•Basic operations in MATLAB

Operation Symbol Example

Addition + 5+8

Subtraction - 5-8

Multiplication * 5*8

Division / 5/8

Power ^ 5^8

Lowest

Highest

5+3/3*9

Running MATLAB

MATLAB Command Example (number 15.793)

format long 15.79300000000000

format short e 1.5793e+001

format long e 1.579300000000000e+001

format hex 402f9604189374bc

format bank 15.79

format + +

format rat 5417/343

format short 15.7930

Display formats

•Up to 31 characters• Case sensitive• Start with a letter

• Information about variables•WHO•WHOS

Variables

MATLAB Environment

• Command Window

• Command History• Workspace• Current Directory

Function Description

abs(x) Absolute value of x

sqrt(x) Square root of x

sin(x) sine of x where x is in radians

cos(x) cosine of x where x is in radians

tan(x) tangent of x where x is in radians

ceil(x) Round towards plus infinity

floor(x) Round towards minus infinity

round(x) Round towards nearest integer

exp(x) Exponential of x (ex )

log(x) log to base e of x

sign(x) Returns sign of x

rem(x,y) Remainder of x/y

“pi” is a predefined variable (= 3.14....)

Mathematical functions

• Vectors and vector computation•first_nb : step : last_nb

(y = 2 : 0.5 : 4) y=[2 2.5 3 3.5 4]

*y = 1 : 3 y = [1 2 3] Default step is 1

• linspace(first_nb , last_nb , n_points) (y = linspace(2 , 4 , 5)) y = [2 2.5 3 3.5 4]

• z = [x y] x=[1 2 3], y=[4 5] z = 1 2 3 4 5

•Accesing elements: x(3), x(2:4), x(1:2:5), x([3 1 4])

• Column vector• x = [1;2;3;4] , x = [1 2 3 4]’

• Array operations (mult.(*), div.(/), add.(+),.. )

x = [1 2 3;4 5 6;7 8 9], x = [1:2:7 ; 3:-1:0 ; -1:2]• Special matrices

• zeros(3,2)• ones(3,2)• eye(3) (identity matrix)

• size(a), length(b)• Matrix operations• det(x), inv(x)• System of linear equations

0 0 0 00 0

Matrices and matrix computation

• Input• variable = input(‘text’)

r = input(‘ Enter a number ’)

• Output• disp(x), disp(‘the value is ’), • disp ( [ ‘ The value is ’ num2str ( x ) ] )

Input-Output Commands

• plot(x , y), plot(x , y , ’r+’)

Colour Symbol Linestyle Symbol

Yellow y Point .

Magenta m Circle o

Cyan c X-mark x

Red r Plus +

Green g Star *

Blue b Solid line -

White w Dotted line :

Black k Dash-dot line

-.

Dashed line --

2D Graphics

x = -pi : .1 : pi;y = sin(x);plot(x,y)

x = -pi : .1 : pi;y = sin(x);plot(x,y,’m*’’m*’)

• fplot(‘function’, [xmin xmax ])

• fplot('sin(x.*x)', [0 4])

2D Graphics

• xlabel('x values'), title('exp(-x) and x*x curves') title(‘text’) writes the text as a title at the top of the current

plotxlabel(‘text’) adds text to the current plot beneath the x-axisylabel(‘text’) adds text to the current plot beside the y-axisgrid on adds grid lines on the current axesgrid off takes them offtext(x,y,’text’) adds text to the location identified by the point

(x, y)gtext(‘text’) text is positioned at a location by pressing the

mouse

Try to run this code:

plot([5 5 4 3 2],[8 2 1 1 2],’r', [4 6],[8 8],‘y'); xlim([0 10]); ylim([0 10]);

2D Graphics

3D Graphics

• >> t=[0:pi/30:6*pi]; x=t.*cos(t); y=t.*sin(t); z=t; plot3(x,y,z)

• File New M-file• sample.m

% roots of the quadratic equation ax2+bx+c=0a = input('Enter the coefficient a: ');b = input('Enter the coefficient b: ');c = input('Enter the coefficient c: ');

disc=b*b-4*a*c;

x1 = (-b +sqrt(disc)) / (2 * a);x2 = (-b - sqrt(disc)) / (2 * a);

% Displays the rootsdisp(['Roots are ', num2str(x1),' and ',num2str(x2)])

Script files

Operators in Matlab

• Relational Operators< Less than

<= Less than or equal

> Greater than

>= Greater than or equal

== Equal

~= Not Equal

• Logical Operators~ not

& and | or

Priority Increases

if expression-1commands-1elseif expression-2

commands-2...

elseif expression-(n-1) commands-(n-1)else

commands-nend

A=[1 2; -3 6]; if det(A)>0

Ainv=inv(A); disp(Ainv) end

if – else – end

switch (selector) case label-1

commands-1 case label-2

commands-2 . . .

case label-ncommands-n

otherwise commands-mend

switch (det(a)) case 1 b=a'; disp(b) case 2 b=a*a; disp(b) end

switch

for x=arraycommands

end

for num=[6 37 23 -1] disp([num2str(k), ' th element is ', num2str(num)]) k=k+1; end

for loops

while expression commandsend

while x>=0 y=y+x; x=x-1; disp(y) end

while loops

• function [output-parameters]=function-name(input-parameters)

function [x1,x2] = quadratic(a,b,c)% Finds the roots of the quadratic equation% ax2+bx+c=0disc=b*b-4*a*c;x1=(-b+sqrt(disc))/(2*a);x2=(-b-sqrt(disc))/(2*a);

>> [a,b] = quadratic (1, -2 ,7)

User defined functions

function [top,cik,bol,carp] = islem(a,b)top = a+b;cik = a-b;bol = a/b;carp = a*b;

end

Example (islem.m)

function [top,cik,dot] = vectorislem(a,b)top = a+b;cik = a-b;dot = a*b';

end

Example (vectorislem.m)

Example 1

• The series ex is given by

• Write a MATLAB script to find the sum of the series while the value of the current term is greater than to the variable tol. Your program should input x and tol and should output the sum with proper messages. The result should be checked by using the MATLAB function exp().

...!3!2!1

132

xxx

e x

Possible Matlab Codex = input('Enter a value for x of exp(x)');tol = input('Enter the tolerance');k=1;sum=1;term=1;fact=1;sq=x;format long;while term>tol

term=sq/fact; % a single term is calculated: xn / n! sum=sum+term; % calculated term is added to general sum sq=sq*x; % next xn+1 is calculated fact=fact*(k+1); % next (x+1)! is calculated

k=k+1;enddisp(sum)disp(term)

Example 2

• Write a MATLAB function to generate and return the matrix in the form

• Your function should accept the parameters d, t, s and the size of the square matrix.

Possible Matlab Code

function matrix = matrix_ex(d,t,s,N) sM = [zeros(N-1,1) , eye(N-1) ; zeros(1,N)] * s; % superior 1'stM = [zeros(1,N) ; eye(N-1) , zeros(N-1,1)] * t; % lower 1'sdM = eye(N) * d; % identitymatrix = sM + tM + dM;