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

42396512 7123

3923 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

1816141210

BA column vector

values are separated by semi–colon (;)



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

>>>



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>>>



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



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

>>> 1/0Warning: Divide by zero.ans = Inf>>> pians = 3.1416>>> ians = 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+3ans = 4 5 6 7 8 9 10 11 12

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




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




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



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




Roots- Logarithms


Random Number


Random Real Number


Random Integer Number


Practice


Characters and Encoding


Practice


Relational Expressions


Logical Operators


Truth Table for Logical Operators


Logical Error


Practice


While Loop

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


FOR Loop

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


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

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