Matlab
March 13, 2023 | Author: Anonymous | Category: N/A
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ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب Introduction to Matlab Programming
اﻋﺪاد د/ﺧﺎﻟﺪ ﻋﺒﺪاﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ ر ﻴﺲ ﻗﺴﻢ هﻨﺪﺳﺔ اﻟﺤﺎﺳﺐ اﻵﻟﻲ آﻠﻴﺔ اﻟﺤﺎﺳﺐ اﻵﻟﻲ وﻧﻈﻢ اﻟﻤﻌﻠﻮﻣﺎت ﺟﺎﻣﻌﺔ م اﻟﻘﺮى ﺑﻤﻜﺔ اﻟﻤﻜﺮﻣﺔ
ﺟﻤﻴﻊ ﻟﺤﻘﻮق ﻣﺤﻔﻮﻇ
© 2007
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ ﻣﻌﻠﻮﻣﺎ اﻟﻔﺼﻞ اﻷو )اﻟ ﻘﺪﻣ ( )Information in Chapter 1 (Introduction ﻣﺆﺳﺴﻮ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب
آﻠﻴﻒ ﻣﻮﻟ
) (Cleve Moler
ﻩﻮ أﺳﺘﺎذ اﻟﺮﻳﺎﺿﻴﺎت وﻋﻠﻮم اﻟﺤﺎﺳﺐ ﻷﺁﺜﺮ ﻣﻦ ﻋﺸﺮﻳﻦ ﻋﺎﻣ ﻓﻲ ﺟﺎﻣﻌﺔ ﻣﺘﺸﻴﺠﻴﻦ وﺟﺎﻣﻌﺔ ﺳﺘﺎﻧﻔﻮرد وﺟﺎﻣﻌﺔ ﻧﻴﻮﻣﻜﺴﻴﻜﻮ وﻗﺪ أﻣﻀﻰ ﺧﻤﺲ ﺳﻨﻮات ﻋﻨﺪ اﺛﻨ ﻦ ﻣﻦ ﻣﺼﻨﻌﻲ اﻟــ Hardwareوﻩﻤﺎ Intel Hypercube organization و Ardentﻗﺒﻞ أن ﻳﻘﻮم ﺑﺎﻻﻧﺘﻘﺎل إﻟﻰ ﺷﺮﺁﺔ Mathworksاﻟﺸﺮﺁﺔ اﻷم ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼ ﺁﻤﺎ أﻧﻪ ﻩﻮ اﻟﻤﺆﻟﻒ ﻷول ﺑﺮﻧﺎﻣﺞ ﻟﻠﻤﺎﺗﻼ .
ﺟﺎك ﻟﻴﻞ ) (jack little
ﻩﻮ اﻟﻤﺆﺳﺲ ﻟﺸﺮﺁﺔ Mathworksﺁﻤﺎ أﻧﻪ اﻟﻤﺴﺎﻋﺪ ﻓﻲ وﺿﻊ ﺨﻄﻴﻂ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼ وﻩﻮ ﺣﺎﺻﻞ ﻋﻠﻰ ﺑﻜﺎﻟﻮرﻳﻮس اﻟﻬﻨﺪﺳﺔ اﻟﻜﻬﺮﺑﻴﺔ وﻋﻠﻮم اﻟﺤﺎﺳﺐ ﻣﻦ ﺟﺎﻣﻌﺔ MIT ﻋﺎ 1978ﺁﻤﺎ أﻧﻪ ﺣﺼﻞ ﻋﻠﻰ ﺷﻬﺎدة M.S.E.Eﻣﻦ ﺟﺎﻣﻌﺔ ﺳﺘﺎﻧﻔﻮرد ﻋﺎم . 1980
ﺗ ﺎرﻳﺦ اﻟﻤﺎﺗﻼب ﻓﻲ ﻣﻨﺘﺼﻒ اﻟﺴﺒﻌﻴﻨﺎت ﻋﺎم 1970ﻗﺎم ﺁﻠﻴﻒ ﻣﻮﻟﺮ اﻟﺬي ﺁﺎن رﺋﻴﺴﺎ ﻟﻘﺴﻢ ﻋﻠﻮم اﻟﺤﺎﺳﺐ ﻓﻲ ﺟﺎﻣﻌﺔ ﻧﻴﻮﻣﻜﺴﻴﻜﻮ وﻋﺪد ﻣﻦ زﻣﻼﺋﻪ ﺑﺘﻄﻮﻳﺮ ﻣﻜﺘﺒﺎت اﻟﻔﻮرﺗﺮان واﻟﺘﻲ ﺁﺎﻧﺖ ﺗﺪﻋﻰ LINPACK EISPACK ﺗﺤﺖ ﻣﻨﺤﺔ ﻣﻦ اﻟﻤﺆﺳﺴﺔ اﻟﻘﻮﻣﻴﺔ ﻟﻠﻌﻠﻮ .
EISPACK LINPACK ﻩﻤﺎ اﻟﻠﺒﻨﺔ اﻟﺒﺮﻣﺠﻴﺔ اﻷﺳﺎﺳﻴﺔ ﻓﻲ ﺑﺮﻣﺠﻴﺎت ﺣﺴﺎﺑﺎت اﻟﻤﺼﻔﻮﻓﺎ
.
ﺑﺪأ ﺁﻠﻴﻒ ﺑﻜﺘﺎﺑﺔ ﺑﺮﻧﺎﻣﺞ ﻟﻠﻮﺻﻮل إﻟﻰ EISPACK و LINPACK ﺑﻜﻞ ﺑﺴﺎﻃﺔ وﺳﻤﻲ ﺑﺮﻧﺎﻣﺠﻪ MATLAB واﻟﺘﻲ ﺗﻌﻨﻲ ) (Matrix Laboratoryأي ﻣﺨﺘﺒﺮ اﻟﻤﺼﻔﻮﻓ . اﻧﺘﺸﺮ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب ﻟﻠﺠﺎﻣﻌﺎت اﻷﺧﺮى ووﺟﺪ ﻩﺬا اﻟﺒﺮﻧﺎﻣﺞ ﺟﻤﻬﻮر ﻗﻮي ﻣﻦ ﻗﺒﻞ اﻟﻤﺨﺘﺼﻴﻦ ﺑﺎﻟﺮﻳﺎﺿﻴﺎت اﻟﺘﻄﺒﻴﻘﻴ .
ﻓﻲ ﻋﺎم 1983ﻋﺮض ﻋﻠﻰ اﻟﻤﻬﻨﺪس ﺟﻮن ﻟﻴﺘﻞ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب أﺛﻨﺎ زﻳﺎر ﻣﻮﻟﺮ ﻟﺠﺎﻣﻌﺔ ﺳﺘﺎﻧﻔﻮرد وﺑﻌﺪ ذﻟﻚ اﻧﻈﻢ ﻟﻴﺘﻞ إﻟﻰ ﻣﻮﻟﺮ وﺳﺘﻴﻒ ﺑﺎﻧﺠﺮت وأﻋﻴﺪت ﺁﺘﺎﺑﺔ اﻟﻤﺎﺗﻼب ﺑﻠﻐﺔ اﻟﺴﻲ .
أﺳ ﺖ ﻓﻲ ﻋﺎم 1984ﺷﺮﺁ Mathworksﻟﻤﻮاﺻﻠﺔ ﺗﻄﻮﻳ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼ
.
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
1
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﺗﺎﺑﻊ ﻣﻠﺨﺺ ﻣﻌﻠﻮﻣﺎ اﻟﻔﺼﻞ اﻷو )اﻟ ﻘﺪﻣ ( )Information in Chapter 1 (Introduction
ﺗﻌﺮﻳﻒ اﻟﻤﺎﺗﻼ
ﻟﻐﺔ ذات ﻣﺴﺘﻮى ﻋﺎﻟﻲ ﻟﻠﺤﺴﺎﺑﺎت واﻟﺒﺮﻣﺠﺔ وﺗﻤﺘﺎز ﺑﻮﺟﻮد ﺑﺮاﻣﺞ ﺗ ﻬﻞ ﻋﻤﻠﻴﺔ اﻟﺘﻌﺎﻣﻞ ﻣﻊ ﻩﺬﻩ اﻟﻠﻐ
اﻟﻤﺎﺗ ب اﻟﺒﺮاﻣﺞ ﻋﻠﻰ:
o o o o o o o
ﺗ ﻤﻞ
اﻟﺤﺴﺎﺑﺎت اﻟﺮﻳﺎﺿﻴﺔ ﺗﻄﻮﻳﺮ اﻟﺨﻮارزﻣﻴﺎت ﻣﻌﺎﻟﺠﺔ اﻟﺒﻴﺎﻧﺎت اﻟﻨﻤﺬﺟﺔ واﻟﻤﺤﺎﺁﺎة وﺗﺼﻤﻴﻢ اﻟﻤﺨﻄﻄﺎت اﻷوﻟﻴﺔ ﻟﻠﻤﺸﺎرﻳﻊ ﺗﺤﻠﻴﻞ اﻟﺒﻴﺎﻧﺎت ﻋﺮﺿﻬﺎ ﻋﻤﻞ اﻟﺮﺳﻮﻣﺎت اﻟﻬﻨﺪﺳﻴﺔ واﻟﻌﻠﻤﻴﺔ ﺗﻄﻮﻳﺮ اﻟﺘﻄﺒﻴﻘﺎت ﺿﻤﻦ واﺟﻬﺎت ﻣﻦ ﻧﻮ )(GUI
وﻳﻌﺘﻤﺪ اﻟﻤﺎﺗﻼب ﻋﻠﻰ ﺗﻨﺴﻴﻖ اﻟ ﺎﻧﺎت ﻓﻲ ﺻﻮرة ﻣﺼﻔﻮﻓﺎت وﻳﻜﻮن اﻟﺒﺮﻧﺎﻣﺞ ﻣﺜﻞ أﻏﻠ ﻐﺎت اﻟﺒﺮﻣﺠ .
