Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB

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Numerical Methods for Engineers and Scientists
Lecturer: Assistant Prof. Dr. AYDIN AZIZI

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.
Third Edition
Amos Gilat • Vish Subramaniam
Numerical Methods
for
Engineers and Scientists

Lecturer: Assistant Prof. Dr. Aydin Azizi
Introduction to MATLAB

Example of MATLAB Release 13 desktop

Variables
– Vectors and Matrices –
• ALL variables are matrices
Variables
•They are case–sensitive i.e. x  X
•Their names can contain up to 31 characters
•Must start with a letter
•Variables are stored in workspace
e.g. 1 x 1 4 x 1 1 x 4 2 x 4






4239
6512 7123












3
9
2
3
 4

How do we assign a value to a variable?
>>> v1=3
v1 =
3
>>> i1=4
i1 =
4
>>> R=v1/i1
R =
0.7500
>>>
>>> whos
Name Size Bytes Class
R 1x1 8 double array
i1 1x1 8 double array
v1 1x1 8 double array
Grand total is 3 elements using 24 bytes
>>> who
Your variables are:
R i1 v1
>>>

How do we assign values to vectors?
>>> A = [1 2 3 4 5]
A =
1 2 3 4 5
>>>
>>> B = [10;12;14;16;18]
B =
10
12
14
16
18
>>>
A row vector values
are separated by
spaces
 54321A 

















18
16
14
12
10
B
A column vector
values are
separated by
semi–colon (;)

• If we want to construct a vector of, say, 100 elements between 0 and 2 – linspace
>>> c1 = linspace(0,(2*pi),100);
>>> whos
c1 1x100 800 double array
>>>

If we want to construct an array of, say, 100 elements between 0 and 2
– colon notation
>>> c2 = (0:0.0201:2)*pi;
>>> whos
>>>

How do we assign values to matrices ?
Columns separated by
space or a comma
Rows separated by
semi-colon
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>>










987
654
321

How do we access elements in a matrix or a vector?
>>> A(2,3)
ans =
6
>>> A(:,3)
ans =
3
6
9
>>> A(1,:)
ans =
1 2 3
>>> A(2,:)
ans =
4 5 6

Some special variables
pi ()
inf (e.g. 1/0)
i, j ( )1
>>> 1/0
Warning: Divide by zero.
ans =
Inf
>>> pi
ans =
3.1416
>>> i
ans =
0+ 1.0000i

Arithmetic operations – Matrices
Performing operations to every entry in a matrix
Add and subtract>>> A=[1 2 3;4 5 6;7 8
9]
A =
1 2 3
4 5 6
7 8 9
>>>
>>> A+3
ans =
4 5 6
7 8 9
10 11 12
>>> A-2
ans =
-1 0 1
2 3 4
5 6 7

Multiply and divide>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>>
>>> A*2
ans =
2 4 6
8 10 12
14 16 18
>>> A/3
ans =
0.3333 0.6667 1.0000
1.3333 1.6667 2.0000
2.3333 2.6667 3.0000

Power
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>>
A^2 = A * A
To square every element in A, use
the element–wise operator .^
>>> A.^2
ans =
1 4 9
16 25 36
49 64 81
>>> A^2
ans =
30 36 42
66 81 96
102 126 150

Performing operations between matrices
>>> A=[1 2 3;4 5 6;7 8 9]
A =
1 2 3
4 5 6
7 8 9
>>> B=[1 1 1;2 2 2;3 3 3]
B =
1 1 1
2 2 2
3 3 3
A*B 



















333
222
111
987
654
321
A.*B










3x93x83x7
2x62x52x4
1x31x21x1










272421
12108
321
=
=










505050
323232
141414

Roots- Logarithms

Random Number

Random Real Number

Random Integer Number

Practice

Characters and Encoding

Relational Expressions

Logical Operators

Truth Table for Logical Operators

Logical Error

While Loop
count = 0;
number = 8;
while number > 3
number = number - 2
count = count+1
end

FOR Loop
mat=rand(5,6)
[r c] = size(mat)
for i = 1:r
for j = 1:c
mat(i,j) = mat(i,j) * 2
end
end

IF Loop
x=rand(10,1);
v = [ ]
for i = 1:length(x)
if x(i) > 0
v = [v i]
end
end

Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB

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