Introduction to Matlab

Introduction To Matlab
Prepared by :
1
Prepared by:
Eng. Amr Ezz Eldin Rashed
Assistant lecturer
TAIF university,KSA
TEL:ksa 0554404723

Outlines(First Level) _24 hour
What is Matlab
Basic commands
Vectors and matrices
Statistics for vector and matrix
Control loops(if,for,switch,break)
2D plotting , mathematics(int ,diff ,limit,..)
Exam
2

Outlines(Second Level)_24hour
3D plotting, animation
Dialog box
Simulink
Graphical user interface
Image and sound processing
البرامج الجاهزة
Project
EXAM
3

Outlines(Third Level)_24 hour
Introduction to Image Processing
Point Processing ,Spatial Filtering
Neighborhood Processing
The Fourier Transform
Image Restoration
Image Segmentation
project
4

What is Matlab?
What is possible in Matlab? graphic examples
How Matlab works? matrix, vector & scalar
syntax & important operators
basic commands & plot commands
creating a m-file
Statistics in Matlab some basics & example
Algebraic operations in Matlab
Useful links & other tutorials
5
Introduction to MATLAB

What is MATLAB
The name MATLAB stands for Matrix laboratory(or mathematical laboratory).
MATLAB is an interactive system whose basic data element is an array that does not require dimensioning.
It‟s both a computer programming language, and a software environment for using that language effectively.
Typical
6

What is MATLAB
Matlab is a commercial "Matrix Laboratory" package which operates as an interactive programming environment.
Matlab is available for PC's, Macintosh and UNIX systems.
Matlab is well adapted to numerical experiments.
Matlab program and script files (m-files) always have filenames ending with ".m";
The programming language is exceptionally straightforward since almost every data object is assumed to be an array.
Graphical output (figure) is available to supplement numerical results.
Online help is available from the Matlab prompt (a double arrow) by typing help
7

Typical Uses
Math and computation Algorithm development Modeling, simulation, and prototyping Data analysis, exploration, and visualization Scientific and engineering graphics Application development including GUI
8

Why use Matlab?
Advantages:
Handles vector and matrices very nice
Quick plotting and analysis
EXTENSIVE documentation (type „help‟)
Lots of nice functions: FFT, fuzzy logic, neural nets, numerical integration, OpenGL (!?)
Drawbacks:
Slow compared to C or Java
9

Matlab History
In the 1970‟s, Cleve Moler “Professor of Math & Computer Science, Chief Author of MatLab and one of the Founders of Mathworks.Inc” participated in developing (EISPACK) and (LINPACK). Those were collection of Fortran subroutines for solving linear equations and Eigen value problems.
Later, when teaching courses in mathematics, Moler wanted his students to be able to use LINPACK and EISPACK without requiring knowledge of Fortran, so he developed the first MATLAB in 1977 as an interactive system to access LINPACK and EISPACK.
10

MatLab History
The first Matlab was written in 2000 lines of Fortran, with Matrices as the only data type, 80 functions, no .m files and no toolboxes.
Jack Little, one of Moler‟s students saw Matlab potentials in Control systems & Signal Processing. They founded together Mathworks, Inc. in 1980
Mathworks is now responsible for development, sale, and support for MATLAB
MATLAB was rewritten in C with more functionality (such as plotting routines), and now it contains more than 80,000 functions.
11

The Basic Matlab System
It consists of 5 main parts:
–Development Environment.
–MATLAB Mathematical Function Library.
–MATLAB Language.
–Graphics.
–MATLAB External Interfaces
And finally the MatLab Toolboxes
–Toolboxes are comprehensive collections of MATLAB functions (M- files) that extend the MATLAB environment to solve particular classes of problems.
–Areas in which toolboxes are available include signal processing, control systems, neural networks, communications, wavelets, Data Acquisition, simulation, and many others.
12

MATLAB Development Environment & Basic Math Functions
13

Development Environment
•Run the matlab
14

Development Environment
15
Command Window
History
Work Space
Variables stores here
All of ur previous commands stores here
All commands, programs runs from here

Variables
MATLAB variable names must begin with a letter, which may be followed by any combination of letters, digits, and underscores. MATLAB distinguishes between uppercase and lowercase characters, so A and a are not the same variable(case sensitive). When naming a variable, make sure you are not using a name that is already used as a function name,begin with character .

