Matlab Basics
Contents
The Command Window
MATLAB's command window can be used as a very powerful calculator. The >> indicates that MATLAB is ready to accept a command. It works much like your calculator. For example,
>> 1 + cos(pi/2) ans = 1 >> 5^2 % square 5 ans = 25
Note that anything following a % on a line is ignored. This allows us to include comments in our calculations.
Defining Variables
By using variables instead of numbers, our calculations look much like they would on paper. For example, from physics we know that projectile motion (in the absence of air resistance) is governed by the equations
where and are the position and velocity of the projectile at time and is the acceleration.
Example
Assume that we have the following problem:
A bullet is shot upward with an initial velocity of 300 feet per second (fps). Neglecting air resistance, determine the maximum height of the bullet.
The maximum height occurs when . We can solve the equation for to find
This gives the time at which the bullet reaches its maximum height. We can then use the equation for to determine how high it is at that time.
Let's solve this in MATLAB. First we define the initial height, the initial velocity, and the acceleration. We also know the final velocity  it is zero.
y0 = 0.0; % initial height (feet)
v0 = 300; % initial velocity (feet/s)
vt = 0.0; % final velocity (feet/s)
a = 32.2; % gravitational acceleration (feet^2/s)
Now we can define the time that the projectile reaches its maximum height, and then determine what the maximum height is. We use the variables we just defined:
t = (vtv0)/a; % time (s) when the bullet stops (maximum height)
yt = y0 + v0*t + a*t^2/2; % maximum height (feet).
If we omit the ; on the line for yt MATLAB will print its value. Or we can simply type the variable and MATLAB will print it. Doing this we see that the projectile reaches a height of 1,397.5 feet at 9.317 seconds (neglecting air resistance). This illustrates the convenience of using variables. The MATLAB code reads much like our original equations did.
Tips on Defining Variables
 Variables in MATLAB are casesensitive. That means that myVariable, myvariable, MyVariable and MYVARIABLE are all different variables and can all have different values.
 Variables may be defined by other variables. In that case, the righhand side is evaluated and then stored in the variable. For example:
a=5; % a is 1.
b = a+2; % b is 7.
a=1; % b is still 7, a is 1.
 Variables may hold numbers or strings (characters). For example:
a=pi; % a is 3.14159265...
a = "hello"; % a is now "hello"
 Use a semicolon ; to terminate every MATLAB statement. Omitting the semicolon will result in the results being displayed in the command window. This is not good practice in general.
 To print out variables, use the Input/Output techniques provided by MATLAB.
 See this link for information on defining arrays (vectors & matrices).
The following should NOT be used in variable names:
 Special characters like  + = / * & ^ % $ # @ ! [ ] ( ) : ' " .
 Spaces. For example my variable is NOT a valid variable name.
 Do not start a variable name with a number. Example: 2a is not a valid variable name, but a2 is.
Basic Commands & Operations
Useful Commands
Often we want to see what variables we have defined in the MATLAB workspace. Or we may want to clear a variable. The commands in the following table illustrate several useful tools for managing variables.
Command  Description  Example (try these out) 

who  Lists variables currently defined in MATLAB.  a = 5; b = 6; c = linspace(0,50,10);
who

whos  Similar to who, but gives additional information.  a = 5; b = 6; c = linspace(0,50,10);
whos

clear  Clear all variables defined.  a = 5; b = 6; c = linspace(0,50,10);
clear; % clears all variables
who; % displays nothing  no variables defined.
a=2; b=5; c=a+b;
clear a b; % only clears a and b. c is still here.
who; % tells us that c is defined.

clc  Clears the MATLAB workspace. Doesn't clear variables  clc

save  saves variables to a file that can be loaded later.  clear;
a=5; b=6; c=a+b*2;
save myVariables; % saves all variables to the file "myVariables.mat"
save bcVars b c; % saves b and c only to "bcVars.mat"

load  loads variables from a file  clear;
a=5; b=6; c=a+b*2;
save myVariables; % save all variables to a file
save bcVars b c; % save b and c to a file
clear; % no variables defined.
load bcVars; % b and c are now defined.
who;
clear; % no variables defined.
load myVariables; % a b and c are all defined.
who;

help  provides help on how to use a command  help clear;
help load;
help save;

Basic Operations & Common Functions
In the projectile example above we saw examples of using several basic operators in MATLAB. The following table summarizes the basic operators and gives simple examples of their usage.
Operator  Description  Examples 

+  Addition  1 + 2 % displays 3
b = 1+2; % assigns 3 to the variable b.
a = cos(pi)+2.0; % a=1

  Subtraction  1  2 % displays 1
b = 12; % assigns 1 to the variable b.
a = sqrt(4*b)+2.0; % a=4

*  Multiplication  2.2*3.3 % displays 7.26
a = 2.2*3.3; % assigns 7.26 to a.
b = (pi/4); % assigns pi/4 to b.