ﻳﺸﻤﻞ اﻟﻤﺎﺗﻼب ﻋﻠﻰ ﻣﺠﻤﻮﻋﺔ ﻣﻦ ا ﺒﺮاﻣﺞ واﻟﺘﻲ ﺗﺪﻋﻰ ) (toolboxﻣﻤﺎ ﻳﺘﻴﺢ ﻟﻚ اﻟﺘﻌﺎﻣﻞ ﻣﻊ اﻟ ﻄﺒﻴﻘﺎت اﻟﻤﺘﺨﺼﺼﺔ وﻩﺬﻩ اﻷدوات ﻋﺒﺎرة ﻋﻦ ﺑﺮاﻣﺞ ﻓﻲ ﺻﻮرة ). (M-files
ﺗﻄﺒﻴﻘﺎت اﻟﻤﺎﺗﻼب
ﻓﻲ اﻟﻤﺠﺎل اﻷﺁﺎدﻳﻤﻲ :
o o o o
ﻋﻤﻞ اﻟﺘﻔﺎﺻﻴﻞ واﻟﺘﻜﺎﻣﻞ ﺣﻞ اﻟﻤﻌﺎدﻻت اﻟﺠﺒﺮﻳﺔ ) (Algebraic Equations ﺣﻞ اﻟﻤﻌﺎدﻻت اﻟﺘﻔﺎﺿﻠﻴﺔ ذات اﻟﺮﺗﺐ اﻟﻌﻠﻴ ) (Differential Equations ﻋﻤﻞ اﻟﺘﻔﺎﺿﻞ اﻟﺠﺰﺋﻲ وﻋﻤﻠﻴﺎت اﻟﻜﺴﺮ اﻟﺠﺰﺋ )(Partial fraction
اﻟﻤﺠﺎﻻت اﻟﺘﻄﺒﻴﻘﻴﺔ :
o o o o o o
أﻧﻈﻤﺔ اﻟﺘﺤﻜﻢ ﻓﻲ ﺟﻤﻴﻊ اﻟﻤﺠﺎﻻت اﻟﻬﻨﺪﺳﻴﺔ )(Control System ﻣﻌﺎﻟﺠﺔ اﻟﺼﻮ ﻣﺤﺎﺁﺎة اﻹﻟﻜﺘﺮوﻧﺎ ﻣﺠﺎل ﺻﻨﺎﻋﺔ اﻟﺴﻴﺎرا ﻣﺠﺎل اﻟﻄﻴﺮان واﻟﺪﻓﺎع اﻟﺠﻮ ﻣﺠﺎل اﻟﺮوﺑﻮ
وﻩﻨﺎك اﻟﻜﺜﻴﺮ واﻟﻜﺜﻴﺮ ﻣﻦ اﻟﺘﻄﺒﻴﻘﺎت اﻟﻬﻨﺪﺳﻴﺔ .
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
2
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ ﻣﻌﻠﻮﻣﺎ اﻟﻔﺼﻞ اﻟﺜﺎﻧ )واﺟﻬﺔ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼ ( )Information in Chapter 2 (Matlab Desktop
واﺟﻬﺔ ﺑﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب ﺗﻜﻮن ﻣ
:
oﻧﺎﻓﺬة اﻷواﻣﺮ ) (Command Window oﻣﻨﻄﻘﺔ اﻟﻌﻤﻞ ) (Workspace oﻧﺎﻓﺬة ﺗﺴﺠﻴﻞ اﻻواﻣﺮ ) (Command History
ﺷﺮﻳﻂ اﻟﻘﻮاﺋ وﺗﺘﻜﻮن ﻣ o o o o o
:
ﻗﺎﺋﻤ ﻣﻠﻒ ) (File ﻗﺎﺋﻤﺔ اﻟﺘﻌﺪﻳﻞ ) (Edit ﻗﺎﺋﻤﺔ ) (Debug ﻗﺎﺋﻤﺔ ) (Desktop ﻗﺎﺋﻤﺔ ) (Window
oﻗﺎﺋﻤﺔ ) (Help
ﻣﺤﺘﻮﻳﺎت ﻗﺎﺋﻤ o o o o
ا ﻤﺴﺎﻋﺪة ) :(Help
ﻗﺎﺋﻤﺔ اﻟﻤﺤﺘﻮﻳﺎ ) (Contents ﻗﺎﺋﻤﺔ اﻟﻔﻬﺮ ) (Index ﻗﺎﺋﻤﺔ اﻟﺒﺤﺚ ) (Search ﻗﺎﺋﻤﺔ ) (Demos
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
3
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ ا ﺜﺎﻟ )اﻟ ﺎﺗﻼب آ ﻟﺔ ﺣﺎﺳﺒ ( )Matlab Examples in Chapter 3 (Matlab as a Calculator اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎ ﻓ اﻟﻤﺎﺗﻼ
ﺑﻌﺾ اﻟﻌﻤﻠﻴﺎت اﻟﺮﻳﺎﺿﻴﺔ اﻟﺒﺴﻴﻄﺔ
>> >>6+2 6+2 >>6-2 >>6*2 >>6/2
Some math operations
اﺳﺘﺨﺪام اﻟﻤﺎﺗﻼب ﺁﺂﻟﺔ ﺣﺎﺳﺒﺔ Operations on Variables
اﻟﺪاﻟﺔ اﻷﺳﻴﺔ ﻟﻸﺳﺎس e Exponential Function اﻟﺪاﻟﺔ اﻟﻠﻮﻏﺎرﺗﻤﻴﺔ اﻟﻄﺒﻴﻌﻴﺔ Natural Logarithm Logarithm اﻟﺠﺬر اﻟﺘﺮﺑﻴﻌﻲ Square Root اﻟﺪاﻟﺔ اﻟﻠﻮﻏﺎرﺗﻤﻴﺔ ﻟﻸﺳﺎس 10 Base 10 Logarithm اﻟﻘﻴﻤﺔ اﻟﻤﻄﻠﻘﺔ Absolute Value اﻟﺪاﻟﺔ (sin) ﺑﺎﻟﺮادﻳﺎ
>>exp(1) >>log(1) >>sqrt(36)
ﻣﻼﺣﻈﺎت Notes
ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ اﻷﺳﻴﺔ ﻟﻸﺳﺎس )(e ﻟﻠﻌﺪد (1) ﺣﺴﺎب ﻗﻴﻤﺔ ا ﺪاﻟﺔ اﻟﻠﻮﻏﺎرﺗﻤﻴﺔ اﻟﻄﺒﻴﻌﻴﺔ ﻟﻠﻌﺪد (1) ﺣﺴﺎب اﻟﺠﺬر اﻟﺘﺮﺑﻴﻌﻲ ﻟﻠﻌﺪد ) (36
>>abs(-100)
ﺣﺴﺎب اﻟﻘﻴﻤﺔ اﻟﻤﻄﻠﻘﺔ ﻟﻠﻌﺪد )(-100
>>sin(pi/2)
ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ ) (sinﻟﻠﻌﺪد )( π /2
>>sind(90)
ﺑﺎﺣﻟﺴﺮﺎادﻳ بﺎ ﻗنﻴﻤﺔ اﻟﺪا ﺔ ) (sinﻟﻠﻌﺪد )(90
ﺑﺎﻟﺪرﺟﺎت ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ ) (cosﻟﻠﻌﺪد ) ( π >>cos(pi) ﺑﺎﻟﺮادﻳﺎن >>atan(pi) ﺣﺴﺎب ﻗﻴﻤﺔ داﻟﺔ ﻣﻌﻜﻮس ) (tanﻟﻠﻌﺪد )(100
>>sec(pi) >>sinh(100) >>sin(abs(sqrt(90)))
aboutت ﻋﻦ داﻟﺔ ﻣﻌﻴﻨﺔ اaﻟﻤﻌﻠﻮﻣﺎ Information Matlab Function
>> >>help help sqrt >> >>help help sin
ﻣﻌﻠﻮﻣﺎت ﻣﻄﻮﻟ ﻋﻦ داﻟﺔ ﻣﻌﻴﻨ
>>doc sind
Information about a Matlab Function
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
إﺟﺮا ﺑﻌﺾ اﻟﻌﻤﻠﻴﺎت اﻟﺮﻳﺎﺿﻴﺔ اﻟﺒﺴﻴﻄﺔ وﻩﻲ ﺑﺎﻟﺘﺮﺗﻴﺐ اﻟﺠﻤﻊ ﺛﻢ اﻟﻄﺮح ﺛﻢ اﻟﻀﺮب ﺛﻢ اﻟﻘﺴﻤﺔ
>>log10(20) ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ اﻟﻠﻮﻏﺎرﺗﻤﻴﺔ ﻟﻸﺳﺎس ) (10ﻟﻠﻌﺪد ) (20
Sine Function in Radians اﻟﺪاﻟﺔ (sin) ﺑﺎﻟﺪرﺟﺎ Sine Function in Degrees اﻟﺪاﻟﺔ (cos) ﺑﺎﻟﺮادﻳﺎ )Cosine Function (Radians داﻟﺔ ﻣﻌﻜﻮ ) (tan Tangent Inverse Function اﻟﺪاﻟﺔ ) (sec Secant Function اﻟﺪاﻟﺔ ) (sinh Hyperbolic Sine Function ﺣﺴﺎب داﻟﺔ داﺧﻞ داﻟﺔ أﺧﺮى Command Nesting
ﺷﺮ اﻟﻤﺜﺎ
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ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ ) (secﻟﻠﻌﺪد ) ( π ﺣﺴﺎب ﻗﻴﻤﺔ اﻟﺪاﻟﺔ ) (sinhﻟﻠﻌﺪد )(100