Special Values
Function
description
Ans
Most recent answer (variable). If you do not assign an output variable to an expression, MATLAB automatically stores the result in ans.
pi
3.1415926535897...
inf
Infinity. Calculations like n/0, where n is any nonzero real value, result in inf.
I,J
The imaginary unit √-1
NaN,nan
Not-a-Number, an invalid numeric value. Expressions like 0/0 and inf/inf result in a NaN, as do arithmetic operations involving a NaN. n/0, where n is complex, also returns NaN.

Special Values
Description
Function
Beep sound
beep
Maximum real number that can be used
realmax
minimum real number that can be used
realmin
Specifies the accuracy of floating point
Precision .
الخطوة ب نٌ عدد نٌ أو أصغر عدد مٌكن تعر فٌه
eps
18

Operators
Arithmetic
–numeric computations, e.g., 2^10 Relational
–quantitative comparison of operands
–e.g., a < b Logical
–AND, OR, NOT
–return Boolean variable, 1 (TRUE) or 0 (FALSE)

Arithmetic operators
example
symbol
Operation
3+22
+
Addition
54.6-16.5
_
subtraction
3.14*6
*
Multiplication
10/100
10010
/ or
Division
2^8
^
power
20

Relational Operators
Description
Relational Operator
Less than
<
Less than or equal
<=
Greater than
>
Greater than or equal
>=
Equal to
==
Not equal to
~=
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Examples
Command
Result
5>8
ans=0
A=5<10
A=1
Y=(6<10)+(7>8)+(5*3==60/4)
Y=2
B=[15 6 9]; C=[8 20 9];
D=C>=B
D=[0 1 1]
B= =C
ans=[0 0 1]
B>6
ans=[1 0 1]

Logical Operators
Logical Operator
Description
&
Element by element AND
|
Element by element OR
~
NOT
&&
Scalar AND with short circuiting
||
Scalar OR with short circuiting

Examples
Command
Output
3 & 7
ans=1
A=5 | 0
A=1
~25
ans=0
(12 & 0) +(~0)+(0 | 5)
ans=2
X=[9 3 0]; Y=[2 0 13] X & Y
ans=1 0 0
Z=X | Y
Z=1 1 1

Operator Precedence
Precedence
Operation
1 (highest)
( )
2
^
3
~
4
*, /
5
+, -
6
Relational operations >,<, …
7
&
8
|

Complex functions
Description
Item
Define a complex number
Complex(2,-3)
Absolute value ;|x|
Abs(x)
Angle of complex number x
Angle(x)
Complex conjugate of x
Conj(x)
Imaginary part of a complex number x
Imag(x)
Real part of complex number x
Real(x)
26

Relational and Logical Functions
Function
Description
xor(x,y)
Exclusive OR
any(x)
True if any element is non zero
all(x)
True if all elements are non zero
Isequal(x,y)
True if arrays are numerically equal
Isfloatpt
True for a floating point number
isprime
True for a prime number

System and file commands
Description
Item
Clears command window
clc
Remove variables from memory
Clear , clear all
Display documentation
doc
Checks for existence of file or variable
exist
Declares variables to be global
global
Display help text in the command window
Help
Display help text in the help browser
helpwin
Searches help entries for a keyword
lookfor
Stops Matlab
Quit or exit
List current variables
who
Long display) ) List current variables
whos
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How to open file (mspaint.exe)
35

Trigonometric functions(Radian)
Description
Item
Inverse cosine
Acos(x)
Inverse cotangent
Acot(x)
Inverse cosecant
Acsc(x)
Inverse secant
Asec(x)
Inverse sine
Asin(x)
Inverse tangent
Atan(x)
Cosine
Cos(x)
cotangent
Cot(x)
cosecant
Csc(x)
Sine
Sin(x)
tangent
Tan(x)
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Trigonometric functions(degree)
Description
Item
Inverse cosine
Acosd(x)
Inverse cotangent
Acotd(x)
Inverse cosecant
Acscd(x)
Inverse secant
Asecd(x)
Inverse sine
Asind(x)
Inverse tangent
Atand(x)
Cosine
Cosd(x)
cotangent
Cotd(x)
cosecant
Cscd(x)
Sine
Sind(x)
tangent
Tand(x)
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Hyperbolic function
Description
Item
Inverse cosine
Acosh(x)
Inverse cotangent
Acoth(x)
Inverse cosecant
Acsch(x)
Inverse secant
Asech(x)
Inverse sine
Asinh(x)
Inverse tangent
Atanh(x)
Cosine
Cosh(x)
cotangent
Coth(x)
cosecant
Csch(x)
Sine
Sinh(x)
tangent
Tanh(x)
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Mathematical functions
item
Description
factor
التحل لٌ ال العوامل الاول ةٌ
Primes وٌلد قائمة بالاعداد الاول ةٌ الاقل من
x
isprime عٌ دٌ
true اذا كان العدد اول اٌ
Gcd القاسم المشترك الاكبر
lcm ا جٌاد المضاعف المشترك الاصغر
Factorial(x) لا جٌاد المضروب
Gamma(x) تابع جاما
Beta(x,y) تابع ب تٌا
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System and file Commands
item
Description
cd
Change current directory
Date
Display current date
dir
Lists all files in the current directory
mkdir
Used to make new directory
pwd
Present work directory
what
Lists all matlab files
Clock
Display current clock and date
42

