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

This document is intended for internal use only and shall not be distributed outside of GUtech in Oman

Numerical Methods for Engineers and Scientists

Lecturer: Assistant Prof. Dr. AYDIN AZIZI

Slide 2

Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.

Third Edition

Amos Gilat • Vish Subramaniam

Numerical Methods for

Engineers and Scientists

Slide 3

Lecturer: Assistant Prof. Dr. Aydin Azizi

Introduction to MATLAB


Slide 4


Example of MATLAB Release 13 desktop


Slide 5


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

42396512 7123

3923 4


Slide 6


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

>>>


Slide 7


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

1816141210

BA column vector

values are separated by semi–colon (;)


Slide 8


How do we assign values to vectors?• If we want to construct a vector of, say, 100 elements between 0 and 2 – linspace

>>> c1 = linspace(0,(2*pi),100);

>>> whos

Name Size Bytes Class

c1 1x100 800 double array

Grand total is 100 elements using 800 bytes

>>>


Slide 9


How do we assign values to vectors?

If we want to construct an array of, say, 100 elements between 0 and 2 – colon notation

>>> c2 = (0:0.0201:2)*pi;

>>> whos Name Size Bytes Class c1 1x100 800 double array c2 1x100 800 double arrayGrand total is 200 elements using 1600 bytes>>>


Slide 10


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>>>

987654321


Slide 11


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


Slide 12


Some special variables

pi ()

inf (e.g. 1/0)

i, j ( )1

>>> 1/0Warning: Divide by zero.ans = Inf>>> pians = 3.1416>>> ians = 0+ 1.0000i


Slide 13


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+3ans = 4 5 6 7 8 9 10 11 12

>>> A-2ans = -1 0 1 2 3 4 5 6 7


Slide 14



Performing operations to every entry in a matrix

Multiply and divide>>> A=[1 2 3;4 5 6;7 8 9]A = 1 2 3 4 5 6 7 8 9>>>

>>> A*2ans = 2 4 6 8 10 12 14 16 18

>>> A/3ans = 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 2.3333 2.6667 3.0000


Slide 15



Performing operations to every entry in a matrixPower

>>> 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.^2ans = 1 4 9 16 25 36 49 64 81

>>> A^2ans = 30 36 42 66 81 96 102 126 150


Slide 16


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

333222111

987654321

A.*B

3x93x83x72x62x52x41x31x21x1

27242112108321

=

=

505050323232141414



Slide 17


Roots- Logarithms

Slide 18


Random Number

Slide 19


Random Real Number

Slide 20


Random Integer Number

Slide 21


Practice

Slide 22


Characters and Encoding

Slide 23



Slide 24



Slide 25


Practice

Slide 26


Relational Expressions

Slide 27



Slide 28



Slide 29


Logical Operators

Slide 30


Logical Operators

Slide 31


Logical Operators

Slide 32


Truth Table for Logical Operators

Slide 33


Logical Error

Slide 34


Logical Error

Slide 35


Practice

Slide 36


While Loop

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

Slide 37


FOR Loop

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

Slide 38


IF Loop

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

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

Engineering