ﻳﻤﻜﻦ ﻓﻲ اﻟﻤﺎﺗﻼب ﺣﺴﺎب اﻟﺪاﻟﺔ ﻟﺪاﻟﺔ أﺧﺮى وﻩﻜﺬا ﻣﻊ ﺿﺮورة ﻣﺮاﻋﺎ ﻋﺪد اﻷﻗﻮاس ﻟﻠﺤﺼﻮل ﻋﻠ ﻣﻌﻠﻮﻣﺎت ﻣﻔﺼﻠﺔ ﻋﻦ داﻟﺔ اﻟﻤﺎﺗﻼب ) (sqrtوﻣﻦ ﺛﻢ ﻟﻠﺪاﻟﺔ ) (sinوﺗﺸﻤﻞ ﻣﻌﻠ ﻣﺎت اﻟﺘﻌﺮﻳﻒ وﺁﻴﻔﻴﺔ اﻻﺳﺘﺨﺪام وﻏﻴﺮ ذﻟ ﻟﻠﺤﺼﻮل ﻋﻠ ﻣﻌﻠﻮﻣﺎت ﻣﻄﻮﻟ ﻋﻦ داﻟﺔ اﻟﻤﺎﺗﻼب ) (sindﻣﺜﻞ اﻟﺘﻌﺮﻳﻒ وﺁﻴﻔﻴﺔ اﻻﺳﺘﺨﺪام وﻧﺤﻮﻩ
Dr. Khalid A. Al-Hindi
ﺑﺎﻟﻤﺎﺗﻼب اﻟﺒﺮﻣﺠﺔ ﻓﻲ ﻣﻘﺪﻣﺔ
Introduction to Matlab
Matlab Function
exp xp(( x) l og( x) l og10( x) sqrt(x)
Matlab Function
cos(x) s i n( x) t a n( x ) aco cos( s( x) as i n( x) at an( x) cot(x) c sc ( x ) sec(x) acot(x) acsc(x) ase sec( c( x) at an2( y, x)
Matlab Function
cosh(( x) cosh si nh( x) t anh( x) aco cosh sh(( x) asi nh( x) at anh( x) coth(x) csch csc h( x) sech se ch(( x) aco cott h( x) acsch csch(( x) asech sech(( x)
Dr. Khalid A. Al-Hindi
اﻟﻤﺎﺗ ﻓﻲ ﺑﺮﻧﺎﻣﺞ اﻟﺮﻳﺎﺿﻴﺔ اﻟﻤﻌﺮﻓﺔ ل ﻟﺒﻌﺾ اﻟﺪوالوﺪﺟ Exponential and Logarithmic Functions Definition Mathematical Form x Exponential e
Natural logarithm Common (base 10) logarithm Square root Trigonometric Functions Definition Cosine Sine Tangent Inverse cosine Inverse sine Inverse tangent Cotangent Cosecant Secant Inverse cotangent Inverse cosecant Inverse secant Four-quadrant inverse tangent. Hyperbolic Functions Definition Hyperbolic cosine Hyperbolic sine
Hyperbolic tangent Inverse hyperbolic cosine Inverse hyperbolic sine Inverse hyperbolic tangent Hyperbolic cotangent Hyperbolic cosecant Hyperbolic secant Inverse hyperbolic cotangent Inverse hyperbolic cosecant Inverse hyperbolic secant
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ln( x) log( x) x
Mathematical Form cos( x) sin( x) tan( x) –1 cos ( x) –1 sin ( x) –1 tan ( x) cot( x) csc( x) sec( x) –1 cot ( x) –1 csc ( x) –1 sec ( x)
Mathematical Form cosh( x) sinh( x) tanh( –1 x) cosh ( x) –1 sinh ( x) –1 tanh ( x) coth( x) csch( x) sech( x) –1 coth ( x) –1 csch ( x) –1 sech ( x)
اﻟﻬﻨﺪ اﻟﺤﻤﻴﺪ ﻋﺒﺪ ﺧﺎﻟﺪ/د اﻋﺪاد
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺮاﺑ )اﻟ ﺘﻐﻴﺮا ( )Matlab Examples in Chapter 4 (Variables اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ
إﻧﺸﺎ ﻣﺘﻐﻴﺮ Defining a Variable
ﻃﺮﻳﻘﺔ اﻟﺘﻌﺮﻳ
اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮات Operations on Variables
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ >>a=2 >> >>b=10 b=10
ﻣﻼﺣﻈﺔ ﻩﺎﻣ
>> A=3 A=3
إﻧﺸﺎ ﺛﻼث ﻣﺘﻐﻴﺮات
>> ; A=6 ; A=6
Defining three variables أﻣﺜﻠﺔ ﻟﻌﻤﻠﻴﺎت رﻳﺎﺿﻴﺔ Examples of Simple Math Operations
>> ;>>C=3 C=3; >>A+B+C >>(A*B)/C >>A^2+B^2 >>(sin(A)+cos(B))/2
اﻟﻤﺜﺎل اﻷول ﻟﻠﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮا اﻟﻤﺜﺎل اﻟﺜﺎﻧﻲ ﻟﻠﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮا اﻟﻤﺜﺎل اﻟﺜﺎﻟﺚ ﻟﻠﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮا اﻟﻤﺜﺎل اﻟﺮاﺑﻊ ﻟﻠﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮا اﻟﻌﺪد اﻟﺘﺨﻴﻠﻲ ) (iﻣﻌﺮف ﻣﺴﺒﻘﺎ ﻓﻲ >>i اﻟﻤﺎﺗﻼب ﺑﺸﺮط أن ﻻ ﻳﺘﻢ اﻋﺎدة ﺗﻌﺮﻳﻒ اﻟﻤﺘﻐﻴﺮ (i) أﺛﻨﺎ ﺁﺘﺎﺑﺔ أي ﺑﺮﻧﺎﻣﺞ
إﻧﺸﺎ ﻣﺘﻐﻴﺮﻳﻦ ﻣﺮﺁﺒﻴﻦ Defining two complex numbers
>> >>a=a+i a=a+i >>b=a+2i
ﺑﻌﺾ اﻟﻌﻤﻠﻴﺎت اﻟﺮﻳﺎﺿﻴﺔ ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮﻳﻦ اﻟﻤﺮﺁﺒﻴﻦ
>> >>a+b a+b
Extra Matlab Commands
إﻧﺸﺎ ﻣﺘﻐﻴﺮﻳﻦ ﻣﺮﺁﺒﻴﻦ ) (aو ) ( b
>> >>a-b a-b
إﻧﺸﺎ ﻣﺘﻐﻴﺮ ﻣﺮﺁﺐ
>> إﻧﺸﺎ ﻣﺘﻐﻴﺮ ﻣﺮﺁﺐ ) (z >>z=3+4i z=3+4i
Defining a complex number اﻟﺠﺰ اﻟﺤﻘﻴﻘﻲ ﻟﻤﺘﻐﻴﺮ ﻣﺮﺁﺐ Real part of a complex number اﻟﺠﺰ اﻟﺘﺨﻴﻠﻲ ﻟﻤﺘﻐﻴﺮ ﻣﺮﺁ Imaginary part of a complex number زاوﻳﺔ اﻟﻄﻮر ﻟﻤﺘﻐﻴﺮ ﻣﺮﺁﺐ Phase angle of a complex number in radians اﻟﻘﻴﻤﺔ اﻟﻤﻄﻠﻘﺔ ﻟﻤﺘﻐﻴﺮ ﻣ ﺮﺁ Absolute value of a complex number ﻋﺮض اﻟﻤﺘﻐﻴﺮات اﻟﻤﺴﺘﺨﺪﻣﺔ Display Variables ﻋﺮض ﻣﻔﺼﻞ ﻟﻠﻤﺘﻐﻴﺮات اﻟﻤﺴﺘﺨﺪﻣﺔ Display Variables with Information