Exponential functions
item
Description
exp
ًسلاا عباتلا
log اللوغار تٌم الطب عٌ log10 اللوغار تٌم للاساس
10
log2 اللوغار تٌم للاساس
2
Sqrt(x) الجذر الترب عٌ nthroot الجذر من المرتبة
n
pow2
2^(x)
expm1
Exp(x)-1
log1p
Log(x+1)
44

Erf,erfc,expint,format
47
تابع ا جٌاد الخطأ
المتمم تابع ا جٌاد الخطأ
ا جٌاد التكامل الاسً
15 رقم بفاصلة عائمة

format
48
5 ةتباث ةلصافب ماقرا
5 ارقام بفاصلة عائمة
15 رقم بفاصلة عائمة
الشكل الكسري

الرياضيات في الماتلاب
لا جٌاد جذور المعادلة
X^4+2*x^3+4*x+5=0
>>roots([1 2 0 4 5])
ولا جٌاد المعادلة بمعرفة الحلول
>>poly([1 2 3 4])
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Array orientation
>> c=[1;2;3;4;5] c = 1 2 3 4 5 >> c‟ % transpose of c ans = 1 2 3 4 5

Array orientation
>> s=[1+2i 3-5i 3+4i] s = 1.0000 + 2.0000i 3.0000 - 5.0000i 3.0000 + 4.0000i >> f=s‘ f = 1.0000 - 2.0000i 3.0000 + 5.0000i 3.0000 - 4.0000i >> g=s.‘ dot transpose operator g = 1.0000 + 2.0000i 3.0000 - 5.0000i 3.0000 + 4.0000i

Determine,diagonal,inverse
73

Find location of an element
75

برنامج لحساب زاو ةٌ خط
X=[1 0 0;0 1 0;0 0 1]; [I,j]=find(x==1); Length=max(i)-min(i); Width=max(j)-min(j); Ang=atand(length/width);
76

Determines matrix elements
d=[ 1 2;4 5; 3 2] d = 1 2 4 5 3 2 >> d(1,:) %row 1 and all columns ans = 1 2 >> d(1,2) % row 1 and all column 2 ans = 2 >> d(:,2) %all row and l column 2 ans = 2 5 2

Determines matrix elements
d = 1 2 4 5 3 2 >> d(2:3,:) ans = 4 5 3 2

Special Matrix(zeros,ones,magic,eye)
>> f=zeros(3) zeros=false f = 0 0 0 0 0 0 0 0 0 >> g=ones(4) ones=true g = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Special Matrix
>> v=zeros(2,3) v = 0 0 0 0 0 0
>> h=3*ones(2,4) h = 3 3 3 3 3 3 3 3

Special Matrix
>> eye(3,3) ans = 1 0 0 0 1 0 0 0 1

Special matrix(rand,randn,randint)
85
Zero mean unit variance
Random number between 0 and 1

Unique,intersect,setdiff
87
لحذف ما هو مكرر
وترت بٌ النت جٌة
الحصول عل العناصر
المشتركة ب نٌ مصفوفت نٌ
الحصول عل العناصر
الموجودة ف 1 وغ رٌ
موجودة ف 2

Approximation functions
Floor : rounds value towards negative infinity Ceil: rounds value towards positive infinity Fix: rounds value towards zero Round: normal approximation
100

Introduction to signal and image processing
114

Reading image
>> x=imread('C:Program FilesMATLABR2007atoolboximagesimdemoscameraman.tif');
>>y=imread('cameraman.tif');
>> imshow(y)
115

