis as your calculator would. The
output is "ans=324".
Matlab has several internally defined variables.
Matlab recognizes "pi" as the number that we are
familiar with from geometry.
The output should be
"ans = 3.1416", which is pi rounded off to four
decimal places. Matlab will not recognize "e" as
the number we are accustomed to, but it will
recognize "i" to be the imaginary unit.
>> exp(3) %
%
%
%
%
%
Matlab does not recognize the number "e", so to
evaluate the number e raised to a power you will use
the exp() function. The line entered here will
raise e to the power of 3. The output is
"ans = 20.0855". Notice that once again the answer
is rounded to the 4th decimal place.
>> sin(0) %
%
%
%
%
%
%
Matlab understands all of the basic trigonometric
functions including sin(), cos(), tan(), sec(),
csc(), and cot(). Matlab ALWAYS works in radians.
If you are using degrees, you will first need to
convert your angle to radians before using one of
these function. The output for this line should be
"ans = 0".
>> asin(0)%
%
%
%
%
%
%
%
%
Matlab also understands the inverse trigonometric
functions including asin(), acos(), atan(), asec(),
acsc(), and acot(). Since Matlab only works in
radians then all the output for these functions will
always be expressed in radians. It should also be
pointed out that matlab understands all of the
hyperbolic trignonometric functions including
sinh(), cosh(), tanh(), sech(), csch(), and coth().
The output for this line of code is "ans = 0".
>> log(1) % Matlab can take the log of numbers. Matlab always
% interprets the log() function to mean natural log.
% The output for this line is "ans = 0"
>> sqrt(4)% Matlab can take the square root of a number using
% the sqrt() command. The output for this line is
% "ans = 2"
>> nthroot(64,6)
%
%
%
%
%
%
%
%
%
%
Matlab can take higher order radicals
using the nthroot() command. Notice that
there are two arguments of this function.
The first is the radicand and the second
is the index of the radical. This line
calculates the 6th root of 64. When a
function is set up to receive multiple
arguments, those arguments need to be
separated by commas. The output for this
line is "ans = 2".
>> [1 2 3]
%
%
%
%
%
Vectors are entered into Matlab in this way.
Matlab will interpret this command as the row
vector [1 2 3]. You would have gotten the same
result had you separated each entry with a
comma.
>> [1 ; 2 ; 3] % Matlab interprets this command as a column
% vector. The use of the semicolon tells matlab
% to end the current row and start a new one.
>> [1 0 ; 0 1] %
%
%
%
%
%
Matlab interprets this command as a the 2x2
identity matrix. The first row is entered,
followed by a semicolon, which tells Matlab to
start the second row, and then the second row
is entered. In principle you can define any
matrix of any size in Matlab in this way.
>> x = 4
%
%
%
%
%
%
%
In Matlab you can assign values to letters. This
command sets the variable "x" to the value of 4.
From now on (unless you restart Matlab or reassign
the value of x), the letter x will be interpreted as
the number 4. You can do any operation on x as you
would with a regular number. The output for this
command is "x = 4".
>> x*3
%
%
%
%
This command will take the current value of "x" and
multiply if by 3. Since in the previous line we set
the value of x to 4, we expect the output of this
command to be "ans = 12".
>> A = [1 2
%
%
%
%
; 3 4]
In this command we have assigned the variable "A" to
the 2x2 matrix with entries 1, 2, 3, 4. Notice the
organized way in which the output is given. It is
clear that A represents a matrix.
>> b = [1 ;
%
%
%
0]
In this command we have assigned the variable "b" to
the column vector with entries 1, 0. The output
clearly shows b as a column vector.
>> A*b
Matlab is great at working with matrices and
vectors, in fact, that is exactly what this program
was designed for. In this line we have multiplied
the matrix A by the vector b. The result is the
column vector with entries 1, 3.
%
%
%
%
%
Saving files in Matlab
In many situation, you may have a series of commands that you wish to use quiet often.
Instead of having to enter these commands in the Command Window every time you start
Matlab, it is possible to save these commands to a file, called an m-file.
To create a new m-file go to the "File" menu, then go to "New" and select "Blank MFile". A new window will appear which looks like a blank text file. You will notice there are no
command prompt symbols, ">>", in this file. Matlab will interpret each new line as its own
command and run every line of the file in order when you execute it. We'll talk about how to
execute the file in a minute. Type the following text into the window of the new file (you don't
have to enter the comments, those are just for your own reference):
A = [1 1 ; 0 1]
b = [2 ; 3]
A*b
% This stores the matrix into A
% This stores the column vector into b
% This multiplies matrix A by vector b
Next we will want to save this file. In the window of the new file you will see the menu
bar on top (different from the menu bar in the main window for Matlab), go to the "File" menu
and go to "Save". Matlab will automatically have you save the file in the same folder it is
currently working in. For the purposes of this exercise, don't change folders, save the file in the
folder that Matlab defaults to. Let's call this file "example.m". The .m extension is necessary to
tell Matlab that this is an m-file. Click "Save" once you've named the file. If you return to the
main window in Matlab, and look at the upper left section of the window called "Current
Folder", you should see the "example.m" file.
Executing files in Matlab
To execute the commands saved in the file, example.m, go to the center part of the
window called the "Command Window" and on the command prompt enter the name of the file,
without the .m extension. In other words, you want to enter:
>> example
% This will run the commands in the file
% example.m
If everything works correctly, you should see the following output.
>> example
A =
1
0
b =
2
3
0
1
ans =
5
3
When seeing this output, you realize that it is unnecessary to display the way A and b have been
defined, instead, you would only like for the product to be displayed. Go back to the example.m
file window (if you already closed it, go to the part of the upper left part of the main Matlab
window called "Current Folder" and double click the example.m file to open it). Change the text
in this file so that it looks as follows (again, don't worry about the comments):
A = [1 1 ; 0 1];
b = [2 ; 3];
A*b
% This stores the matrix into A
% This stores the column vector into b
% This multiplies matrix A by vector b
The only thing we have changed here is to add a semicolon to the end of the first and second
lines. This will suppress the output for these two commands. Save the changes you made in this
file by going to the "File" menu and clicking "Save". Now go back to the Command Window
and enter the following command to run the commands in the example.m file:
>> example
This time you should see the following output:
ans =
5
3
Notice that the result of the first two commands in the file were suppressed. In general, when
creating these files to do a long calculation you will want to suppress everything but the final
result (unless perhaps you're searching for mistakes in your code).
Matlab Help File
Matlab has a very extensive help file where you can find a lot of what you need. Go to the
"Help" menu and select "Product Help". A new window will open and you will notice a
searchbox where you can type in whatever you are looking for. There is much more that can be
done in Matlab, this is just a brief introduction. On the course website I have posted other files
that teach you more advanced techniques including how to create loops, functions, data
structures, plots, and much more!