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
إﺟﺮا ﺑﻌﺾ اﻟﻌﻤﻠﻴﺎت اﻟﺮﻳﺎﺿﻴﺔ اﻟﺒﺴﻴﻄﺔ >> >>a*b a*b ﻋﻠﻰ اﻟﻤﺘﻐﻴﺮﻳﻦ اﻟﻤﺮﺁﺒﻴﻦ وﻩﻲ ﺑﺎﻟﺘﺮﺗﻴﺐ >> >>a/b a/b اﻟﺠﻤﻊ ﺛﻢ اﻟﻀﺮب ﺛﻢ اﻟﻘﺴﻤﺔ ﺛﻢ اﻟﻄﺮح
Some math operations
أواﻣﺮ إﺿﺎﻓﻴﺔ ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب
ﻹﻧﺸﺎ اﻟﻤﺘﻐﻴﺮﻳ ) (aوﻳﺴﺎوي )(2 واﻟﻤﺘﻐﻴﺮ ( b) ﻳﺴﺎوي ) (10 ﻻﺣﻆ أن اﻟﻤﺘﻐﻴﺮ ) (aﻻ ﻳﺴﺎوي اﻟﻤﺘﻐﻴﺮ ) (Aن اﻟﻤﺎﺗﻼب Case Sensitive
ﻹﻧﺸﺎ ﺛﻼث ﻣﺘﻐﻴﺮات ﻣﻊ ﻋﺪم إﻇﻬﺎرﻩﻢ >> ;>>B=2 ;B=2 ﻋﻠ اﻟﺸﺎﺷﺔ ﺑﺎﺳﺘﺨﺪام اﻷﻣﺮ );(
اﻟﻌﺪد اﻟﺘﺨﻴﻠﻲ i The complex number i
اﻷﻋﺪاد اﻟﻤﺮﺁﺒﺔ Complex Numbers
ﺷﺮح اﻟﻤﺜﺎ
اﻟﺤﺼﻮل ﻋﻠﻰ اﻟﺠﺰ اﻟﺤﻘﻴﻘﻲ ﻓﻘﻂ >> )>>real(z real(z) ﻟﻠﻤﺘﻐﻴﺮ اﻟﻤﺮﺁﺐ (z) >>imag(z) اﻟﺤﺼﻮل ﻋﻠﻰ اﻟﺠﺰ اﻟﺘﺨﻴﻠﻲ ﻓﻘﻂ ﻟﻠﻤﺘﻐﻴﺮ اﻟﻤﺮﺁﺐ (z) >>angle(z) اﻟﺤﺼﻮل ﻋﻠﻰ زاوﻳﺔ اﻟﻄﻮر ﻟﻠﻤﺘﻐﻴﺮ اﻟﻤﺮﺁﺐ (z) ﺑﺎﻟﺮادﻳﺎ >>abs(z) اﻟﺤﺼﻮل ﻋﻠﻰ اﻟﻘﻴﻤﺔ اﻟﻤﻄﻠﻘﺔ ﻟﻠﻤﺘﻐﻴﺮ اﻟﻤﺮﺁﺐ(z) >>who ﻋﺮض ﺁﺎﻓﺔ اﻟﻤﺘﻐﻴﺮات اﻟﻤﺴﺘﺨﺪﻣﺔ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻋﺮض ﻣﻔﺼﻞ ﻟﻜﺎﻓﺔ اﻟﻤﺘﻐﻴﺮات اﻟﻤﺴﺘﺨﺪﻣﺔ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻣﻊ ﻋﺮض >>whos اﻟﺤﺠﻢ وﻣﻘﺪار اﻟﺬاﺁﺮة اﻟﻤﺤﺠﻮزة ﺑﺎﻟﺒﺎﻳﺖ وﻧﻮع اﻟﻤﺘﻐﻴ
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Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺨﺎﻣ )اﻟ ﺘﺠﻬﺎ ( )Matlab Examples in Chapter 5 (Vectors اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ
اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴ
اﻟﻤﺘﺠﻪ اﻟﺼﻔﻲ Row Vector
ﻃﺮﻳﻘﺔ أﺧﺮى ﻹﻧﺸﺎ اﻟﻤﺘﺠﻪ اﻟﺼﻔ Second Method إﻧﺸﺎ ﻣﺘﺠﻪ ﺻﻔﻲ Row Vector
إﻧﺸﺎ ﻣﺘﺠﻪ
Vector Definition
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ
>> إﻧﺸﺎ ﺘﺠﻪ ﺻﻔﻲ ﻣﻦ ﺧﻤﺴﺔ A=[1 A=[1 2 3 4 5] ﺻﻋﺮﻨﺎ ﺻﺮ ﺑﻄﺮﻳﻘﺔ اﻟﻔﺮاﻏﺎت ﺑﻴﻦ ا ﻌﻨﺎ إﻧﺸﺎ ﻧﻔﺲ اﻟﻤﺘﺠﻪ اﻟﺴﺎﺑﻖ ﺑﺎﺳﺘﺨﺪام اﻷﻣﺮ >> ) (:واﻟﺬي ﻳﻌﻨﻲ ﺁﺎﻓﺔ اﻟﻌﻨﺎﺻﺮ ﻣﻦ ) (1إﻟﻰ A=[1 A=[1:5] ) (5ﺑﺰﻳﺎدة واﺣﺪ ﻋﻦ اﻟﺴﺎﺑ
>>D=[2إﻧﺸﺎ >>D=[2 4 6 8 10]
اﻟﻄﺮﻳﻘﺔ أﺧﺮى ﻹﻧﺸﺎ اﻟﻤﺘﺠﻪ اﻟﺼﻔ
]>>D=[2:2:10 >>D=[2:2:10]
Second Method
اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻟﻤﺘﺠﻬﺎ Operations on Vectors
اﻟﻤﺘﺠﻪ اﻟﻌﻤﻮدي Column Vector
]>>C=[1;2;3;4;5 >>C=[1;2;3;4;5]
إﺿﺎﻓﺔ ﻋﻨﺼﺮ ﺟﺪﻳﺪ ﻟﻠﻤﺘﺠﻪ Element Adding
>> ] A=[1;3;5;7;8 ]A=[1;3;5;7;8 >> A(6)=100 A(6)=100
إﺿﺎﻓﺔ ﻋﻨﺼﺮ ﺟﺪﻳﺪ ﻟﻠﻤﺘﺠﻪ Element Adding
>> A(8)=150 A(8)=150
ﺣﺬف ﻋﻨﺼﺮ ﻣﻦ ﻣﺘﺠﻪ Element Deletion اﺳﺘﺒﺪال ﻗﻴﻤﺔ ﻋﻨﺼﺮ ﻓﻲ ﻣﺘﺠﻪ Element Replacing ﻗﻴﻤﺔ اﻟﻌﻨﺼﺮ اﻷﺁﺒﺮ ﻟﻤﺘﺠ Maximum Value ﻗﻴﻤﺔ اﻟﻌﻨﺼﺮ اﻷﺻﻐﺮ ﻟﻤﺘﺠﻪ Minimum Value ﻃﻮل اﻟﻤﺘﺠﻪ Vector Length
ﺷﺮح اﻟﻤﺜﺎ
]>>B=[1;3;5;7;9 ]>>B=[1;3;5;7;9 ][=)>>B(5 >>B(5)=[] ]>>B=[1;3;5;7;9 ]>>B=[1;3;5;7;9 >>B(3)=20 >>B(3)=20 ]>>A=[7;8;3;4;5 )>>max(A >>max(A) )>>min(A >>min(A)
ﺘﺠﻪ ﺻﻔﻲ ﻣﻦ ﺧﻤﺴﺔ ﻋﻨﺎﺻﺮ
إﻧﺸﺎ ﻧﻔﺲ ﻟﻤﺘﺠﻪ اﻟﺴﺎﺑﻖ ﺑﺎﺳﺘﺨﺪام اﻷﻣﺮ ) (:واﻟﺬي ﻳﻌﻨﻲ ﺁﺎﻓﺔ اﻟﻌﻨﺎﺻﺮ ﻣﻦ ) (2إﻟﻰ ) (10ﺑﺰﻳﺎدة ) (2ﻋﻦ اﻟﺴﺎﺑﻖ إﻧﺸﺎ ﻣﺘﺠﻪ ﻋﻤﻮدي ﻣﻦ ﺧﻤﺴﺔ ﻋﻨﺎﺻﺮ ﺑﺎﺳﺘﺨﺪام اﻷﻣﺮ (;) واﻟﺬي ﻳﻌﻨﻲ ﻧﻬﺎﻳﺔ اﻟﺼﻒ ﻓﻲ اﻟﻤﺘﻐﻴﺮ (C) إﻧﺸﺎ ﻣﺘﺠﻪ ﻋﻤﻮدي ) (Aوﻣﻦ ﺛﻢ إﺿﺎﻓﺔ ﻋﻨﺼﺮ ﺳﺎدس ﺑﻘﻴﻤﺔ (100) إﺿﺎﻓﺔ ﻋﻨﺼﺮ ﺛﺎﻣﻦ ﻟﻠﻤﺘﺠﻪ ) (Aﺑﻘﻴﻤﺔ ) (150وﻳﻼﺣﻆ ﻌﺪ اﻟﺘﻨﻔﻴﺬ أن اﻟﻤﺎﺗﻼب أﺿﺎف ﺁﻟﻴﺎ اﻟﻘﻴﻤﺔ ﺻﻔﺮ ﻟﻠﻌﻨﺼﺮ اﻟﺴﺎﺑﻊ إﻧﺸﺎ ﻣﺘﺠﻪ ﻋﻤﻮدي ) (Bوﻣﻦ ﺛﻢ ﺣﺬف اﻟﻌﻨﺼﺮ اﻟﺨﺎﻣﺲ ﻓﻘﻂ إﻧﺸﺎ ﻣﺘﺠﻪ ﻋﻤﻮدي ) (Bوﻣﻦ ﺛﻢ ﺗﻐﻴﻴﺮ ﻗﻴﻤﺔ اﻟﻌﻨﺼﺮ اﻟﺜﺎﻟﺚ إﻟﻰ اﻟﻘﻴﻤﺔ (20) إﻧﺸﺎ ﻣﺘﺠﻪ ﻋﻤﻮدي ) (Aوﻣﻦ ﺛﻢ إﻳﺠﺎد ﻗﻴﻤﺔ اﻟﻌﻨﺼﺮ اﻷﺁﺒﺮ ﻓﻴﻪ ﻳﺠﺎد ﻗﻴﻤﺔ اﻟﻌﻨﺼﺮ اﻷﺻﻐﺮ ﻟﻠﻤﺘﺠﻪ ) (A
] >>A=[1 7 9 8 6إﻧﺸﺎ ﻣﺘﺠﻪ ﺻﻔﻲ ) (Aوﻣﻦ ﺛﻢ إﻳﺠﺎد >>length(A) ﻃﻮﻟﻪ وﻳﺴﺎوي ﻋﺪد اﻟﻌﻨﺎﺻﺮ ﻓﻴﻪ ]>>x=[1 2 3
) >>norm(x,1إﻧﺸﺎ ﻣﺘﺠﻪ ﺻﻔﻲ ) (xوﻣﻦ ﺛﻢ إﻳﺠﺎد ) >>norm(xﻣﻘﺎﻳﻴﺴﻪ اﻷول واﻟﺜﺎﻧﻲ )ﺑﻄﺮﻳﻘﺘﻴ ( وأﺧﻴﺮا ) >>norm(x,2اﻟﻤﻘﻴﺎس اﻟﻼﻧﻬﺎﺋﻲ
ﻣﻘﻴﺎس اﻟﻤﺘﺠﻪ
Norm Vector ﻣﺜﺎل ﺁﺧﺮ ﻟﻤﻘﻴﺎس اﻟﻤﺘﺠﻪ Vector Norm
ﺿﺮب اﻟﻤﺘﺠﻬﺎت Vector Product
اﻟﻀﺮب اﻟﻤﺘﺠﻪ Dot Product اﻟﻀﺮب اﻟﻤﺘﺠ Cross Product
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