/  Division  7.26/2.2 % dispays 3.3
a = 7.26/2.2; % assigns 3.3 to a.
b = sqrt(a/pi)*exp(a);

^  Power  2^3 % displays 8
a = 2^3 + 243^0.2; % assigns 11 to a.

( )  Parentheses  a = (2+5)*3; % assigns 21 to a
b = 2+5*3; % assigns 17 to b
c = 2*(a10); % assigns 22 to c

NOTE: if you are using arrays, then the / and * operators have different behavior! See the page on array arithmetic for more information.
In addition, MATLAB has many builtin functions. Type help elfun at the MATLAB command prompt for a list. Some commonly used functions are given here:
Function  Description 

cos  The cosine function 
sin  The sine function 
tan  The tangent function 
sqrt  The squareroot, 
exp  The exponential function 
log10  The base10 log function, 
log  The natural log function, 
abs  The absolute value, 
MFiles
An Mfile is a series of MATLAB commands that you save in a file. Then you can rerun them easily and make changes without reentering everything again. Anything that can be done in the command window can also be done from an mfile. As an example, let's reconsider the projectile example discussed earlier. We had the following MATLAB commands that we entered in the command window:
y0 = 0.0; % initial height (feet)
v0 = 300; % initial velocity (feet/s)
vt = 0.0; % final velocity (feet/s)
a = 32.2; % gravitational acceleration (feet^2/s)
t = (vtv0)/a; % time (s) when the bullet stops (maximum height)
yt = y0 + v0*t + a*t^2/2; % maximum height (feet).
Suppose that we wanted to change the initial velocity. We could reenter everything again, or we could save these commands in a mfile. To use an mfile, follow these steps:
 Choose File→New→MFile.
 Enter the MATLAB commands just as you would in the command window and save the file. You may save it wherever you wish.
 Navigate to the directory where you saved the file. Do this one of two ways: Error creating thumbnail: Unable to save thumbnail to destination
 Type the directory in the location box in the top of the MATLAB command window (the current directory).
 Select the button to navigate to the directory where your mfile is saved.
 Now you can type the name of your mfile in the command window to run it. For example, if I named the file projectile.m, I would type at the command prompt. MATLAB will then execute all of the statements in the mfile as if you had entered them into the command window (although they will not be shown in the command window).
projectile
Step 3 may be ommitted if the directory is already set in Matlab's path, as discussed in the following section.
Naming MFiles
When choosing a name for your file, keep the following guidelines in mind:
 Do not use spaces in the name. You may use an underscore "_" in lieu of a space.
 Do not use any symbols in the name: Examples of things NOT to put in the name: / + =  ^ * ! # % @ ( ) & . Using these symbols confuses MATLAB.
 Do not begin your file name with a number. You may have numbers elsewhere in your file.
The following table illustrates some valid and invalid file names.
Valid File Names  Invalid File Names 

myFile.m  my File.m 
problem5.m  5prob.m 
crazy_file.m  crazyfile.m 
Documenting MFiles
As you know by now, you can use Matlab's "help" command to get help on using various Matlab commands. However, you can document your own mfiles so that you can get help on them as well. For example, consider the following code saved in a file called projectile.m
% This script calculates the maximum height of a projectile
% as a function of its initial height and vertical velocity.
y0 = 0.0; % initial height (feet)
v0 = 300; % initial velocity (feet/s)
vt = 0.0; % final velocity (feet/s)
a = 32.2; % gravitational acceleration (feet^2/s)
t = (vtv0)/a; % time (s) when the bullet stops (maximum height)
yt = y0 + v0*t + a*t^2/2; % maximum height (feet).
disp('The maximum height (feet) is:');
disp(yt);
disp('This occurs at time (seconds):');
disp(t);

Typing help projectile in the command window will result in the following:
 This script calculates the maximum height of a projectile
 as a function of its initial height and vertical velocity.
Matlab's Path
 path
 A list of directories that MATLAB looks in to find mfiles.
When you type a command in the MATLAB command window, MATLAB decides what to do based on the following:
 Look to see if a variable by that name exists. If so, use it.
 If no variables match, then MATLAB looks in the current directory to see if there are any mfiles that match the command name.
 If no mfiles match in the current directory, then MATLAB looks through all directories in its path to see if there is an mfile in those directories whose name matches the command.
If no variables and no mfiles match the command, then MATLAB issues an error message.
To set MATLAB's path, go to File→Set Path. You will see an image similar to the one at the right. Choose the Add Folder button and navigate to a folder containing mfiles that you want to add to MATLAB's path. Then click Save. Now you don't have to have MATLAB running in the same directory where you saved your mfile.