EE211 | Introduction to MATLAB
EE211
MATLAB CODE BASICS – AN OVERVIEW
Basic Math Function
Function
Add
Subtract
Multiply
Divide
Absolute Value
Command
+
*
/
abs(number)
Notes
Cosine
Sine
Tangent
Inverse Cosine
Inverse Sine
cos(angle)
sin(angle)
tan(angle)
acos(angle)
asin(angle)
angle must be in radians
angle must be in radians
angle must be in radians
angle must be in radians
angle must be in radians
x=cos(0.5)
x=sin(0.5)
x=tan(0.5)
x=acos(0.5)
x=asin(0.5)
Powers
Square root
Exponential
x^y
sqrt(number)
exp(number)
x raised to the y power
will return imaginary if number<0
returns e^(number)
x=theta^2
x=sqrt(theta)
x=exp(theta)
Natural log
Log base 10
Log base 2
log(number)
log10(number)
log2(number)
* and / take precedence over + and -
Example
x=a+b
x=a-b
x=a*b
x=a/b
x=abs(y)
x=log(0.5)
x=log10(0.5)
x=log2(0.5)
Logical Operators
Operator
==
~=
<
>
<=
>=
and(A,B)
or(A,B)
Logic
is equal to
is NOT equal to
is less than
is greater than
is less than or equal to
is greater than or equal to
True if A and B are true
True if A or B is true
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EE211 | Introduction to MATLAB
Create Symbolic Functions
Use syms to create symbolic variables. Then use symfun to create a symbolic function with these
variables as its input arguments.
Eg.
syms x y
f = symfun(x + y, [x y])
--f(x, y) =
x + y
--f(1,2)
--ans =
3
Or use
syms x y
f(x,y) = x + y
For Vectors or matrices:
A = eye(3);
A(1,1) = sym('pi')
A =
3.1416
0
0
0
1.0000
0
0
0
1.0000
Using Symbolic Parameter Functions for sinusoids
EXAMPLE: Using symbolic variable declaration syms to evaluate sinusoids.
Consider two sinusoids of frequency 50Hz.
v1  120cos(100 t  15);
v1  240sin(100 t  30)
Find vt  v1  v2 ;
We can see that the value for omega (  ) is same for both. However, one is a sine and the other is cosine
function.
Nonetheless, MATLAB provides an easy method to add two functions using symbolic operators.
>>
>>
>>
>>
syms V1 V2 fi1 fi2 w t
v1=V1*cos(w*t+fi1);
v2=V2*cos(w*t+fi2);
vt=v1+v2
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EE211 | Introduction to MATLAB
vt =
V1*cos(fi1 + t*w) + V2*cos(fi2 +
t*w)
Notice that in the “Workspace” window, MATLAB has produced placeholders for all the variables that we
have declared symbolically (i.e V1, V2, fi1, fi2, w, t) and evaluated (i.e v1, v2, vt).
However, the foregoing expression is not of much use. We need to evaluate and graph those two functions
and their sum.
Let’s first assign the parameters with values.
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
syms V1 V2 fi1 fi2 w t
V1=120;
V2=240;
fi1=15*pi/180;
fi2=30*pi/180;
w=2*50*pi;
t=0:1e-4:0.02;
v1=V1*cos(w*t+fi1);
v2=V2*sin(w*t+fi2);
vt=v1+v2;
plot(t,vt,t,v1,t,v2),grid
Few things to note:
When we end each line of code with a semicolon “;”, MATLAB does not return the value of the parameter to
the command window. Makes the code more readable.
However, you can see the Workspace data has changed.
The following command: t=0:1e-4:0.02; sets an interval for the time domain (x-axis) from 0 to 1/50
(i.e. one full period of the waveform of a standard sinusoid without a phase shift i.e. v  Vm cos(t ) ).
The plot function in MATLAB is smart enough to recognize that you are adding 3 different waveforms each
having its own x- and y-axis parameter.
The grid function can be written in separate line or in the same with the comma. Sometimes we write grid
on and grid off. This function simply draws grid in the plot window as the name implies. See Figure 1
for plot output of v1, v2 and vt.
Hence MATLAB is built for engineers and mathematicians to intuitively use it to solve any mathematical
parameter as they would do in manual calculation.
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EE211 | Introduction to MATLAB
Figure 1
In the Plot window: You can go on Tools menu and select Edit Plot. And click on any of the waveform to
edit its properties as shown in Figure 2. Use help plot command to access more details on how to make
your graphs more presentable.
Figure 2
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