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

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

>>> i1=4

>>> R=v1/i1

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

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

333222111

987654321

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

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