>>norm(x,inf) ]>>a=[-10 -5 3 )>>norm(x,1 >>norm(x,inf) ]>>A=[1 2 3 ]>>B=[4 5 6 >>dot(A,B)
إﻧﺸﺎ ﻣﺘﺠﻪ ﺻﻔﻲ ) (aوﻣﻦ ﺛﻢ إﻳﺠﺎد ﻣﻘﺎﻳﻴﺴﻪ اﻷول واﻟﻼﻧﻬﺎﺋﻲ
إﻧﺸﺎ ﻣﺘﺠﻬﻴﻦ ﺻﻔﻴﻴﻦ ) (Aو ) (Bوﻣﻦ ﺛﻢ إﻳﺠﺎد ﻗﻴﻤﺔ اﻟﻀﺮب (dot) ﺑﻴﻨﻬﻤ إﻳﺠﺎد ﻗﻴﻤﺔ اﻟﻀﺮب ﻣﻦ ﻧﻮع )(cross >>cross(A,B) ﻟﻠ ﺘﺠﻬﻴﻦ ) (Aو ) (B
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Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺴﺎدس )اﻟﻤﺼﻔﻮﻓﺎ ( )Matlab Examples in Chapter 6 (Matrices اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ إﻧﺸﺎ ﻣﺼﻔﻮﻓﺔ
Matrix Definition
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ
اﻟﻄﺮﻳﻘﺔ اﻷوﻟﻰ First Method
>> A=[1 ;A=[1 2 2;4 4 5;7 6]
اﻟﻄﺮﻳﻘﺔ اﻟﺜﺎﻧﻴﺔ Second Method
>> ] A=[1,2;4,5;7,6 A=[1,2;4,5;7,6]
اﻟﻤﺼﻔﻮﻓﺔ اﻟﺼﻔﺮﻳﺔ اﻟﻤﺮﺑﻌﺔ
>>o=zeros(3)
Square Zeros Matrix
اﻟﻤﺼﻔﻮﻓﺔ اﻟﺼﻔﺮﻳﺔ اﻟﻤﺴﺘﻄﻴﻠﺔ
اﻟﻤﺼﻔﻮﻓﺎت اﻟﺨﺎﺻﺔ Special Matrices
Rectangular Zeros Matrix ﻣﺼﻔﻮﻓﺔ اﻟﻮاﺣﺪ اﻟﻤﺮﺑﻌﺔ Square Ones Matrix ﻣﺼﻔﻮﻓﺔ اﻟﻮاﺣﺪ اﻟﻤﺴﺘﻄﻴﻠﺔ Rectangular Ones Matrix ﻣﺼﻔﻮﻓﺔ اﻟﻮﺣﺪة اﻟﻤﺮﺑﻌﺔ Square Identity Matrix ﻣﺼﻔﻮﻓﺔ اﻟﻮﺣﺪة اﻟﻤﺴﺘﻄﻴﻠ Rectangular 1’s Diagonal Matrix اﻟﻤﺼﻔﻮﻓﺔ ا ﻌﺸﻮاﺋﻴ اﻟﻤﺮﺑﻌﺔ Square Random Matrix اﻟﻤﺼﻔﻮﻓﺔ ا ﻌﺸﻮاﺋﻴ اﻟﻤﺴﺘﻄ ﻠ Rectangular Random Matrix
ﺗﻌﺮﻳﻒ ﻣﺼﻔﻮﻓﺔ ﺁﻤﺜﺎ
اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ ﻣﺼﻔﻮﻓﺔ واﺣﺪة Operations on a Single Matrix
ﻗﻠﺐ اﻷﻋﻤﺪة ﺁﺼﻔﻮف Matrix Transpose ﺟﻤﻊ أﻋﻤﺪة اﻟﻤﺼﻔﻮﻓ Matrix Sum اﺳﺘﺨﻼص ﻋﻨﺎﺻﺮ ﻗﻄﺮ اﻟﻤﺼﻔﻮﻓ Matrix Diagonal Elements ﺟﻤﻊ ﻋﻨﺎﺻﺮ ﻗﻄﺮ اﻟﻤﺼﻔﻮﻓ Sum Matrix Diagonal Elements أﻳﺠﺎد ﻣﻌﻜﻮس اﻟﻤﺼﻔﻮﻓ اﻟﻤﺮﺑﻌ Square Matrix Inversion أﻳﺠﺎد درﺟﺔ اﻟﻤﺼﻔﻮﻓ Matrix Rank أﻳﺠﺎد ﻣﺤﺪد اﻟﻤﺼﻔﻮﻓ اﻟﻤﺮﺑﻌ Square Matrix Determinate
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
>>B=zeros(3,2) >>A=ones(3) >>I=ones(4,2) >>I=eye(2)
ﺷﺮح اﻟﻤﺜﺎ ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ) (Aﺑﺤ 2 ﺻ ﻓﺮﻲ ﺻﻒ ت ﺠﺑﻢﻴﻦ ﻋﻨﺎ 3أﻋﻤﺪة ﺑﻄﺮﻳﻘﺔ اﻟﻔﺮاﻏﺎ اﻟﺼﻒ اﻟﻮاﺣﺪ ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ) (Aﺑﺤﺠﻢ 2ﺻﻒ ﻓﻲ 3أﻋﻤﺪة ﺑﻄﺮﻳﻘﺔ اﻟﻔﻮا ﺑﻴﻦ ﻋﻨﺎﺻﺮ اﻟﺼﻒ اﻟﻮاﺣﺪ ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻤﺮﺑﻌﺔ ) (oذات ﻋﻨﺎﺻﺮ ا ﺻﻔﺎر ﺑﺤﺠﻢ 3×3 ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻤﺴﺘﻄﻴﻠﺔ ) (Bذات اﻷﺻﻔﺎر ﺑﺤﺠﻢ 3ﺻﻒ ﻓﻲ 2أﻋﻤﺪة ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻤﺮﺑﻌﺔ ) (Aذات اﻟﻌﻨﺎﺻﺮ واﺣ ﺑﺤﺠﻢ 3×3 ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻤﺴﺘﻄﻴﻠﺔ ) (Iذات اﻟﻌﻨﺎﺻﺮ واﺣﺪ ﺑﺤﺠﻢ 4ﺻﻒ ﻓﻲ 2أﻋﻤﺪة ﻹﻧﺸﺎ ﻣﺼﻔﻮﻓﺔ ا ﻮﺣﺪة ا ﻤﺮﺑﻌ ) (Iﺑﺤﺠﻢ 2×2
>>Y=eye(3,4)
ﻹﻧﺸﺎ ﻣﺼﻔﻮﻓﺔ ا ﻮﺣﺪة اﻟﻤﺴﺘﻄﻴﻠﺔ )(Y ﺑﺤﺠﻢ 3 ﺻﻒ ﻓﻲ 4أﻋﻤﺪ
>>I=rand(5)
ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻌﺸﻮاﺋﻴﺔ ا ﻤﺮﺑﻌ )(I ﺑﺤﺠﻢ 5×5
>>I=rand(3,2)
ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ا ﻌﺸﻮاﺋﻴﺔ اﻟﻤﺴﺘﻄﻴﻠﺔ )(I ﺑﺤﺠﻢ 3 ﺻﻒ ﻓﻲ 2أﻋﻤﺪ
>>B=[1ﻹﻧﺸﺎ ا ﻤﺼﻔﻮﻓﺔ ) (Bﺑﺤﺠﻢ 3ﺻﻒ ﻓﻲ >>B=[1 -5 3;6 10 3 -9; 11 8 4] أﻋﻤﺪة ﻗﻠﺐ اﻷﻋﻤﺪة ﺁﺼﻔﻮف واﻟﺼﻔﻮف ﺁﺄﻋﻤﺪ ’>>B >>B’ ﻟﻠﻤﺼﻔﻮﻓﺔ (B) )>>sum(B (>>sum B) )>>diag(B (>>diag B) ))>>sum(diag(B (>>sum(diag B)) )>>inv(B (>>inv B) )>>rank(B (>>rank B) )>>det(B (>>det B)
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ﺟﻤﻊ أﻋﻤﺪة اﻟﻤﺼﻔﻮﻓ )(B اﺳﺘﺨﻼص ﻋﻨﺎﺻﺮ ﻗﻄﺮ اﻟﻤﺼﻔﻮﻓ ) (B ﺟﻤﻊ ﻋﻨﺎﺻﺮ ﻗﻄﺮ اﻟﻤﺼﻔﻮﻓ ) (B إﻳﺠﺎد اﻟﻤﻌﻜﻮس ﻟﻠﻤﺼﻔﻮﻓﺔ اﻟﻤﺮﺑﻌﺔ ) (B إﻳﺠﺎد درﺟﺔ اﻟﻤﺼﻔﻮﻓ ) (B إﻳﺠﺎد اﻟﻤﺤﺪد ﻟﻠﻤﺼﻔﻮﻓﺔ اﻟﻤﺮﺑﻌﺔ ) (B
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﺗﺎﺑﻊ ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺴﺎدس )اﻟﻤﺼﻔﻮﻓﺎ اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ
ﺗﺎﺑﻊ اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ ﻣﺼﻔﻮﻓﺔ واﺣﺪة Operations on a Single Matrix
