MATLAB
Jirawat Kanjanapitak (Tae)
What is MATLAB

A computer program for doing numerical
computation including; Arithmetic, Polynomials,
Graphics, 2-D Plots, Matrices, Systems of
Equations etc.
Getting Started
Open Program

Click “MATLAB R2006a” on
Desktop
OR
Go to “Start”
 All Program > MATLAB >
MATLAB R2006a

MATLAB Desktop


Default layout
Arranging the
Desktop including
resizing, moving,
and closing tools.
Taken from MATLAB Help
MATLAB for Problem Solving
Arithmetic Calculator


Type in any basic
arithmetic as shown

Click “Enter”
>> 1+1
ans =
2
>> (7*5)+2
ans =
37
>> [(8+2^2)/(1*3)]
ans =
4
Basic Operations
Operation
x+y
x-y
xy
x/y
xy
ex
|x|
π
MATLAB
x+y
x-y
x*y
x/y
x^y
exp(x)
abs(x)
pi
sqrt(x)
Vectors





To increment using colon

>> v = [1:5]
v=1 2 3 4 5

To increment other than1
To transpose a column
vector to a row vector,
use an apostrophe “‘“

>>v = [5:0.5:7]
v = 5 5.5 6 6.5 7
>>v = [1 2 3]’

To view individual entries
in this vector

v(2)
Ans = 5.5
To enter a vector
>> v = [1 2 3]
v=1 2 3
v= 1
2
3
Vector Examples
>> v = [1:5];
 >> u = [0:-1:4];
 u+v
 Ans: 1 1 1 1 1
 v^2
 Ans: 1 4 9 16 25


Note: Error
message will
appear from adding
two vectors whose
dimensions are
different.
Matrices

To enter a matrix
1
3

Use command
>> a = [ 1 2; 3 4 ]
2
4
Matrix Examples






>> a = [ 1 2; 3 4 ];
>> b = [ 0 1; 2 3 ];
>> a+b
ans =
1 3
5 7
>>a*b
ans =
4 7
8 15
T = a+b;
 >> inv(t)
 ans =
-0.8750 0.3750
0.6250 -0.1250
 >> inv(t)/t
 ans =
1.0000 -0.3750
-0.6250 0.2500

Plotting

Use “plot” command
Format: plot(x,y, ‘m’)

The third input is a
characteristic of the
graph.
y
m
c
r
g
b
yellow
magenta
cyan
red
green
blue
k
black
*
star
.
dotted
-x
dashed
x-mark
Plotting Examples
x = 0:0.1:100;
 y = 2*x;
 plot (x,y,'--')

200
180
160
140
120
100
80
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
Plotting Examples 2
x = 0:0.1:5;
 y = sin (x);

1
0.8
0.6
0.4

plot (x,y,'x')
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Plotting Examples 3




x = linspace(0,2*pi,50);
y = sin (x);
z = cos (x);
plot (x,y, x,z)
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4
5
6
7
Sub-Plotting

Use “subplot” command to put more than one
plot in the same figure
subplot (m,n,p)
where; m = number of rows
n = number of column
p = plot number
Sub-Plotting Example







x=
linspace(0,2*pi,50);
y = sin (x);
z = cos (x);
subplot (1,2,1)
plot (x,y)
subplot (1,2,2)
plot (x,z)
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
0
2
4
6
8
-1
0
2
4
6
8
Adding Text

Below are the text adding related
commands
title (‘title name’)
xlabel (‘label of the x-axis’)
ylabel (‘label of the y-axis’)
gtext (‘put text in the middle of plot’)
Adding Text Example
title name







x = 0:0.1:100;
y = 2*x;
plot (x,y,'--')
title ('title name')
xlabel ('label of the x-axis')
ylabel ('label of the y-axis')
gtext ('put text in
the middle of plot')
180
put text in the middle of plot
160
140
label of the y-axis

200
120
100
80
60
40
20
0
0
10
20
30
40
50
60
label of the x-axis
70
80
90
100
Polynomials
Vector is used to
represented polynomial
in MATLAB.

For example;
t3+4t2-3t+1
t = [1 4 -3 1]
or
x5+3x2-6
x = [1 0 0 3 0 -6]
Polynomial Examples

To multiply two
polynomial

x = [1 2 3];
y = [2 4 6 8];
z = conv(x,y)

[xx, w] = deconv(z,y)
 xx =
1 2 3
w=
z=
2
8
20
32
34
To devide two
polynomial
24
0
0
0
0
0
0
Symbolic Math
Use for factoring solving, root finding,
differentiating, and integrating.
 Use sym command to create a symbolic
object.

Example:
sqrt(2)
ans
1.4142
With sym command
a = sqrt(sym(2))
ans
a = 2^(1/2)
Symbolic Math Cont.
Use double
command to get the
value of the
symbolic object.
 double(a)
ans =
1.4142

Use sym command
to find common
denominator.
 sym(2)/sym(5) +
sym(1)/sym(3)
ans =
11/15

Solve Command Example
Eqn = ax^2 + bx + c = 0
 To solve symbolically for the variable x use
solve(Eqn,'x')
 To find the value of b which makes this true
solve(QuadEqn,'a=3','c=-1','x=-1')

A more complicated example
solve(QuadEqn,'a=sqrt(c)','b=2','x=-1')

Getting HELP!

Use “help” command
help commandname
References


MATLAB Help
MATLAB Tutorials
 http://www.cyclismo.org/tutorial/matlab/
 http://www.math.utah.edu/lab/ms/matlab/matlab.html
 http://www.engin.umich.edu/group/ctm/basic/basic.ht
ml
 http://physics.gac.edu/~huber/matlab/mtlabsym.htm