Operations on image
>> diag(y);
>> trace(y) ans = 27029 >> imshow(flipud(y)) >>imresize(y,[128 128]);
118

imwrite
imwrite(z,'amr.jpg') imwrite(y,„d:amr2.jpg')
125

Reading and writing sound
>>[y,fs]=wavread('C:WINDOWSMediachimes.wav');
>>Help auread
>> soundsc(y) or wavplay(y,fs)
>>size(y)
>>wavwrite(y,‟c:aa.wav‟) or auwrite
>>نأخذ جزء من الصوت ونتعامل معه
126

Flow Control
MATLAB has several flow control constructs:
For loop.
If statement.
Switch and case.
While.
Continue.
Break.
Try – catch.
Return.

For Loop
for x = array
(commands)
end The (commands) are executed once for every column in array At each iteration, x is assigned to the next column of the array

Example
For i=1:10 i end نٌفذ طالما i≤10
132

Example
for i=1:10 disp(i) end لا عٌرض كلمة I بجانب كل ق مٌة
133

Example♣♣
disp(„the numbers from 1 to 10 are:‟) for i=1:10 disp(i) end
134

Factorial
n=5; f=1; for i=2: n f=f*i; end disp(f)
135

لإ جٌاد مجموع الأعداد من ◄ 1:5
n=5 s=0 for i=1: n s=s+i; end disp(s)
136

لإ جٌاد مجموع مربعات الأعداد من ◄ 1:5
n=5 s=0 for i=1: n s=s+i^2; end disp(s)
137

لإ جٌاد جذور الأعداد من ◄ 1:5
n=5; for i=1: n disp(sqrt(i)) end
138

Example
n=5 disp(„number square root‟) disp(„ „) for i=1: n AA=sqrt(I); disp([ I AA ]) لعرض مجموعة من المتغ رٌات
End
139

Example
N=10 12/1! + 22/2!+………..+n2/n! الإشارة ثابتة
12/1! -22/2!+…-……..+n2/n! الإشارة متغ رٌة
140

Example
n=5;
fact=1;
Sum=0;
For I=1:n
fact=fact*I;
T=(I^2)/fact;
sum=sum+ T;
End
Disp(sum)
141

Example
ملحوظة ◄
لعمل إشارة أحد الحدود موجب والآخر سالب
(-1) i+1
Fact=-1
Fact= - fact *i
142

Example
n=input („enter any integer‟); Sum =0; For i=1: n Sum=sum+i End Disp(sum);
143

Example
What is your name? How old are you? طٌبع age, name
144

Example
Nam=input („what is your name?‟ , ‟s‟);
character حٌتوي على string
Age=input („how old are you?‟);
Disp(nam)
Disp(age)
145

Note
ملحوظة:
لك تٌرك سطر نستخدم علامة
ولك طٌبع backslash نستخدم علامة
ولطبع name ,age بجانب بعضهم
Disp ([x, y]);
إما أن كٌون ⤾ x, y
أي جٌب أن كٌونا من نفس النوع String or num
Disp ([nam, num2str (age)]);
146

Example
اطبع مجموع الأعداد التى تقبل القسمة على 5
sum=0;
For i=0:5:100
sum=sum+I;
end
Disp(sum)
147

Nested Loops
for n=1:5
for m=5:-1:1
A(n,m)=n^2+m^2;
end
end
A =
2 5 10 17 26
5 8 13 20 29
10 13 18 25 34
17 20 25 32 41
26 29 34 41 50

While Loops
while expression
(commands)
end Commands are executed as long as all elements in expression are true. Usually evaluation of expression gives scalar
–In case of array all elements must be true

Example
while x<=15
x=2*x;
end
Be careful and try to avoid infinite loops!
To stop the execution of an infinite loop use Ctrl+C
x =3
x =24

If-End Structure
if expression
(commands)
end The (commands) are evaluated if all elements in expression are true (nonzero)

If-Else-End Structure
if (expression)
(commands evaluated if true)
else
(commands evaluated if false)
end

Flow control - selection
The if-elseif-else construction
if <logical expression> <commands> elseif <logical expression> <commands> else <commands> end
if height>170
disp(’tall’)
elseif height<150
disp(’small’)
else
disp(’average’)
end

Example
X=input ('enter any value'); If (x>0) disp ('positive'); End IF (x<0) disp ('negative'); End لا غٌلق برنامج ال matlab ب end
155