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ أﻳﺠﺎد اﻟﻘﻴﻢ اﻟﺬاﺗﻴﺔ ﻟﻤﺼﻔﻮﻓ ﻣﺮﺑﻌ Eigenvalues of Square Matrix أﻳﺠﺎد اﻟﻘﻴﻢ واﻟﻤﺘﺠﻬﺎت اﻟﺬاﺗﻴﺔ ﻟﻤﺼﻔﻮﻓ ﻣﺮﺑﻌ Eigenvalues and Eigenvectors اﺧﺘﻴﺎر ﺻﻒ ﻣﺤﺪد ﻣﻦ ﻣﺼﻔﻮﻓ Matrix Row Selection اﺧﺘﻴﺎر ﻋﻤﻮد ﻣﺤﺪد ﻣﻦ ﻣﺼﻔﻮﻓ Matrix Column Selection اﺧﺘﻴﺎر اﻟﺼﻒ اﻷﺧﻴﺮ ﻣﻦ ﻣﺼﻔﻮﻓ Matrix Last Row Selection اﺧﺘﻴﺎر اﻟﻌﻤﻮد اﻷﺧﻴﺮ ﻣﻦ ﻣﺼﻔﻮﻓ Matrix Last Column Selection
)>>eig(B (>>eig B)
)>>B(2,: >>B(2,:) )>>B(:,2 >>B(:,2) )>>B(end,: >>B(end,:) )>>B(:,end >>B(:,end)
اﺧﺘﻴﺎر ﻣﺼﻔﻮﻓﺔ ﺟﺰﺋﻴﺔ ﻣﻦ ﻣﺼﻔﻮﻓ Submatrix Selection
)>>B(1:2,1:2 >>B(1:2,1:2)
اﺧﺘﻴﺎر ﻣﺼﻔﻮﻓﺔ ﺟﺰﺋﻴﺔ ﻣﻦ ﻣﺼﻔﻮﻓ Submatrix Selection
)>>B(3,2:3 >>B(3,2:3)
اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ أﺁﺜﺮ ﻣﻦ ﻣﺼﻔﻮﻓﺔ واﺣﺪ
ﺣﻞ ﻣﻨﻈﻮﻣﺔ ﻣﻌﺎدﻻت ﺧﻄﻴﺔ
إﻧﺸﺎ اﻟﻤﻌﺎدﻻت وﺣﻠﻬﺎ Building and Solving the System
ﺷﺮح اﻟﻤﺜﺎ إﻳﺠﺎد اﻟﻘﻴﻢ اﻟﺬاﺗﻴﺔ ﻟﻠﻤﺼﻔﻮﻓﺔ اﻟﻤﺮﺑﻌﺔ ) (B
إﻳﺠﺎد اﻟﻘﻴﻢ اﻟﺬاﺗﻴ ) (Vواﻟﻤﺘﺠﻬﺎت اﻟﺬاﺗﻴ )>>[V,D] = eig(B eig(B) ) (Dﻟﻠﻤﺼﻔﻮﻓﺔ اﻟﻤﺮﺑﻌﺔ ) (B
اﺧﺘﻴﺎر ﻣﺼﻔﻮﻓﺔ ﺟﺰﺋﻴﺔ ﻣﻦ ﻣﺼﻔﻮﻓ Submatrix Selection
ﺟﻤﻊ ﻣﺼﻔﻮ ﺘﻴ Matrix Addition ﻃﺮح ﻣﺼﻔﻮ ﺘﻴ Matrix Subtraction ﺿﺮب ﻣﺼﻔﻮ ﺘﻴ Matrix Multiplicat Multiplication ion ﻗﺴﻤﺔ ﻣﺼﻔﻮ ﺔ ﻋﻠﻰ ﻋﺪ Matrix Multiplication Multiplication
Solving a System of Linear Equations
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ
)>>B(1:2,2 >>B(1:2,2)
ﺗﻌﺮﻳﻒ ﻣﺠﻤﻮﻋﺔ ﻣﺼﻔﻮ ﺎ
Operations on Matrices
(
>> A=[3 ;]A=[3 4 6;5 1 8 >>B=[7 ;]>>B=[7 9 4;8 1 1 ;]>>C=[1;3;4 >>C=[1;3;4];
اﺧﺘﻴﺎر اﻟﺼﻒ اﻟﺜﺎﻧﻲ ﻓﻘﻂ ﻣﻦ اﻟﻤﺼﻔﻮﻓ ) (B
اﺧﺘﻴﺎر اﻟﻌﻤﻮد اﻟﺜ ﻧﻲ ﻓﻘﻂ ﻣﻦ اﻟﻤﺼﻔﻮﻓ
) (B
اﺧﺘﻴﺎر اﻟﺼﻒ اﻷﺧﻴﺮ ﻓﻘﻂ ﻣﻦ اﻟﻤﺼﻔﻮﻓ
) (B
اﺧﺘﻴﺎر اﻟﻌﻤﻮد اﻷﺧﻴﺮ ﻓﻘﻂ ﻣﻦ اﻟﻤﺼﻔﻮﻓ ) (B
اﺧﺘﻴﺎر اﻟﻌﻨﺎﺻﺮ اﻟﻤﺘﻘﺎﻃﻌﺔ ﻣﺎ ﺑﻴﻦ اﻟﺼﻔﻴﻦ اﻷول واﻟﺜﺎﻧﻲ ﻣﻊ ﻋﻨﺎﺻﺮ اﻟﻌﻤﻮد اﻟﺜﺎﻧﻲ ﻣﻦ اﻟﻤﺼﻔﻮﻓﺔ ) (B اﺧﺘﻴﺎر اﻟﻌﻨﺎﺻﺮ اﻟﻤﺘﻘﺎﻃﻌﺔ ﻣﺎ ﺑﻴﻦ اﻟﺼﻔﻴﻦ ل اﻷول واﻟﺜﺎﻧﻲ ﻣﻊ ﻋﻨﺎﺻﺮ اﻟﻌﻤﻮدﻳﻦ اﻷو واﻟﺜﺎﻧﻲ ﻣﻦ اﻟﻤﺼﻔﻮﻓ ) (B اﺧﺘﻴﺎر اﻟﻌﻨﺎﺻﺮ اﻟﻤﺘﻘﺎﻃﻌﺔ ﻓﻲ اﻟﺼﻒ اﻟﺜﺎﻟﺚ ﻣﻊ ﻋﻨﺎﺻﺮ اﻟﻌﻤﻮدﻳﻦ اﻟﺜﺎﻧﻲ واﻟﺜﺎﻟﺚ ﻣﻦ اﻟﻤﺼﻔﻮﻓﺔ ) (B إﻧﺸﺎ ﺛﻼث ﻣﺼﻔﻮﻓﺎت ﻟﻐﺮض ﺗﻄﺒﻴﻖ اﻷﻣﺜﻠﺔ اﻟﺘﺎﻟﻴﺔ
>>A+B >>A+ B
ﻋﻤﻠﻴﺔ ﺟﻤﻊ ا ﻤﺼﻔﻮﻓﺘﻴ ) (Aو ) (B
>>A-B >>AB
ﻋﻤﻠﻴﺔ ﻃﺮح ا ﻤﺼﻔﻮﻓﺘﻴ ) (Aو ) (B
>>A*C *>>A C
ﻋﻤﻠﻴﺔ ﺿﺮب ا ﻤﺼﻔﻮﻓﺘﻴ ) (Aو ) (C
>>A/3
ﻋﻤﻠﻴﺔ ﻗﺴﻤﺔ ا ﻤﺼﻔﻮﻓﺔ ) (Aﻋﻠﻰ ﻋﺪ
ﻗﻢ ﺑﺘﻄﺒﻴﻖ اﻷواﻣﺮ اﻟﻤﻮﺿﺤﺔ وذﻟﻚ ﻟﺤﻞ >> A=[1 A=[1 -1 1;1 2 ﻣﻨﻈﻮﻣﺔ اﻟﻤﻌﺎدﻻت اﻟﺨﻄﻴﺔ اﻟﺘﺎﻟﻴﺔ: ]2;3 0 1 ]>>b=[5;10;1 ]>>b=[5;10;1 >>x=inv(A)*b >>x=inv(A)*b
اﻟﺘﺄﺁﺪ ﻣﻦ اﻟﺤﻞ
>> A*x A*x
x- y+ z=5 x+2 y+2 z=10 3x+ z=1 ﺎﺗﺞ ﻋﻤﻠﻴﺔ اﻟﻀﺮب ) (A*xﻳﺠﺐ أن ﻳﺴﺎوي اﻟﻤﺼﻔﻮﻓﺔ )( b
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
9
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺴﺎﺑ )اﻟﺮﺳﻢ ﺛﻨﺎﺋﻲ اﻷﺑﻌﺎ ( )Matlab Examples in Chapter 7 (Introduction to 2D Plots اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺮﺳﻢ ﺛﻨﺎﺋﻲ اﻷﺑﻌﺎد Introduction to 2D Plots
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ إﻧﺸﺎ ﻣﺘﺠﻪ
Defining a Vector
ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ >> )>>x=linspace(5,20,10 x=linspace(5,20,10)
اﻟﺮﺳﻢ ﺛﻨﺎﺋﻲ اﻷﺑﻌﺎ
>> ;)>>x=linspace(0,10,100 ;)x=linspace(0,10,100 ;)>>y=sin(x >>plot(x,y)
إﻧﺸﺎ ﻣﺘﺠﻪ
>> ;)>>x=linspace(0,1,100 ;)x=linspace(0,1,100 ;)>>y=exp(-x).*cos(6*pi*x >>plot(x,y)
2D Plot
Defining a Vector
>>plot(x,y,’r’)
ﺗﻐﻴﻴﺮ ﻟﻮن ﺧﻂ اﻟﺮﺳﻢ Line Color
>>plot(x,y,’g’)
إﺿﺎﻓﺔ ﻋﻼﻣﺔ ﻟﺨﻂ اﻟﺮﺳﻢ
>>plot(x,y,’*’)
Line Mark ﺗﻐﻴﻴﺮ ﻧﻮع ﺧﻂ اﻟﺮﺳﻢ Line Style
إﺿﺎﻓﺔ ﺧﺼﺎﺋﺺ إﻟﻰ اﻟﺮﺳﻮﻣﺎت Setting 2D Plot Properties
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
20ﻦ ﻰن ﻣ ﺿﺘﻤﺠﻦﻪ ا)ﻟﻔxﺘ(ﺮةو اﻟﻣﺬﻦي5ﻳ ﺘإﻟﻜﻮ 10ﺸﻗﺎﻴﻢ ا ﻤ ﻹﻧ وﺗﻜﻮن اﻟﻘﻴﻢ ﻣﻮزﻋﺔ ﺑﺎﻟﺘﺴﺎوي ﻹﻧﺸﺎ ا ﻤﺘﺠﻪ ) (xواﻟﺬي ﻳﺘﻜﻮن ﻣﻦ 100ﻗﻴﻤﺔ ﺿﻤﻦ اﻟﻔﺘﺮة ﻣﻦ 0إﻟﻰ 10وﺗﻜﻮن اﻟﻘﻴﻢ ﻣﻮزﻋﺔ ﺑﺎﻟﺘﺴﺎوي وﻣﻦ ﺛﻢ إﻧﺸﺎ داﻟﺔ ) (sinوﺣﻔﻈﻬﺎ ﻓﻲ اﻟﻤﺘﻐﻴﺮ (y) وﻣﻦ ﺛﻢ رﺳﻢ اﻟﺪاﻟ ﻹﻧﺸﺎ اﻟﻤﺘﺠﻬﻴﻦ ) (xو ) (yوﻣﻦ ﺛﻢ رﺳﻢ اﻟﺪاﻟﺔ ﺗﻤﺎﻣﺎ ﺁﻤﺎ ﻓﻲ اﻟﺨﻄﻮة اﻟﺴﺎﺑﻘﺔ ﺗﻐﻴﻴﺮ ﻟﻮن ﺧﻂ اﻟﺮﺳﻢ إﻟﻰ اﻟﻠﻮن اﻷﺣﻤﺮ ﺗﻐﻴﻴﺮ ﻟﻮن ﺧﻂ اﻟﺮﺳﻢ إﻟﻰ اﻟﻠﻮن اﻷﺧﻀﺮ إﺿﺎﻓﺔ ﻋﻼﻣﺔ اﻟﻨﺠﻤﺔ ﻟﺨﻂ اﻟﺮﺳﻢ
