This is an introduction to MATLAB. It was prepared for 4th grade students at university of Khartoum - surveying engineering department - along with the geometrical geodesy course.

1. Introduction To MATLAB
Mohamed Jaafar
wadjaafar@gmail.com
wadjaafar@student.uofk.edu
Mahmoud Badreldin
mahmoudelgabbani@yahoo.com

2. Course
In this course we’ll use Piazza Q&A web service.
◦ Every student must join the class in Piazza.
◦ Course link : https://piazza.com/uofk/winter2017/sur412

3. Outline
• What Is MATLAB?
• MATLAB Environment.
• Variables.
• Operators.
• Vectors And Matrices.
• Mathematical Functions.
• Two Dimensional Plotting.

4. What is MATLAB?
• MATLAB is a high-performance language for technical
computing.
• Stands for MATrix LABoratory.
• MATLAB has many functions and toolboxes to help in
various applications.

5. What is MATLAB?
• MATLAB (commercial)
•MATLAB is too expensive.
• Octave (Free)
• Scilab (Free)

6. MATLAB Environment
Command Window
• Type commands
Current Folder
• View folders
and m-files
Workspace
• View program
variables
Command History
• View past commands

7. Variables
• There is no need to declare variable type in MATLAB.
• All variables are created with double precision unless specified and
they are matrices.
• After these statements, the variables are 1x1 matrices with double
precision.
int a;
double b;
float c;
Example:
>> x=5;
>> y=2;

8. Simple MATLAB Program
>> x=5
x =
5
>> y=2
y =
2
>> ans = x * y
ans =
10
• Note:
• Creates the ans variable automatically
when you specify no output argument.

9. Operators (arithmetic)
Symbol Operation
+ Addition
- Subtraction
* Multiplication
/ Division
^ Power

10. Operators (arithmetic)
>> 5 + 7
ans =
12
>> 64 / 8
ans =
8
>> 12 * 5
ans =
16
>> 40 - 7
ans =
33
>> 2 ^ 5
ans =
32
>> 3 /0
ans =
Inf
>> 0/0
ans =
NaN
• Examples
• Special Cases
• Inf: Infinity.
•NaN: Not a Number.

11. Vectors And Matrices
• In MATLAB matrices are easy to define:
• Use ‘ ’ to separate row elements.
• Use ‘;’ to separate rows.
>> y = [1 2 3; 4 5 6; 7 8 9]
y =
1 2 3
4 5 6
7 8 9

12. Vectors And Matrices
• Order of Matrix
◦m = no. of rows.
◦n = no. of columns.
• Vectors are special case
m = 1 row vector n = 1 column vector
A =
0.9501 0.6068 0.4231
0.2311 0.4860 0.2774m
n
>> x = [1 2 3 4]
x =
1 2 3 4
>> x = [1; 2; 3; 4]
x =
1
2
3
4

13. Long Vector, Matrix
>> x = 1:10
x =
1 2 3 4 5 6 7 8 9 10
>> x = 1:0.5:5
x =
1 1.5 2 2.5 3 3.5 4 4.5 5
>> [1:4; 5:8]
x =
1 2 3 4
5 6 7 8
• If you want to create a row
vector, containing numbers
from 1 to 10, you write
• If you want to specify an
increment value other than
one, for example
• Also you can create a matrix
using the colon.

14. Creating Vectors, Matrices from functions
>> x = zeros(2,3)
x =
0 0 0
0 0 0
>> x = ones(1,3)
x =
1 1 1
>> x = rand(1,3)
x =
0.8147 0.9058 0.1270
• zeros(m,n) m x n matrix of
zeros.
• ones(m,n) m x n matrix of
ones.
• rand(m,n) m x n matrix of
uniformly
distributed random number in
the interval (0,1).

15. Creating Vectors, Matrices from functions
Function Description
zeros(m,n) Matrix with all zeros
ones(m,n) Matrix with all ones.
eye(m,n) The identity matrix
rand(m,n) Uniformly distributed random
randn(m,n) Normally distributed random

16. Matrix Index
• The matrix indices begin from 1 (not 0 (as in Java)).
• The matrix indices must be positive integer.
• Given:
A =
1 2 3
4 5 6
7 8 9
>> A(4)
ans =
2
>> A(1,2)
ans =
2
>> A(3,:)
ans =
7 8 9
>> A(:,2)
ans =
2
5
8
>> A(1:2,1)
ans =
1
4

17. Matrix Index
• Given
A =
1 2 3
4 5 6
7 8 9
>> A(-2), A(0)
Error: Subscript indices must either be real positive integers or logicals.
>> A(4,2)
Error: Index exceeds matrix dimensions.