Example
iF (x>0) disp ('positive'); else if (x<0) disp ('negative'); else disp ('zero'); End ملحوظة : وٌجد دالة جاهزة تقوم بنفس الوظ فٌة
sign
156

Example
أدخل ق مٌة x,y
ونحدد هل x اكبر من y ام لا ونطبع x,y
X is greater than y X is lower than y X is equal to y
157

Example
لطباعة الأعداد التى لا تقبل القسمة على 5
For i=0:100 If (rem(I,5)~=0) disp(i); End End
159

برنامج لا جٌاد جذور معادلة ترب عٌ ةٌ
Disp.→this program is used to solve the quadratic eqn Disp→ Ax2+Bx+c=0 a=input→enter the value of A:___ b=input→enter the value of B:___ c=input→ enter the value of C:___ D=B2- 4AC
•X1=x2=-b/2a X1= (-B+sqrt (d))/ (2*a))
X2= (-B-sqrt (d) )/ (2*a))
160
0
Non zero

Example
X=floor (rand*6) +1; If (x==1) disp ('that is 1'); Else if (x==2) disp ('that is 2'); Else if (x==3) disp ('that is 3'); Else if (x==4) disp ('that is 4'); Else if (x==5) disp ('that is 5'); Else disp ('that is 6'); Or else if (x==6) disp ('that is 6'); end
162

برنامج درجات الطلاب
163

Example
apples=10;
cost=apples*25;
if apples > 5
cost=(1 -20/100)*cost % 20% discount
end

Switch-Case Construction
switch expression
case test_expression1
(commands1)
case {test_expression2, test_expression3}
(commands2)
otherwise
(commands 3)
end

Example
method = 'Bilinear';
switch (method)
case 'linear'
disp('Method is linear')
case 'cubic'
disp('Method is cubic')
otherwise
disp('Unknown method.')
end
Method is Unknown method

باستخدام switch فى حالة multiple cases
X=floor (rand*6)+1; Switch x → expression or variable مٌكن أن كٌون
Case 1 Disp ('that is 1'); Case 2 Disp ('that is 2'); Case 3 Disp ('that is 3'); Case 4 Disp ('that is 4'); Case 5 Disp ('that is 5'); Case 6 Disp ('that is 6'); Or Otherwise Disp ('that is 6'); End
167

Example
لحساب أكثر من حالة مع بعض
X=floor (rand*6)+1; 1-if (x==1 | x==2 | x==3) 2-if (1<=x<=3) 3-case {1,2,3} disp ('from 1 to 3') case {4,5} disp ('4 or 5') case 6 / otherwise disp (that is 6'); end
169

برنامج لعمل password
172

program
المطلوب ف البرنامج السابق جعل عدد المحاولات 3 ف حالة كلمة السر الخطأ وواحدة ف حالة الكلمة الصح حٌة.
175

لحساب الوقت المستغرق لتنف ذٌ برنامج
179

program
Enter the no. of student=n Vector (x) Average = mean (x) The first = max (x) الطالب الأول
The last = min (x) الطالب الأخ رٌ
180

Example
A=[2 3;0 4]; B=[-5 7;10 2]; Display 1-add a to b 2-max value of a 3-Diag of b 4-exit
182

لادخال عناصر مصفوفة
Enter the number of raws Enter the number of column Enter the values
186

Security program
0
5
0
1
2
3
4
6
0
10
15
20
1
8
0
2
3
5
0
1
2
3
4
6
188

Simulink Power Window Controller Hybrid System Model
206

Simple models(simpower system)
216

Power electronic models(simpower sys)
217

Code
% --- Executes on button press in put. function put_Callback(hObject, eventdata, handles) % hObject handle to put (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) distor=200; set(handles.edit1,'String',distor);
240

حل المعادلة الترب عٌ ةٌ
245

برنامج عرض صورة الوان وابضٌ واسود
247

برنامج كلمة المرور
248

البرامج الجاهزة
252

تحد دٌ مركز الهزة الارض ةٌ
254

رسم اشارة وتصم مٌ المرشح المرغوب به
255

List dialog
d = dir;
str = {d.name};
[s,v] = listdlg('PromptString','Select a file:',... 'SelectionMode','single',...'ListString',str)
277

List dialog
smpl_length={'20','25','30','100','200','500'};
entry2=listdlg('name','input for sample lengths','promptstring',...
'enter sample length values','liststring',smpl_length);
278