>>plot(x,y,’:’) ﺗﻐﻴﻴﺮ ﻧﻮع ﺧﻂ اﻟﺮﺳﻢ إﻟﻰ اﻟﻨﻮع اﻟﻤﻨﻘﻂ ﺗﻐﻴﻴﺮ ﻟﻮن ﺧﻂ اﻟﺮﺳﻢ إﻟﻰ اﻟﻠﻮن >>plot(x,y,’g+’) اﻷﺧﻀﺮ ﻣﻊ إﺿﺎﻓﺔ ﻋﻼﻣﺔ زاﺋﺪ ﻟﺨﻂ اﻟﺮﺳﻢ >>grid on ﻳﺘﻢ إﺿﺎﻓﺔ ﺷﺒﻜﺔ ﻟﻠﺮﺳﻢ ﻟﺘﺴﻬﻴﻞ ﻋﻤﻠﻴﺔ ﻗﺮا ة اﻟﻘﻴﻢ ﻣﻦ اﻟﺮﺳﻢ
دﻣﺞ ﻣﺠﻤﻮﻋﺔ ﺧﺼﺎﺋﺺ ﻟﺨﻂ اﻟﺮﺳﻢ
إﺿﺎﻓﺔ ﺷﺒﻜﺔ ﻟﻠﺮﺳﻢ Adding Grid to Plot إزاﻟﺔ ﺷﺒﻜﺔ اﻟﺮﺳﻢ Removing Grid إﺿﺎﻓﺔ ﺗﺴﻤﻴﺔ ﻟﻤﺤﻮر اﻟﺴﻴﻨﺎت Adding Label to x-axis إﺿﺎﻓﺔ ﺗﺴﻤﻴﺔ ﻟﻤﺤﻮر اﻟﺼﺎدات Adding Label to y-axis إﺿﺎﻓﺔ ﻋﻨﻮان ﻟﻠﺮﺳﻢ Adding Title to Plot إﺿﺎﻓﺔ ﻧﺺ ﻟﻠﺮﺳ Adding Text to Plot إﺿﺎﻓﺔ دﻟﻴﻞ ﻟﻤﻨﺤﻨﻴﺎت اﻟﺮﺳﻢ Adding Legend to Plot
ﺷﺮح اﻟﻤﺜﺎ
>>grid off
ﻳﺘﻢ إزاﻟﺔ ﺷﺒﻜﺔ اﻟﺮﺳﻢ
>>xlabel(’x’) ﻳﺘﻢ إﺿﺎﻓﺔ ﺗﺴﻤﻴﺔ ﻟﻤﺤﻮر اﻟﺴﻴﻨﺎت ﺑﺎﻟﺮﻣﺰ ‘x’ >>ylabel(’y’) ﻳﺘﻢ إﺿﺎﻓﺔ ﺗﺴﻤﻴﺔ ﻟﻤﺤﻮر اﻟﺼﺎدات ﺑﺎﻟﺮﻣﺰ ‘y’ >>title(’graph’) ﻳﺘﻢ إﺿﺎﻓﺔ ﻋﻨﻮان ﻟﻠﺮﺳﻢ ﺑﺎﻻﺳﻢ ’ ‘graph
>>text(0.35,0.6,’plot’) ﻳﺘﻢ إﺿﺎﻓﺔ اﻟﻨﺺ ’ ‘plotﻟﻠﺮﺳﻢ وذﻟﻚ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﻤﺤﺪد ﻓﻲ اﻷﻣﺮ >>legend(‘X-Y Relation’) ﻳﺘﻢ إﺿﺎﻓﺔ دﻟﻴﻞ ﻟﻤﻨﺤﻨﻴﺎت اﻟﺮﺳﻢ وذﻟﻚ ﻓﻲ ﻳﻤﻴﻦ اﻟﺮﺁﻦ اﻟﻌﻠﻮي ﻟﻠﺮﺳﻢ
10
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﺗﺎﺑﻊ ﻣﻠﺨﺺ واﻣﺮ اﻟﻔﺼﻞ اﻟﺴﺎﺑﻊ )اﻟﺮﺳﻢ ﺛﻨﺎﺋﻲ اﻷﺑﻌﺎ اﻟﻤﻮﺿﻮع اﻟﺮﺋﻴﺴﻲ
اﻟﻤﻮﺿﻮع اﻟﻔﺮﻋ إﻧﺸﺎ ﻣﺘﺠﻪ Defining a Vector
إﻧﺸﺎ رﺳﻮﻣﺎت ﻣﻨﻔﺼﻠﺔ ﻓﻲ ﻧﺎﻓﺬة واﺣﺪة Multiple 2D Plots in a Window
ﺷﺮح اﻟﻤﺜﺎ ﺗﻨﻔﻴﺬ اﻟﻤﺜﺎل ﻓﻲ اﻟﻤﺎﺗﻼ إﻧﺸﺎ ا ﻤﺘﺠﻪ ) (xوذﻟﻚ ﺸﺮح >> ;>>x=0:0.1:10 x=0:0.1:10; ا ﻣﺜ ﺔ اﻟﺘﺎﻟﻴ >>subplot(2,2,1), plot(x,sin(x));
ﺗﻘﺴﻴﻢ ﻧﺎﻓﺬة اﻟﺮﺳﻢ Subplots in Matlab
(
>>subplot(2,2,2), plot(x,sin(2*x)); >>subplot(2,2,3), plot(x,cos(x)); >>subplot(2,2,4), plot(x,exp(x));
)2 ﺗﻘﺴﻴﻢ ﻧﺎﻓﺬة اﻟﺮﺳﻢ إﻟﻰ أر sinﺑ( ﻊﻓ ﻧﻲﻮ ااﻓﻟﻨﺬﺎﻓﺬة ﻓﻲ (2 ورﺳﻢ اﻟﺪاﻟ ) اﻷوﻟﻰ )ﻳﺴﺎر اﻟﺼﻒ اﻷو ( ﺗﻘﺴﻴﻢ ﻧﺎﻓﺬة اﻟﺮﺳﻢ إﻟﻰ أرﺑﻊ ﻧﻮاﻓﺬ ورﺳﻢ اﻟﺪاﻟﺔ (sin 2x) ﻓﻲ اﻟﻨﺎﻓﺬة اﻟﺜﺎﻧﻴﺔ) ﻳﻤﻴﻦ اﻟﺼﻒ اﻷو ( ﺗﻘﺴﻴﻢ ﻧﺎﻓﺬة اﻟﺮﺳﻢ إﻟﻰ أرﺑﻊ ﻧﻮاﻓﺬ ورﺳﻢ اﻟﺪاﻟﺔ (cos) ﻓﻲ اﻟﻨﺎﻓﺬة اﻟﺜﺎﻟﺜﺔ )ﻳﺴﺎر اﻟﺼﻒ اﻟﺜﺎﻧ ( ﺗﻘﺴﻴﻢ ﻧﺎﻓﺬة اﻟﺮﺳﻢ إﻟﻰ أرﺑﻊ ﻧﻮاﻓﺬ ورﺳﻢ اﻟﺪاﻟﺔ ) (expﻓﻲ اﻟﻨﺎﻓﺬة اﻟﺮاﺑﻌﺔ) ﻳﻤﻴﻦ اﻟﺼﻒ اﻟﺜﺎﻧ (
>> ;>>x=0:0.1:10 x=0:0.1:10;
;) >>y=sin(xﻳﺘﻢ دﻣﺞ اﻟﺮﺳﻮم ﺑﺎﺳﺘﺨﺪام اﻷﻣﺮ ;) (hold on) >>z=cos(xواﻟﺬي ﻘﻮم ﺑﺘﺜﺒﻴﺖ ﻧﺎﻓﺬة
اﻟﻄﺮﻳﻘﺔ اﻷوﻟﻰ First Method
دﻣﺞ اﻟﺮﺳﻮم Combining 2D Plots
اﻟﻄﺮﻳﻘﺔ اﻟﺜﺎﻧﻴﺔ Second Method
>>hold on ;)>>plot(x,y ;)’>>plot(x,z,’r >>hold off >> ;>>x=0:0.1:10 x=0:0.1:10; ;)>>y=sin(x ;)>>z=cos(x >>plot(x,y,x,z,’r’);
دﻣﺞ ﻣﺠﻤﻮﻋﺔ ﺧﺼﺎﺋﺺ ﻟﺨﻂ اﻟﺮﺳﻢ
اﻟﺮﺳﻮم اﻹﺣﺼﺎﺋﻴﺔ Statistical Plots
رﺳﻢ اﻹﺷﺎرات اﻟﻤﺘﻘﻄﻌﺔ Plotting Discrete Signals
ﻗﻄﺎﻋﺎت ﻣﻦ اﻟﺪاﺋﺮة Pie Chart
>>plot(x,y,’g+’, x,z,’:’); ;]>>x=[8 17 21 18 6 >>pie(x)
اﻟﻤﺪرج اﻟﺘﻜﺮاري Bar Chart اﻹﺷﺎرات اﻟﻤﺘﻘﻄﻌﺔ Discrete Signals
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
>>bar(x) >> ;)>>x=linspace(0,2*pi,60 ;)x=linspace(0,2*pi,60
;)>>y=sin(x >>stem(x,y)
11
ي ﻢ رﺑﺘﺳﻨﻔﻢﻴ ﺬﺟ اﺪﻳﻷﺪ وإاﻟﻣﻰﺮ ﺿ ﺎﻓ ﺔﻟ ﺬأا ﻗ اﻧﻟﻔﺮﺲﺳ اﻢﻟ ﻨوﺎإﻓﺬة
ﺣﺴﺐ اﻟﺘﺮﺗﻴﺐ اﻟﻤﻮﺿﺢ
أﻳﻀﺎ ﻳﻤﻜﻦ أن ﻳﺘﻢ دﻣﺞ اﻟﺮﺳﻮم ﺑﺎﺳﺘﺨﺪام ﻩﺬﻩ اﻟﻄﺮﻳﻘﺔ اﻟﻤﺨﺘﺼﺮة ﺁﺬﻟﻚ ﻳﻤﻜﻦ ﻓﻲ اﻟﻤﺎﺗﻼب دﻣﺞ اﻟﺮﺳﻮم وﺗﻐﻴﻴﺮ ﺧﺼﺎﺋﺺ اﻟﺮﺳﻢ ﻟﻜﻞ ﻣﻨﺤﻨﻰ ﺑﺸﻜﻞ ﻣﺒﺎﺷ إﻧﺸﺎ ﻣﺘﻐﻴﺮ ) (xوﻣﻦ ﺛﻢ رﺳﻢ اﻟﻨﺴ اﻟﻤﺌﻮﻳﺔ ﻟﻌﻨﺎﺻﺮﻩ ﻋﻠﻰ ﺷﻜﻞ ﻗﻄﺎﻋﺎت ﻣﻦ اﻟﺪاﺋﺮة رﺳﻢ اﻟﻨﺴﺐ اﻟﻤﺌﻮﻳﺔ ﻟﻌﻨﺎﺻﺮ اﻟﻤﺘﻐﻴﺮ ) (xﻋﻠﻰ ﺷﻜﻞ ﻣﺪرج ﺗﻜﺮار إﻧﺸﺎ اﻹﺷﺎرات اﻟﻤﺘﻘﻄﻌﺔ ) (xو )(y وﻣﻦ ﺛﻢ رﺳﻢ ﺗﻠﻚ اﻹﺷﺎرات
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
ﺟﺪول اﻷﻟﻮان ) (Colorاﻟﻤﻌﺮﻓﺔ ﻓﻲ رﺳﻢ اﻟﻤﻨﺤﻨﻴ
اﻟﺮﻣﺰ اﻟﻤﺴﺘﺨﺪم اﻟﻠﻮن
c
r
g
b
أﺻﻔ
ﻣﺎﺟﻴﻨﺘ
ﺳﻤﺎو
أﺣﻤ
أﺧﻀ
أزر
أﺑﻴ
Color
yellow
magenta
cyan
red
green
blue
white
y
m
w
ﺟﺪول ﻧﻮاع اﻟﺨﻄﻮط ) (Line Styleاﻟﻤﻌﺮﻓﺔ ﻓﻲ رﺳﻢ اﻟﻤﻨﺤﻨﻴ اﻟﺮﻣﺰ اﻟﻤﺴﺘﺨﺪم ﻧﻮع اﻟﺨﻂ Line Style
-
ﻣﺘﺼ solid
:
ﻧﻘ dotted
-.