18. Matrices Operations
• Given A and B: A =
1 2 3
4 5 6
7 8 9
B =
6 4 9
2 8 1
5 1 3
>> A + B
ans =
7 6 12
6 13 7
12 9 12
>> A - B
ans =
-5 -2 -6
2 -3 5
2 7 6
>> A * B
ans =
25 23 20
64 62 59
103 101 98
>> A’
ans =
1 4 7
2 5 8
3 6 9
• Subtraction• Addition • Product • Transpose

19. Matrices Operations (Element by Element)
Symbol Operation
.* Element-by-element multiplication
./ Element-by-element division
.^ Element-by-element power

20. Matrix Functions
Function Definition
det Determinant
diag Diagonal matrices and diagonals of a
matrix
eig Eigenvalues and eigenvectors
inv Matrix inverse
norm Matrix and vector norms
rank Number of linearly independent rows
or columns

21. Matrix Functions
• Given: A =
1 2
3 4
>> det(A)
ans =
-2
>> diag(A)
ans =
1
4
>> inv(A)
ans =
-2 1
1.5 -0.5
>> norm(A)
ans =
5.4650

22. Concatenation of Matrices
>> x = [1 2]
x =
1 2
>> y = [3 4]
y =
3 4
>> A = [x y]
A =
1 2 3 4
>> B = [x; y]
B =
1 2
3 4
• Given:
• you can create a matrix or construct one from other matrices.

23. Mathematical Functions
Function Definition Function Definition
sqrt(x) Square root exp(x) Exponential
angle(x) Phase angle round(x) Round to nearest
integer
abs(x) Absolutevalue ceil(x) Round towards
plus infinity
rem(x) Reminder after
division
floor(x) Round towards
minus infinity
size(x) The dimensions
of a matrix
log(x) Natural logarithm
min(x) Minimum value length(x) The length of a
matrix
max(x) Maximum value sign(x) Signum function

24. Trigonometric Functions
Function Definition Function Definition
sin(x) Sine in radians sind(x) Sine in degrees
cos(x) Cosine in radians cosd(x) Cosine in degrees
tan(x) Tangent in
radians
tand(x) Tangent in
degrees
sec(x) Secant in radians secd(x) Secant in degrees
csc(x) Cosecant in
radians
cscd(x) Cosecant in
degrees
cot(x) Cotangent in
radians
cotd(x) Cotangent in
degrees
deg2rad(x) Convert angle
from degrees to
radians
rad2deg(x) Convert angle
from radians to
degrees

25. Trigonometric Functions (Inverse)
Function Definition Function Definition
asin(x) Inverse sine in
radians
asind(x) Inverse sine in
degrees
acos(x) Inverse cosinein
radians
acosd(x) Inverse cosinein
degrees
atan(x) Inverse tangent
in radians
atand(x) Inverse tangent
in degrees
asec(x) Inverse secantin
radians
asecd(x) Inverse secantin
degrees
acsc(x) Inverse cosecant
in radians
acscd(x) Inverse cosecant
in degrees
acot(x) Inverse
cotangent in
radians
acotd(x) Inverse
cotangent in
degrees

26. Trigonometric Functions
>> sin(60)
ans =
-0.3048
>> cosd(60)
ans =
0.5
>> asind(0.5)
ans =
30
>> deg2rad(180)
ans =
3.1416

27. 2D Plotting In MATLAB
• Note:
• The semicolon(;) tells MATLAB not to
display any output from that command.
>> x = [0:0.1:2*pi];
>> y = sin(x);
>> plot(x, y)
Sine function in range 0 ≤ x ≤ 2π.
• We are going to plot the function sin(x) between 0 ≤ x ≤ 2π.
• First, we define the range of the independent variable, x to be between 0 and
2π. i.e. between 0 and 360.
• Then, we define the dependent variable,
y by writing the command y = sin(x).
• We plot using the function, plot(x,y).

28. Labels
• title()
• xlabel()
• ylabel()
>> title(‘Sine function in range 0 ≤ x ≤ 2π’)
>> xlabel(‘Angles x’)
>> ylabel(‘y = sin(x)’)