[file,path] = uiputfile('animinit.m','Save file name');
283

Sine wave
285
01234567-1-0.8-0.6-0.4-0.200.20.40.60.81

Figure
287
00.511.522.533.540123456

figure
289
00.511.522.533.540123456aaaaaaatime distance

figure
291
00.511.522.533.540123456aaaaaaatime distance xxxxmove with mouse

figure
293
123456789100100200300400500600700800

Figure
295
01234567-50510152025303540

الرسم بإستخدام الاحداث اٌت الدائر ةٌ
297

figure
298
0.1 0.2 0.3 0.4 0.53021060240902701203001503301800

Figuer
301
123456789100102030405060708090100

figure
303
123456789100501001234567891000.51

Figure
307
02468-1-0.500.5102468-1-0.500.5102468-1-0.500.51-50510-1-0.500.51

Figure
309
02468-1-0.500.51number one02468-1-0.500.51number two02468-1-0.500.51number three-50510-1-0.500.51number four

ezplot
310
-6-4-20246-1-0.500.51xsin(x)

cont
311
-6 -4 -2 0 2 4 6
0
0.2
0.4
0.6
0.8
1
x
sin(x)2

312
-505020406080100120140160x4 x2-505-50-40-30-20-1001020304050x8 x-50577.27.47.67.888.28.48.68.89x8-505-1-0.8-0.6-0.4-0.200.20.40.60.81x0

Figure
314
00.20.40.60.8100.20.40.60.8100.20.40.60.81x axisy axis z label

program
[X,Y] = meshgrid(-2:.2:2, -2:.2:2); Z = X .* exp(-X.^2 - Y.^2); surf(X,Y,Z)
315

figure
316
-2-1012-2-1012-0.500.5

program
[X,Y] = meshgrid(-2:.2:2, -2:.2:2); Z = X .* exp(-X.^2 - Y.^2); subplot(221) mesh(Z) subplot(222) mesh(Z) view(-37.5,70) subplot(223) mesh(Z) view(-37.5,10) subplot(224) mesh(Z) view(0,0)
317

figure
318
0204002040-0.500.5020400102030-0.500.50204002040-0.500.50102030-0.500.5

sphere
319
-1-0.500.51-1-0.500.51-1-0.500.51

Sphere(40)
320
-1-0.500.51-1-0.500.51-1-0.500.51

mesh
[x,y,z]=sphere(40);
Mesh(x,y,z)
321

Figure
322
-1-0.500.51-1-0.500.51-1-0.500.51

cylinder
323
-1-0.500.51-1-0.500.5100.20.40.60.81

Cylinder(r,n)
324
-505-50500.20.40.60.81

program
[x,y,z]=cylinder(5,30);
Mesh(x,y,z)
325

figure
326
-505-50500.20.40.60.81

program
t = 0:pi/50:10*pi;
plot3(sin(t),cos(t),t,‟r‟);
Grid;axis square
327

figure
328
-1-0.500.51-1-0.500.51010203040

Pie,pie3
Subplot(211)
pie([1 2 3 5],{'North','South','East','West'})
Subplot(212)
pie3([2 4 3 5],[0 1 1 0],{'North','South','East','West'})
329

figure
330
NorthSouthEastWestEastWestSouthNorth

figure
332
11.522.53456700.5100.20.40.60.8100.5100.20.40.60.8100.5100.20.40.60.81

program
333
rectangle('Position',[0.59,0.35,3.75,1.37],...
'Curvature',[0.8,0.4 ],...
'LineWidth',2,'LineStyle','--')

figure
334
0.511.522.533.544.50.20.40.60.811.21.41.61.8

program
'Curvature',[0 0],...
335

figure
336
0.511.522.533.544.50.20.40.60.811.21.41.61.8

program
clf;close all;clear all;
337

Figure
338
0.511.522.533.544.50.20.40.60.811.21.41.61.8

program
clf;close all;clear all;
'facecolor','g')
339

figure
340
0.511.522.533.544.50.20.40.60.811.21.41.61.8

Figure
342
024681005100246810

Figure
344
0204002040-0.500.5020400102030-0.500.50204002040-0.500.50102030-0.500.5

Figure
346
05101520250102030-30-20-100102030

PROGRAM
المطلوب هو عمل برنامج لوضع الاسم والدرجة والتقد رٌ
كل واحدة ف مصفوفة و عٌرضهم
349

functions
Main program for i=1:10 disp(i) s(i) end Function s(i) for k=1:i fprintf(„*‟) end fprintf(„ „)
351

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