ﻧﻘﻄﺔ وﺷﺮﻃ dash dotted
k
--
ﺷﺮﻃ dashed
اﻟﺮﻣﺰ اﻟﻤﺴﺘﺨﺪ
اﻟﻮﺻ إﺷﺎرة زاﺋ داﺋﺮ ﻧﺠ ﻤ ﻧﻘﺎ إﺷﺎرة ﺗﻘﺎﻃ ﻣﺮﺑ ﻣﻌ ﻴ ﻣﺜﻠﺚ ﻳﺸﻴﺮ ﻟﻸﻋﻠ
Plus sign Circle Asterisk Point Cross Square Diamond Upward-pointing triangle
v > >edit
ﻗﻢ ﺑﻔﺘﺢ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ )(Editor وذﻟﻚ ﻟﻜﺘﺎﺑ ﻣﻠﻒ ) (M-File ﻗﻢ ﺑﻜﺘﺎﺑﺔ اﻷواﻣﺮ اﻟﻤﻮﺿﺤﺔ ﻓﻲ ﺷﺎﺷﺔ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ(Editor) وﺑﻌﺪ اﻻﻧﺘﻬﺎ ﻗﻢ ﺑﺤﻔﻆ اﻟﻤﻠﻒ ﺑﺎﺳﻢ ) (script.m ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻟﺒﺮﻧﺎﻣﺞ )(script.m وذﻟﻚ ﺑﻜﺘﺎﺑﺔ اﺳﻢ اﻟﻤﻠﻒ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب ﻟﺘﻌﻠﻢ ﺁﻴﻔﻴﺔ اﺳﺘﺨﺪام اﻷﻣﺮ ) (for ﻗﻢ ﻗﻢ ﺑﻔﺘﺢ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ(Editor) ﻹﻧﺸﺎ اﻟﻤﻠ )( program1.m واﻟﺬي ﻳﺤﺘﻮي ﻋﻠﻰ اﻷواﻣﺮ اﻟﻤﻮﺿﺤﺔ ﺛﻢ ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻟﺒﺮﻧﺎﻣﺞ ﻗﻢ ﺑﺈﺟﺮا اﻟﺘﻌﺪﻳﻼت اﻟﻤﻮﺿﺤﺔ ﻋﻠﻰ
for i=1:10 ;)x(n,i)=sin(pi*n/10 end end x
ﻧﻔﺲ اﻟﺒﺮﻧﺎﻣﺞ اﻟﺴﺎﺑﻖ واﻟﻤﺴﻤﻰ ) ( program1.mﺑﻮاﺳﻄﺔ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ (Editor) وﻣﻦ ﺛﻢ ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻟﺒﺮﻧﺎﻣﺞ ﻟﺘﻌﻠﻢ ﺁﻴﻔﻴﺔ اﺳﺘﺨﺪام اﻷﻣﺮ )(While ﻗﻢ ﺑﻔﺘﺢ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ )(Editor ﻹﻧﺸﺎ اﻟﻤﻠ )( program2.m واﻟﺬي ﻳﺤﺘﻮي ﻋﻠﻰ اﻷواﻣﺮ اﻟﻤﻮﺿﺤﺔ ﺛﻢ ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻟﺒﺮﻧﺎﻣﺞ
ﻣﻠﻒ اﻷواﻣﺮ )The Script File (M-File
;x=pi/100:pi/100:10*pi ;y=sin(x)./x )plot(x,y grid on
ﺗﺸﻐﻴﻞ ﻣﻠﻒ اﻷواﻣﺮ Executing the Script File
>>script
اﻷﻣﺮ )(For For Loop
for n=1:10 ;)x(n)=sin(pi*n/10 end x for n=1:10
اﻷﻣﺮ )(For Nested For Loop Loop
a=1 while a>for i=1:10 program4 end
ﺗﺸﻐﻴﻞ ﻣﻠﻒ اﻷواﻣﺮ Executing the Script File
ﺁﺘﺎﺑﺔ داﻟﺔ Writing a Function
اﺳﺘﺪﻋﺎ اﻟﺪاﻟﺔ Calling the Function اﻟﺪاﻟﺔ The Function
ﺁﺘﺎﺑﺔ داﻟﺔ أﺧﺮى Writing another Function
function )[u,v]=myfunc(a,b ;u=a+b v=a-b;
اﻟﻻﻤﺳﻮﺘﺪﺿﻋﺎﺤﺔ اﻟ ﺪاﻟﺔ ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻷﻣﺮ >>[u,v]=myfunc(3,7) اﻟﻤﻮﺿﺢ وذﻟﻚ ﺑﻜﺘﺎﺑﺔ اﺳﻢ ﻣﻠﻒ اﻟﺪاﻟﺔ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب
)function y=stat(a,b if a>b )’disp(‘a is greater than b elseif a>stat(5,3اﻟﻤﻮﺿﺤﺔ وذﻟﻚ ﺑﻜﺘﺎﺑﺔ اﺳﻢ ﻣﻠﻒ )>>stat(6,6 >>stat(2,8) اﻟﺪاﻟﺔ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب
اﺳﺘﺪﻋﺎ اﻟﺪاﻟﺔ Calling the Function
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
ﻗﻢ ﺑﺘﻨﻔﻴﺬ اﻟﺒﺮﻧﺎﻣﺞ )( program4 ﻟﻌﺪد ﻋﺸﺮ ﻣﺮات ﻣﺘﺘﺎﻟﻴﺔ وذﻟﻚ ﺑﻜﺘﺎﺑﺔ ﻩﺬﻩ اﻷواﻣﺮ ﻓﻲ ﻧﺎﻓﺬة اﻷواﻣﺮ ﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺎﺗﻼب ﻗﻢ ﺑﻔﺘﺢ ﺑﺮﻧﺎﻣﺞ اﻟﺘﺤﺮﻳﺮ )(Editor ﻹﻧﺸﺎ ﻣﻠﻒ اﻟﺪاﻟ )(myfunc.m واﻟﺬي ﻳﺤﺘﻮي ﻋﻠﻰ اﻷواﻣﺮ
14
Dr. Khalid A. Al-Hindi
ﻣﻘﺪﻣﺔ ﻓﻲ اﻟﺒﺮﻣﺠﺔ ﺑﺎﻟﻤﺎﺗﻼب
Introduction to Matlab
اﻟﻌﻼﻗﺎت اﻟﻤﻨﻄﻘﻴﺔ ) (Logical Expressionاﻟﻤﻌﺮﻓﺔ ﻓﻲ اﻟﻤﺎﺗﻼ ﺟﺪول ﻋﻼﻗﺎت اﻟﻤﻘﺎرﻧ اﻟﺮﻣﺰ اﻟﻤﺴﺘﺨﺪم
) (Relation Operators
وﺻ اﻟﻌﻼﻗ ﻳﺴﺎو ﻻ ﻳﺴﺎو أ ﻗﻞ أﻗﻞ أو ﻳﺴﺎو أﺁﺒ أﺁﺒﺮ أو ﻳﺴﺎو
== =~
Description Equal to Not equal Less than Lese than or equal Greater than Greater than or equal
ﺟﺪول اﻟﻌﻼﻗﺎت اﻟﻤﻨﻄﻘﻴﺔ ) (Logical Operators
اﻟﺮﻣﺰ اﻟﻤﺴﺘﺨﺪم & | ~ xorr xo
وﺻ اﻟﻌﻼﻗ اﻟﻌﻼﻗﺔ " " اﻟﻌﻼﻗﺔ "أ " اﻟﻌﻼﻗﺔ " " اﻟﻌﻼﻗﺔ ) (xor
Description And or Not XOR
ﻣﺜﻠﺔ اﻻﺳﺘﺨﺪام ﻓﻲ اﻟﻤﺎﺗﻼب ﻃﺮﻳﻘﺔ اﻟﺘﻤﺜﻴﻞ ﻓﻲ اﻟﻤﺎﺗﻼ
اﻟﻘﻴﻢ اﻟﺮﻳﺎﺿﻴﺔ x ∉ [0,5]
)i f ( x>=0) & ( x=0) & ( x>clc
>>clear all
اﻋﺪاد د /ﺧﺎﻟﺪ ﻋﺒﺪ اﻟﺤﻤﻴﺪ اﻟﻬﻨﺪ
ﻣﺴﺢ ﻧﺎﻓﺬة إدﺧﺎل اﻷواﻣﺮ ﻣﺴﺢ ﺁﺎﻓﺔ اﻟﻤﺘﻐﻴﺮات واﻟﺪوال اﻟﻤﺴﺘﺨﺪﻣﺔ ﻓﻲ ﻧﺎﻓﺬة اﻟﻤﺘﻐﻴﺮات ﻣﻦ ذاﺁﺮة اﻟﺤﺎﺳﺐ
16
Dr. Khalid A. Al-Hindi
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