matlab2

1. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻌﺎﻟﻤﻴﻦ‬ ‫رب‬ ‫ﷲ‬ ‫اﻟﺤﻤﺪ‬
,
‫اﻟﻤﺮﺳﻠﻴﻦ‬ ‫ﺧﻴﺮ‬ ‫ﻋﻠﻰ‬ ‫واﻟﺴﻼم‬ ‫واﻟﺼﻼة‬
,
‫ﻣﺤﻤﺪ‬ ‫ﺳﻴﺪﻧﺎ‬
‫واﻟﺘﺴﻠﻴﻢ‬ ‫اﻟﺼﻼة‬ ‫أﻓﻀﻞ‬ ‫ﻋﻠﻴﻪ‬
‫ﺑﺨﻄﻮة‬ ‫ﺧﻄﻮة‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺗﻌﻠﻴﻢ‬ ً
‫ﺎ‬‫ﻣﻌ‬ ‫ﻧﺒﺪأ‬ ‫أﺧﻮاﻧﻲ‬
,
‫واﻟﺬي‬
‫أن‬ ‫اﷲ‬ ‫اﺳﺄل‬
‫ﻟﻠﺠﻤﻴﻊ‬ ‫أداة‬ ‫ﺧﻴﺮ‬ ‫ﻳﻜﻮن‬
,
‫ﻳﻜﻮن‬ ‫وأن‬
‫هﺬا‬ ‫ﺧﺪﻣﺔ‬ ‫أﺟﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻟﻬﺬا‬ ‫ﺗﻌﻠﻤﻬﻢ‬
‫اﻟﺤﻨﻴﻒ‬ ‫اﻟﺪﻳﻦ‬
,
‫اﻹﺳﻼم‬ ‫راﻳﺔ‬ ‫رﻓﻊ‬ ‫أﺟﻞ‬ ‫وﻣﻦ‬
.
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﻌﻠﻴﻢ‬ ‫ﺗﻘﺴﻴﻢ‬ ‫ﺳﻴﺘﻢ‬
‫أﻗﺴﺎم‬ ‫إﻟﻰ‬
,
‫اﻟﺘﻄﺒﻴﻖ‬ ‫ﻟﻨﻮع‬ ً
‫ﺎ‬‫ﺗﺒﻌ‬
,
ً
‫ﺎ‬‫ﺗﺒﻌ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫إﻟﻰ‬ ‫اﻟﺘﻄﺮق‬ ‫وﺳﻴﺘﻢ‬
‫اﻟﺘﺎﻟﻲ‬ ‫ﻟﻠﺘﺮﺗﻴﺐ‬
:
‫وﻣﺆﺳﺴﻪ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﻌﺮﻳﻒ‬
.....
....................................................................
3
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫واﺟﻬﺔ‬
...................................................................................................
5
‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺗﻌﺮﻳﻒ‬
.............................................
....................................
10
‫اﻟﺒﺮﻣﺠﺔ‬ ‫أﺛﻨﺎء‬ ‫ﻋﻨﺎوﻳﻦ‬ ‫وﺿﻊ‬
...................................................................................
16
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻷواﻣﺮ‬
..............................................................
....
......
24
‫اﻟﻤﺼﻔﻮﻓﺎت‬
...................................................................
..............................
.......
35
‫واﻟﻤﺘﺠﻬﺎت‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
.........................
........................
.
..........
..
.
....
44
‫اﻟﻤﺘﺠﻬﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
................
................................................................
...
...
45
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
...................................................................................
55
M-File
..
.......................................
........................................................
...........
65
‫اﻷﺑﻌﺎد‬ ‫ﺛﻨﺎﺋﻲ‬ ‫اﻟﺮﺳﻢ‬
2
D Plotting
..............................................................
....
......
81
‫اﻟﻤﺎﺗﻼب‬ ‫داﺧﻞ‬ ‫اﻟﺮﺳﻮﻣﺎت‬ ‫إﻟﻰ‬ ‫ﺧﺼﺎﺋﺺ‬ ‫إﺿﺎﻓﺔ‬
............
.........................
......
84
‫ا‬ ‫ﻋﻠﻰ‬ ‫ﺷﺒﻜﺔ‬ ‫وﺿﻊ‬ ‫ﻋﻤﻠﻴﺔ‬
‫ﻟﺮﺳﻢ‬
......
........
............................
................
...........
88
‫ﻣﻨﻔﺼﻠﺔ‬ ‫ﻧﻮاﻓﺬ‬ ‫ﻓﻲ‬ ‫اﻟﺮﺳﻮﻣﺎت‬ ‫وﺿﻊ‬ ‫ﻋﻠﻤﻴﺔ‬
.....
..................................
...........
91
‫واﺣﺪة‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫رﺳﻮﻣﺎت‬ ‫إﻧﺸﺎء‬
...
.........................................
.......
94
‫ﺗﺴﻤﻴﺔ‬
‫اﻟﻤﺤﺎور‬
…
....................................................................................
.
99
‫ﺗﻄﺒﻴﻘﻲ‬ ‫ﻣﺜﺎل‬
.
109….......................................................................................
‫اﻷﺑﻌﺎد‬ ‫ﺛﻼﺛﻲ‬ ‫اﻟﺮﺳﻢ‬
111..................................................................................
‫ﻣﻌﺎدﻻت‬ ‫ﺛﻼﺛﺔ‬ ‫ﺣﻞ‬
116…...................................................................................
119....….................................................................................. Zero Crossing
‫اﻟﻤﻨﺤﻨﻰ‬ ‫ﺗﺤﺖ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫إﻳﺠﺎد‬
127…..................................................................
131…........................................................................................Curve Fitting
‫آﻤﺎ‬
‫ﺗﺮوا‬
‫ﻃﻮﻳﻞ‬ ‫اﻟﻤﺸﻮار‬ ‫ﻓﺈن‬ ‫اﻟﻜﺮام‬ ‫إﺧﻮاﻧﻲ‬
,
‫ا‬ ‫وأﺳﺄل‬
‫إﻟﻰ‬ ‫اﻟﻤﺸﻮار‬ ‫هﺬا‬ ‫إﺳﺘﻜﻤﺎل‬ ‫ﻋﻠﻰ‬ ‫ﻳﻌﻴﻨﻨﺎ‬ ‫أن‬ ‫ﷲ‬
‫ﺁﺧﺮ‬
‫وهﻤﺎ‬ ‫اﻟﺘﻄﺒﻴﻖ‬ ‫ﻓﻲ‬ ‫اﻟﺸﺮوع‬ ‫ﻗﺒﻞ‬ ‫أﺧﺬﻩ‬ ‫ﻣﻦ‬ ‫ﻻﺑﺪ‬ ‫ﻣﻮاﺿﻴﻊ‬ ‫ﺛﻼﺛﺔ‬ ‫هﻨﺎﻟﻚ‬ ‫وﺳﻜﻮن‬
1-
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻣﻘﺪﻣﺔ‬
2-
‫اﻟﻤﺤﺎآﺎة‬ ‫ﻓﻲ‬ ‫ﻣﻘﺪﻣﺔ‬
3-
‫ﺑﺈﺳﺘﺨﺪام‬ ‫اﻟﺘﺤﻜﻢ‬ ‫أﻧﻈﻤﺔ‬
‫اﻟﻤﺎﺗﻼب‬
‫اﻟﻜﺮﻳﻤﺔ‬ ‫اﻷﻣﺔ‬ ‫ﺑﻬﺬﻩ‬ ‫اﻟﻨﻬﻮض‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫ﺟﻤﻴﻌ‬ ‫ﻳﻌﻴﻨﻨﺎ‬ ‫ان‬ ‫اﷲ‬ ‫أﺳﺄل‬

2. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ا‬ ‫أﺧﻮاﻧﻲ‬
‫ﻟﻜﺮام‬
,
‫اﻟﺒﺪء‬ ‫ﻗﺒﻞ‬ ً
‫ﺎ‬‫وأﻳﻀ‬
,
‫ﻟﺨﺪﻣﺔ‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻟﻤﻮاﻗﻊ‬ ‫ذآﺮ‬ ‫ﻣﻦ‬ ‫ﻻﺑﺪ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬
,
‫ﺧﻼﻟﻬﺎ‬ ‫ﻣﻦ‬ ‫واﻟﺘﻲ‬
‫ﺑﺈذن‬ ‫اﻟﻤﻄﻠﻮب‬ ‫اﻟﺘﻄﺒﻴﻖ‬ ‫إﻟﻰ‬ ‫ﺗﺼﻞ‬ ‫أن‬ ‫ﺗﺴﺘﻄﻴﻊ‬
‫اﷲ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﻤﺼﻨﻌﺔ‬ ‫اﻟﺸﺮآﺔ‬ ‫ﻣﻮﻗﻊ‬
http://www.mathworks.com
‫ﺳ‬ ‫ﺣﻴﺚ‬
‫ﺁﺧﺮ‬ ‫اﻟﻤﻮﻗﻊ‬ ‫هﺬا‬ ‫ﻓﻲ‬ ‫ﺘﺠﺪ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺒﺮﻧﺎﻣﺞ‬ ‫اﻹﺻﺪارات‬
,
‫ﺑﺎﻟﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻟﺘﺤﺪﻳﺜﺎت‬ ‫وآﺬﻟﻚ‬
,
‫ﻳﻮﻓﺮ‬ ‫آﻤﺎ‬
ً
‫ﺎ‬‫ﺷﺮﺣ‬
(
‫اﻹﻧﺠﻠﻴﺰﻳﺔ‬ ‫ﺑﺎﻟﻠﻐﺔ‬
(
‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺒﺮﻧﺎﻣﺞ‬
.
University of Utah
http://www.math.utah.edu/lab/ms/matlab/matlab.html
‫ﻳﻮﻓﺮ‬ ‫ﺣﻴﺚ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺒﺮﻧﺎﻣﺞ‬ ‫وﻣﺒﺴﻄﺔ‬ ‫ﺳﺮﻳﻌﺔ‬ ‫ﻣﻘﺪﻣﺔ‬ ‫اﻟﺠﺎﻣﻌﺔ‬ ‫ﻣﻮﻗﻊ‬
Indiana University
http://www.indiana.edu/~statmath/math/matlab/
ً
‫ﺎ‬‫أﻳﻀ‬ ‫ﻳﻘﺪم‬
‫ﻟﻤﺤ‬ ‫اﻟﺠﺎﻣﻌﺔ‬ ‫ﻣﻮﻗﻊ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺣﻮل‬ ‫ﺳﺮﻳﻌﺔ‬ ‫ﺔ‬

3. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺷﺮح‬ ‫ﺑﺪء‬ ‫ﻓﻲ‬ ‫اﷲ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻮآﻠﻨﺎ‬ ‫اﻟﻜﺮام‬ ‫أﺧﻮاﻧﻲ‬
‫اﻟﻤﺎﺗﻼب‬
‫ﻓﻲ‬ ‫اﷲ‬ ‫ﺑﺈذن‬ ‫ﺳﻨﺘﻨﺎول‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻣﻘﺪﻣﺔ‬
‫اﻟﺘﺎﻟﻲ‬
:
1-
‫وﻣﺆﺳﺴﻪ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﻌﺮﻳﻒ‬
2-
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫واﺟﻬﺔ‬
3-
‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻷواﻣﺮ‬ ‫ﺑﻌﺾ‬
4-
‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺗﻌﺮﻳﻒ‬
5-
‫اﻟﻤﺘﻐﻴﺮات‬ ‫ﺑﻌﺾ‬ ‫ﺗﻌﺮﻳﻒ‬
6-
‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬
7-
‫اﻟﻤﺼﻔﻮﻓﺎت‬
8-
‫ﻧﻈﺎم‬ ‫ﻓﻲ‬ ‫اﻟﺮﺳﻢ‬
‫اﻟﺜﻨﺎﺋﻲ‬ ‫اﻹﺣﺪاﺛﻲ‬
2
D Plotting
9-
‫اﻷﺑﻌﺎد‬ ‫اﻟﺜﻼﺛﻲ‬ ‫اﻹﺣﺪاﺛﻲ‬ ‫ﻧﻈﺎم‬ ‫ﻓﻲ‬ ‫اﻟﺮﺳﻢ‬
3
D Plotting
10-
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫اﻟﺒﺮﻣﺠﺔ‬
‫أوﻻ‬
:
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﻌﺮﻳﻒ‬
‫ﺑﺮﻧﺎﻣﺞ‬ ‫هﻮ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬
‫هﻨﺪﺳﻲ‬
)
‫أﺧﺮى‬ ‫ﻣﺠﺎﻻت‬ ‫وﻟﻪ‬
(
‫ﺗﺤ‬ ‫ﺑﻌﻤﻠﻴﺎت‬ ‫ﻳﻘﻮم‬
‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫وﺗﻤﺜﻴﻞ‬ ‫ﻠﻴﻞ‬
‫ﺗﻠﻚ‬ ‫ﻣﻌﺎﻟﺠﺔ‬
‫ﺑﻪ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻟﻘﺎﻋﺪة‬ ً
‫ﺎ‬‫ﺗﺒﻌ‬ ‫اﻟﺒﻴﺎﻧﺎت‬
,
‫اﻟﺘﻔﺎﺿﻞ‬ ‫ﻋﻤﻞ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻳﺴﺘﻄﻴﻊ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
differentiation
‫واﻟﺘﻜﺎﻣﻞ‬
Integration
‫اﻟﺠﺒﺮﻳﺔ‬ ‫اﻟﻤﻌﺎدﻻت‬ ‫ﺑﺤﻞ‬ ‫ﻳﻘﻮم‬ ‫آﺬﻟﻚ‬ ‫و‬
Algebric Equations
‫وآﺬﻟﻚ‬
‫اﻟﺘﻔﺎﺿﻠﻴﺔ‬ ‫اﻟﻤﻌﺎدﻻت‬
Differential Equations
‫ذ‬
‫اﻟﻌﻠﻴﺎ‬ ‫اﻟﺮﺗﺐ‬ ‫ات‬
‫ﺗﺼﻞ‬ ‫ﻣﺎ‬ ‫اﻟﺼﻌﻮﺑﺔ‬ ‫ﻣﻦ‬ ‫ﺗﺼﻞ‬ ‫ﻗﺪ‬ ‫واﻟﺘﻲ‬
,
‫ﻟﻴﺲ‬
‫اﻟﺘﻔﺎﺿﻞ‬ ‫ﻋﻤﻞ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻳﺴﺘﻄﻴﻊ‬ ‫ﺑﻞ‬ ‫ذﻟﻚ‬ ‫ﻓﻘﻂ‬
‫اﻟﺠﺰﺋﻲ‬
,
‫اﻟﺠﺰﺋﻲ‬ ‫اﻟﻜﺴﺮ‬ ‫ﻋﻠﻴﺎت‬ ‫ﺑﻌﻤﻞ‬ ‫وﻳﻘﻮم‬
Partial fraction
‫ﺗﺴﺘﻠﺰم‬ ‫واﻟﺘﻲ‬ ‫وﻳﺴﺮ‬ ‫ﺑﺴﻬﻮﻟﺔ‬
‫اﻟﺘﻘﻠﻴﺪﻳﺔ‬ ‫ﺑﺎﻟﻄﺮق‬ ‫ﻟﻌﻤﻠﻬﺎ‬ ً
‫ا‬‫آﺒﻴﺮ‬ ً
‫ﺎ‬‫وﻗﺘ‬
,
‫اﻷآﺎدﻳﻤﻴﺔ‬ ‫اﻟﻨﺎﺣﻴﺔ‬ ‫ﻣﻦ‬ ‫هﺬا‬
,
‫ﻣﻦ‬ ‫أﻣﺎ‬
‫اﻟﻨﺎﺣﻴﺔ‬
‫اﻟﺘﻄﺒ‬
‫اﻟﺘﺤﻜﻢ‬ ‫أﻧﻈﻤﺔ‬ ‫ﻣﺜﻞ‬ ‫اﻟﻬﻨﺪﺳﻴﺔ‬ ‫اﻟﻤﺠﺎﻻت‬ ‫ﺟﻤﻴﻊ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻤﻞ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻓﻴﺴﺘﻄﻴﻊ‬ ‫ﻴﻘﻴﺔ‬
Control
System,
‫اﻟﻤﻴﻜﺎﻧﻴﻜﺎ‬ ‫ﻣﺠﺎل‬ ‫وﻓﻲ‬
Mechanical Field,
‫اﻹﻟﻜﺘﺮوﻧﻴﺎت‬ ‫ﻣﺤﺎآﺔ‬ ‫وآﺬﻟﻚ‬
Electronics
‫وﺻﻨﺎﻋﺔ‬
‫اﻟﺴﻴﺎرات‬
Automotive Industry,
‫واﻟﺪﻓﺎع‬ ‫اﻟﻄﻴﺮان‬ ‫ﻣﺠﺎل‬ ‫وآﺬﻟﻚ‬
‫اﻟﺠﻮي‬
Aerospace and Defense,
‫و‬
‫اﻟﻜﺜﻴﺮ‬
‫اﻟﻬﻨﺪﺳﻴﺔ‬ ‫اﻟﺘﻄﺒﻴﻘﺎت‬ ‫ﻣﻦ‬
.
‫ﻟﻠﺠﻤﻴﻊ‬ ‫أؤآﺪ‬ ‫وﺣﺘﻰ‬
‫ذﻟﻚ‬
,
‫ﻧﻴﺴﺎن‬ ‫اﻟﻤﺮﻣﻮﻗﺔ‬ ‫اﻟﺴﻴﺎرات‬ ‫ﺷﺮآﺔ‬ ‫ﻗﺎﻣﺖ‬
Nissan
‫إﻟﻰ‬ ‫اﻟﺘﻄﻮﻳﺮ‬ ‫وﻗﺖ‬ ‫ﺑﺘﺨﻔﻴﺾ‬
50
%
‫ﻋﻨﺪﻣﺎ‬
‫اﻷوراق‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﺼﻤﻴﻢ‬ ‫ﺑﺈﺳﺘﺒﺪال‬ ‫ﻗﺎﻣﺖ‬
Paper Model Based Design
‫اﻟﻤﺘﻄﻮرة‬ ‫اﻷداة‬ ‫إﻟﻰ‬
‫وهﻮ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬
Model Based Design,
‫اﻟﻤ‬ ‫ﻳﻘﻮل‬
‫آﺎآﻴﺰاآﻲ‬ ‫ﺷﻴﺠﺎﻳﺎآﻲ‬ ‫اﻟﻤﺴﺎﻋﺪ‬ ‫ﺪﻳﺮ‬
‫ﻓﻲ‬
‫ﻧﻴﺴﺎن‬ ‫ﻟﺸﺮآﺔ‬ ‫اﻟﻤﺤﺮك‬ ‫ﻧﻈﺎم‬ ‫إدارة‬ ‫هﻨﺪﺳﺔ‬ ‫ﻣﺠﻤﻮﻋﺔ‬
)
‫ﻣﺤﺪودة‬ ‫ﺷﺮآﺔ‬
)
Without MathWorks tools for Model-Based Design, Nissan would not have become the first
company to meet the CARB PZEV standard
CARB= California Air Resources Board
PZEV= Partial Zero Emission Vehicle
‫ﻳﻤﻜﻨﻜﻢ‬
‫اﻟﺮاﺑﻂ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺘﻘﺮﻳﺮ‬ ‫هﺬا‬ ‫ﻣﺘﺎﺑﻌﺔ‬
http://www.mathworks.com/company/use...ml?by=industry
‫ﻓﻤﻊ‬
‫ا‬ ‫ﻓﻲ‬ ‫اﻟﺴﺮﻳﻊ‬ ‫اﻟﺘﻘﺪم‬
‫ﺣﺘﻰ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫هﺬا‬ ‫ﻣﺜﻞ‬ ‫ﺗﻌﻠﻢ‬ ‫ﻋﻠﻰ‬ ‫ﻣﻠﺤﺔ‬ ‫اﻟﺤﺎﺟﺔ‬ ‫أﺻﺒﺤﺖ‬ ‫ﻟﺘﻜﻨﻮﻟﻮﺟﻴﺎ‬
‫ﻓﻲ‬ ‫ﻧﺼﺒﺢ‬
‫اﻟﺼﻨﺎﻋﻲ‬ ‫اﻟﺘﻨﺎﻓﺲ‬ ‫ﺳﺒﺎق‬
.
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺑﻤﺆﺳﺲ‬ ‫اﻟﺘﻌﺮﻳﻒ‬
‫ﺑﺘﺄﺳﻴﺲ‬ ‫ﻗﺎم‬
‫ﺷﺨﺼﺎن‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬
,
‫ﻟﻴﺘﻞ‬ ‫ﺟﺎك‬ ‫واﻟﺜﺎﻧﻲ‬ ‫ﻣﻮﻟﺮ‬ ‫آﻠﻴﻒ‬ ‫هﻮ‬ ‫اﻷول‬
‫آﻠﻴﻒ‬
‫ﻣﻮﻟﺮ‬
‫اﻟﺤﺎﺳﺐ‬ ‫وﻋﻠﻮم‬ ‫اﻟﺮﻳﺎﺿﻴﺎت‬ ‫إﺳﺘﺎذ‬ ‫هﻮ‬
Computer Science
‫ﻣﻦ‬ ‫ﻷآﺜﺮ‬
‫ﻋﺸﺮﻳﻦ‬
‫و‬ ‫ﻣﺘﺸﻴﺠﻴﻦ‬ ‫ﺟﺎﻣﻌﺔ‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫ﻋﺎﻣ‬
‫ﻣﻜﺴﻴﻜﻮ‬ ‫ﻧﻴﻮ‬ ‫وﺟﺎﻣﻌﺔ‬ ‫ﺳﺘﺎﻧﻔﻮرد‬ ‫ﺟﺎﻣﻌﺔ‬
.
‫ﺧﻤﺲ‬ ‫أﻣﻀﻰ‬
‫اﻟــ‬ ‫ﻣﺼﻨﻌﻰ‬ ‫ﻣﻦ‬ ‫إﺛﻨﻴﻦ‬ ‫ﻋﻨﺪ‬ ‫ﺳﻨﻮات‬
Hardware
‫وهﻤﺎ‬
Intel Hypercube organization
‫و‬
Ardent Computer
‫ﺷﺮآﺔ‬ ‫إﻟﻰ‬ ‫ﺑﺎﻹﻧﺘﻘﺎل‬ ‫ﻳﻘﻮم‬ ‫أن‬ ‫ﻗﺒﻞ‬
Mathworks
‫ﻟﺒﺮﻧﺎﻣﺞ‬ ‫اﻷم‬ ‫اﻟﺸﺮآﺔ‬
‫اﻟﻤﺎﺗﻼب‬
,
‫أﻧﻪ‬ ‫آﻤﺎ‬
‫ﺑﺮ‬ ‫ﻷول‬ ‫اﻟﻤﺆﻟﻒ‬ ‫هﻮ‬
‫ﻟﻠﻤﺎﺗﻼب‬ ‫ﻧﺎﻣﺞ‬
.

4. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻣﻮﻟﺮ‬ ‫آﻠﻴﻒ‬
‫ﻟﻴﺘﻞ‬ ‫ﺟﺎك‬
‫هﻮ‬
‫ﻟﺸﺮآﺔ‬ ‫اﻟﻤﺆﺳﺲ‬
Mathworks
‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﺨﻄﻴﻂ‬ ‫وﺿﻊ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺴﺎﻋﺪ‬ ‫أﻧﻪ‬ ‫آﻤﺎ‬
‫اﻟﻤﺎﺗﻼب‬
.
‫اﻟﺤﺎﺳﺐ‬ ‫وﻋﻠﻮم‬ ‫اﻟﻜﻬﺮﺑﻴﺔ‬ ‫اﻟﻬﻨﺪﺳﺔ‬ ‫ﺑﻜﻠﻮرﻳﻮس‬ ‫ﻋﻠﻰ‬ ‫ﺣﺎﺻﻞ‬ ‫ﺟﺎك‬
‫ﺟﺎﻣﻌﺔ‬ ‫ﻣﻦ‬
MIT
‫ﻋﺎم‬
1978
‫ﺷﻬﺎدة‬ ‫ﻋﻠﻰ‬ ‫ﺣﺎﺻﻞ‬ ‫أﻧﻪ‬ ‫آﻤﺎ‬
M.S.E.E
‫ﻋﺎم‬ ‫ﺳﺘﺎﻧﻔﻮرد‬ ‫ﺟﺎﻣﻌﺔ‬ ‫ﻣﻦ‬
1980
‫ﺟﺎك‬
‫ﻟﻴﺘﻞ‬

5. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
ً
‫ﺎ‬‫ﺛﺎﻧﻴ‬
:
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫واﺟﻬﺔ‬
‫ﻣﻌ‬ ‫اﻟﺘﻌﺎﻣﻞ‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﺴﻬﻮﻟﺔ‬ ‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫واﺟﻬﺔ‬ ‫ﺗﺘﺴﻢ‬
‫ﻬﺎ‬
,
‫ﺛﻼث‬ ‫إﻟﻰ‬ ‫ﺑﻬﺎ‬ ‫اﻟﻌﻤﻞ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ﺗﻘﺴﻴﻢ‬ ‫ﻳﺘﻢ‬ ‫ﺣﻴﺚ‬
‫رﺋﻴﺴﻴﺔ‬ ‫ﻣﻨﺎﻃﻖ‬
,
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫آﺎﻟﺘﺎﻟﻲ‬ ‫وهﻲ‬
Command Window
‫اﻟﻌﻤﻞ‬ ‫ﻣﻨﻄﻘﺔ‬ ‫و‬
Workspace
‫و‬
‫اﻷواﻣﺮ‬ ‫ﺗﺎرﻳﺦ‬
Command History
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫إﻧﻈﺮ‬
.
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬
Command Window
:
‫اﻟﻤﺪﺧﻼت‬ ‫إدﺧﺎل‬ ‫ﻳﺘﻢ‬ ‫ﺣﻴﺚ‬
Inputs
‫واﻷواﻣﺮ‬
Commands
,
‫ﻣﻨﻪ‬ ‫اﻟﻤﻄﻠﻮﺑﺔ‬ ‫ﻟﻠﻮﻇﻴﻔﺔ‬ ‫اﻟﻤﺪﺧﻼت‬ ‫ﻣﻄﺎﺑﻘﺔ‬ ‫وﻣﺪى‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺗﻠﻚ‬ ‫ﺗﺤﻠﻴﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫وﻳﻌﻤﻞ‬
,
‫ﺣﺘﻰ‬
‫اﻟﺸﺎﺷﺔ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻲ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺼﻞ‬
.
‫اﻟﻌﻤﻞ‬ ‫ﻣﻨﻄﻘﺔ‬
Workspace
:
‫اﻟﻤﺪﺧﻼت‬ ‫ﺑﺘﺴﺠﻴﻞ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬ ‫ﺣﻴﺚ‬
Inputs
‫واﻟﻤﺨﺮﺟﺎت‬
Outputs
‫اﻟﺸﺎﺷﺔ‬ ‫هﺬﻩ‬ ‫ﻓﻲ‬
.
‫ﻣﻼﺣﻈﺔ‬
:
‫ﻷول‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻞ‬ ‫ﺑﺪء‬ ‫ﻋﻨﺪ‬
‫ﻣﺮة‬
,
‫ﻧﺎﻓﺬة‬ ‫ﻻﺗﻈﻬﺮ‬
Workspace
,
‫إﺿﻐﻂ‬ ‫ﺗﻈﻬﺮ‬ ‫وﺣﺘﻰ‬
‫آﻠﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﺄرة‬ ‫ﺑﺰر‬
Workspace
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬

6. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻷواﻣﺮ‬ ‫ﺗﺴﺠﻴﻞ‬ ‫ﻧﺎﻓﺬة‬
Command History
:
‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﺨﺪم‬ ‫ﺑﻪ‬ ‫ﻳﻘﻮم‬ ‫ﻣﺎ‬ ‫آﻞ‬ ‫ﺗﺴﺠﻴﻞ‬ ‫ﻳﺘﻢ‬
‫اﻟﻨﺎﻓﺬة‬ ‫هﺬﻩ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺎﺗﻼب‬
.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫إﻧﻈﺮ‬
‫إﺑﺪأ‬ ‫ﻗﺎﺋﻤﺔ‬
Start
:
‫هﺬﻩ‬ ‫ﺗﺴﺘﺨﺪم‬
‫ﺗﻨﻔﻴﺬﻩ‬ ‫اﻟﻤﺮاد‬ ‫اﻟﺘﻄﺒﻴﻖ‬ ‫إﻟﻰ‬ ‫ﻟﻠﻮﺻﻮل‬ ‫اﻟﻘﺎﺋﻤﺔ‬
,
‫هﺬﻩ‬ ‫ﺗﺴﺘﺨﺪم‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﻤﺮاﺣﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻘﺎﺋﻤﺔ‬
‫ﺻﻮرة‬
4
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻟﻤﺴﺘﺨﺪﻣﻲ‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻷﺳﺎﺳﻴﺎت‬ ‫ﺑﻌﺾ‬
‫اﻟﻘﻮاﺋﻢ‬ ‫ﻋﻠﻰ‬ ‫اﷲ‬ ‫ﺑﺈذن‬ ‫ﺳﻨﺘﻌﺮف‬
,
‫إﺧﺘﻴﺎر‬ ‫آﻞ‬ ‫ﺑﻪ‬ ‫ﻳﻘﻮم‬ ‫وﻣﺎ‬
.
‫ﻣﻠﻒ‬ ‫ﻗﺎﺋﻤﺔ‬
File
‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﻌﺪﻳﺪ‬ ‫ﻣﻦ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫هﺬﻩ‬ ‫ﺗﺘﻜﻮن‬
‫ﺨﻴﺎرات‬
,
‫اﻟﺒﺮاﻣﺞ‬ ‫ﺑﺎﻗﻲ‬ ‫ﻣﺤﺪدة‬ ‫وﻇﻴﻔﺔ‬ ‫ﻣﻨﻬﺎ‬ ‫آﻞ‬ ‫ﺗﻨﻔﺬ‬ ‫واﻟﺘﻲ‬

7. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﻌﺪﻳﻞ‬ ‫ﻗﺎﺋﻤﺔ‬
Edit
‫أواﻣﺮ‬ ‫ﻧﺠﺪ‬ ‫أن‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫ﺗﻠﻚ‬ ‫ﻓﻲ‬ ‫ﺗﻌﻮدﻧﺎ‬ ‫ﻓﻜﻤﺎ‬
)
‫ﻧﺴﺦ‬
Copy
,
‫ﻗﺺ‬
Cut
,
‫ﻟﺼﻖ‬
Paste
,
‫ﺑﺤﺚ‬
Find
(
,
‫وهﻢ‬ ‫ﺑﻬﺎ‬ ‫هﺎﻣﺔ‬ ‫أدوات‬ ‫ﺛﻼث‬ ‫هﻨﺎﻟﻚ‬ ‫وﻟﻜﻦ‬
Clear Command Window
Clear Command History
Clear Workspace
‫ﺗﻌ‬ ‫ﺣﻴﺚ‬
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻣﻦ‬ ‫واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻤﺪﺧﻼت‬ ‫ﺟﻤﻴﻊ‬ ‫ﻣﺴﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻷدوات‬ ‫ﺗﻠﻚ‬ ‫ﻤﻞ‬
‫ﻗﺎﺋﻤﺔ‬
Debug
‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺑﻤﻌﺎﻟﺠﺔ‬ ‫ﺧﺎﺻﺔ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫هﺬﻩ‬
,
‫ﻣﻮاﺟﻬﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻗﺒﻞ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺒﻌﺔ‬ ‫واﻟﻄﺮﻳﻘﺔ‬
‫اﻷﺧﻄﺎء‬
.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫ﺑﺈﺧﺘﻴﺎر‬ ‫ﻗﻢ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
Stop If Errors/Warnings…

8. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻧﺎﻓﺬة‬ ‫ﻇﻬﻮر‬ ‫ﺳﺘﻼﺣﻆ‬
,
‫ﺗﻌﻄﻴﻚ‬
‫أو‬ ‫أﺧﻄﺎء‬ ‫ﺣﺪوث‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﺗﺼﺮف‬ ‫ﻓﻲ‬ ‫اﻹﺧﺘﻴﺎر‬ ‫ﺣﺮﻳﺔ‬
‫ﺗﺤﺬﻳﺮات‬
‫ﻣﻼﺣﻈﺔ‬
:
‫ﺗﻐﻴﻴﺮ‬ ‫دون‬ ‫اﻟﻨﺎﻓﺬة‬ ‫هﺬﻩ‬ ‫ﺗﺮك‬ ‫ﻳﺮﺟﻰ‬
,
‫اﻵن‬ ‫ﻟﻬﺎ‬ ‫ﺑﺤﺎﺟﺔ‬ ‫ﻓﻠﺴﻨﺎ‬
.
‫ﻗﺎﺋﻤﺔ‬
Desktop
:
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻟﻮاﺟﻬﺔ‬ ‫ﺑﻤﺤﺘﻮى‬ ‫اﻟﺘﺤﻜﻢ‬ ‫ﻳﺘﻢ‬ ‫اﻟﻘﺎﺋﻤﺔ‬ ‫هﺬﻩ‬ ‫ﻓﻲ‬
,
‫ﻧﺎﻓﺬة‬ ‫إﻇﻬﺎر‬ ‫ﻳﻤﻜﻨﻨﺎ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
‫إﺧﻔﺎﺋﻬﺎ‬ ‫أو‬ ‫اﻷواﻣﺮ‬
)
‫ﻧﺸﺘﻐﻞ‬ ‫ﺣﻨﻌﺮف‬ ‫ﻣﺶ‬ ‫أﺧﻔﻴﻨﺎهﺎ‬ ‫ﻟﻮ‬ ً
‫ﺎ‬‫ﻃﺒﻌ‬
(
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

9. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫هﺎﻣﺔ‬ ‫ﻣﻌﻠﻮﻣﺔ‬
:
‫اﻟﻮﺿﻌﻴﻦ‬ ‫أﺣﺪ‬ ‫ﻓﻲ‬ ‫اﻟﻨﻮاﻓﺬ‬ ‫ﺗﻜﻮن‬
1
-
Docked
:
‫ﻣﻜﺎﻧﻬﺎ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﺮﻳﻚ‬ ‫ﻗﺎﺑﻠﺔ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻨﺎﻓﺬة‬ ‫ﺗﻜﻮن‬ ‫ﺣﻴﺚ‬
.
2
-
Undocked
:
ً
‫ﺎ‬‫أﻳﻀ‬ ‫ﻣﻘﺎﺳﻬﺎ‬ ‫وﺗﻌﺪﻳﻞ‬ ‫ﻟﻠﺘﺤﺮﻳﻚ‬ ‫ﻗﺎﺑﻠﺔ‬ ‫اﻟﻨﺎﻓﺬة‬ ‫ﺗﻜﻮن‬ ‫ﺣﻴﺚ‬
‫هﻤﺎ‬ ‫ﻗﺎﺋﻤﺘﺎن‬ ‫ﻟﺪﻳﻨﺎ‬ ‫ﻳﺘﺒﻘﻰ‬
‫ﻗﺎﺋﻤﺔ‬
Window
:
‫ﺣﻴﺚ‬
‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻣﻠﻔﺎت‬ ‫ﺑﻴﻦ‬ ‫اﻟﺘﻨﻘﻞ‬ ‫ﻳﻤﻜﻨﻚ‬
,
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻣﺜﻞ‬ ‫اﻟﻨﻮاﻓﺬ‬ ‫وآﺬﻟﻚ‬
Command
Window
‫اﻟﻜﺜﻴﺮ‬ ‫وﻏﻴﺮهﺎ‬
.
‫ﻗﺎﺋﻤﺔ‬
Help
:
‫اﻟﻘﺎﺋﻤﺔ‬ ‫ﺗﻠﻚ‬ ‫ﺗﻘﻮم‬ ‫ﺣﻴﺚ‬
,
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ‫اﻟﻀﺮورﻳﺔ‬ ‫اﻟﻤﺴﺎﻋﺪات‬ ‫ﺑﺘﻮﻓﻴﺮ‬
,
‫ﺑﺎﻟﺸﺮآﺔ‬ ‫اﻹﺗﺼﺎل‬ ‫ووﺳﺎﺋﻞ‬
‫اﻟﻤﺼﻨﻌﺔ‬
,
‫اﻟﺘﺤﺪﻳﺜﺎت‬ ‫وﺁﺧﺮ‬
,
‫ﺑﺎﻟﻠﻐﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺗﻌﻠﻢ‬ ‫وآﺬﻟﻚ‬
‫اﻹﻧﺠﻠﻴﺰﻳﺔ‬

10. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺗﻌﺮﻳﻒ‬
‫اﻟﻜﺮام‬ ‫أﺧﻮاﻧﻲ‬
,
‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫اﷲ‬ ‫ﺑﺈذن‬ ‫اﻟﻴﻮم‬ ‫وﻧﺘﻨﺎول‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻧﺴﺘﻜﻤﻞ‬
)
‫و‬ ‫اﻟﺠﻤﻊ‬
‫واﻟﻘﺴﻤﺔ‬ ‫واﻟﻀﺮب‬ ‫اﻟﻄﺮح‬
(
‫ﻟﻌﺪد‬ ‫اﻷس‬ ‫وﺿﻊ‬ ‫ﻣﺜﻞ‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫وﺑﻌﺾ‬
,
‫ﺑﻌﺾ‬ ‫ﻋﻠﻰ‬ ‫ﺳﻨﺘﻌﺮف‬ ‫آﻤﺎ‬
‫اﻟﻬﺎﻣﺔ‬ ‫اﻷواﻣﺮ‬
.
‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬
‫اﻟﺠﻤﻊ‬ ‫ﻋﻼﻣﺔ‬ ‫ﺗﺄﺧﺬ‬
‫وهﻮ‬ ‫ﻟﻠﺠﻤﻊ‬ ‫اﻟﻤﻌﺮوف‬ ‫اﻟﺮﻣﺰ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬
"+"
‫ﺑﺠﻤﻊ‬ ‫ﻗﻤﻨﺎ‬ ‫إذا‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
3
+
2
‫وهﻮ‬ ‫أرﻗﺎم‬ ‫ﺻﻮرة‬ ‫ﻓﻲ‬ ‫اﻹﺟﺎﺑﺔ‬ ‫ﺑﻮﺿﻊ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺳﻴﻘﻮم‬
5
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﺘﺎﻟﻴﺔ‬
‫ﻧﺎﻓﺬة‬ ‫إﻟﻰ‬ ‫إذهﺐ‬
Workspace
‫ﻣﺰدوﺟﺔ‬ ‫ﺑﻘﺮة‬ ‫ﺑﺎﻟﻤﺎوس‬ ‫ﺑﺎﻟﻨﻘﺮ‬ ‫وﻗﻢ‬
,
‫ﻣﺤﻞ‬ ‫ﺣﻠﺖ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻇﻬﻮر‬ ‫ﺳﺘﻼﺣﻆ‬
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫وأﺻﺒﺤﺖ‬ ‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬
‫اﻷﺳﻔﻞ‬ ‫ﻓﻲ‬
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

11. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻨﺎﺗﺞ‬ ‫ﺑﺘﻐﻴﻴﺮ‬ ‫ﻗﻤﻨﺎ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻔﺘﺮض‬
5
‫إﻟﻰ‬
3
,
‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻌﺪﻳﻞ‬ ‫ﻧﺎﻓﺬة‬ ‫ﺑﺈﻏﻼق‬ ‫ﻗﻢ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬

12. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻷﺳﺎﺳﻲ‬ ‫ﻟﻮﺿﻌﻬﺎ‬ ‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻋﻮدة‬ ‫ﺳﺘﻼﺣﻆ‬
,
‫ﺑﻜﺘﺎﺑﺔ‬ ‫ﻗﻢ‬
ans
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬
,
‫ﻇﻬﻮر‬ ‫ﺳﺘﻼﺣﻆ‬
‫وهﻲ‬ ‫اﻟﺠﺪﻳﺪة‬ ‫ﺑﺎﻟﻘﻴﻤﺔ‬ ‫اﻟﻨﺎﺗﺞ‬
3
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

13. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻋﻤ‬
‫اﻟﻄﺮح‬ ‫ﻠﻴﺔ‬
:
‫رﻣﺰ‬ ‫اﻟﻄﺮح‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺗﺄﺧﺬ‬
)
-
(
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬
,
ً
‫ﻼ‬‫ﻓﻤﺜ‬
3
-
2
=
1
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻀﺮب‬ ‫ﻋﻤﻠﻴﺔ‬
‫رﻣﺰ‬ ‫اﻟﻀﺮب‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺗﺄﺧﺬ‬
( * )
,
ً
‫ﻼ‬‫ﻓﻤﺜ‬
15
*
12
=
180
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻘﺴﻤﺔ‬ ‫ﻋﻤﻠﻴﺔ‬
:
‫رﻣﺰ‬ ‫اﻟﻘﺴﻤﺔ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺗﺄﺧﺬ‬
( / )
,
ً
‫ﻼ‬‫ﻓﻤﺜ‬
12
‫ﻋﻠﻰ‬
3
‫ﺗﺴﺎوى‬
4
,
‫ﻟﻠﺘﺘﺄآﺪ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

14. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻷ‬ ‫وﺿﻊ‬ ‫ﻋﻤﻠﻴﺔ‬
‫س‬
:
‫اﻷس‬ ‫رﻣﺰ‬ ‫ﻳﺄﺧﺬ‬
)
^
(
,
‫ﻋﻠﻰ‬ ‫اﻟﻀﻐﻂ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺮﻣﺰ‬ ‫هﺬا‬ ‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫ﻳﻤﻜﻦ‬
Shift + 6
‫ﻟﻮﺣﺔ‬ ‫ﻓﻲ‬
‫اﻟﻤﻔﺎﺗﻴﺢ‬
,
ً
‫ﻼ‬‫ﻓﻤﺜ‬
12
^
2
=
144
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

15. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺮﺑﻴﻌﻲ‬ ‫اﻟﺠﺬر‬ ‫أﺧﺬ‬
:
‫اﻷﻣﺮ‬ ‫آﺘﺎﺑﺔ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫رﻗﻢ‬ ‫ﻷي‬ ‫اﻟﺘﺮﺑﻴﻌﻲ‬ ‫اﻟﺠﺬر‬ ‫أﺧﺬ‬ ‫ﻳﺘﻢ‬
sqrt
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

16. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺒﺮﻣﺠﺔ‬ ‫أﺛﻨﺎء‬ ‫ﻋﻨﺎوﻳﻦ‬ ‫وﺿﻊ‬
‫ﺑﺮاﻣﺞ‬ ‫ﻓﻲ‬ ‫ﺗﻌﻮدﻧﺎ‬ ‫آﻤﺎ‬
Qbasic
‫و‬
C++
‫اﻟﺒﺮﻣﺠﺔ‬ ‫ﺑﺮاﻣﺞ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜﻴﺮ‬ ‫وﻏﻴﺮهﺎ‬
,
‫ﻟﻤﺎ‬ ‫ﻋﻨﺎوﻳﻦ‬ ‫وﺿﻊ‬ ‫ﻓﻴﺘﻢ‬
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻣﻦ‬ ‫ﻣﺎ‬ ‫ﺟﺰء‬ ‫ﻓﻲ‬ ‫ﺑﻪ‬ ‫ﻧﻘﻮم‬ ‫ﻣﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫ﻓﻲ‬ ‫ﻟﻨﺎ‬ ‫اﻟﻤﺮﺟﻊ‬ ‫ﻣﺜﻞ‬ ‫ﺗﻜﻮن‬ ‫ﺣﻴﺚ‬ ‫ﺑﻪ‬ ‫ﻧﻘﻮم‬
.
‫ﻣﺎ‬ ‫ﻋﻨﻮان‬ ‫ﻟﻮﺿﻊ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻔﻲ‬
,
‫ﻣﺌﻮﻳﺔ‬ ‫ﻋﻼﻣﺔ‬ ‫ﺑﻮﺿﻊ‬ ‫ﻧﺒﺪأ‬ ‫أن‬ ‫ﻣﻦ‬ ‫ﻻﺑﺪ‬
( % )
,
‫ﻧﻜﺘﺐ‬ ‫ﺛﻢ‬
‫ﺑﻌﺪهﺎ‬ ‫ﻣﺎﻧﺮﻳﺪﻩ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻻﺣﻆ‬
‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬ ‫ﻣﺸﻜﻠﺔ‬ ‫ﻓﻬﻨﺎﻟﻚ‬ ‫ﺗﻼﺣﻈﻮن‬ ‫آﻤﺎ‬ ‫وﻟﻜﻦ‬
Workspace
,
‫ﻓﻘﻂ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺁﺧﺮ‬ ‫ﺳﺠﻠﺖ‬ ‫أﻧﻬﺎ‬ ‫ﺣﻴﺚ‬
,
‫رﻣﺰ‬ ‫ﺗﺄﺧﺬ‬ ‫اﻷرﺑﻌﺔ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫آﻞ‬ ‫ﻷن‬ ‫وذﻟﻚ‬
ans
ً
‫ا‬‫رﻣﺰ‬ ‫ﻟﻬﺎ‬ ‫ﻧﺠﻊ‬ ‫ﻟﻢ‬ ‫اﻧﻨﺎ‬ ‫ﺣﻴﺚ‬
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

17. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﺑﺤﺮوف‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﻌﺮﻳﻒ‬ ‫ﻳﺘﻢ‬
,
‫ﻟﻪ‬ ‫اﻟﻤﺴﺘﺨﺪم‬ ‫ﻳﺪﺧﻠﻬﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫اﻟﺤﺮف‬ ‫ﻳﺄﺧﺬ‬ ‫ﺑﺤﻴﺚ‬
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

18. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
ً
‫ﺎ‬‫ﺗﻤﺎﻣ‬ ‫إﻧﺘﻬﺖ‬ ‫ﻗﺪ‬ ‫ﻓﺎﻟﻤﺸﻜﻠﺔ‬ ‫ﺗﺮون‬ ‫آﻤﺎ‬
,
‫ﻣﻌﻴﻦ‬ ‫ﺣﺮف‬ ‫ﻗﻴﻤﺔ‬ ‫آﻞ‬ ‫ﺗﺄﺧﺬ‬ ‫ﺣﻴﺚ‬
.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻤﺸﻜﻠﺔ‬
,
‫ﻗﻴﻤﺔ‬ ‫أدﺧﻠﻨﺎ‬ ‫آﻠﻤﺎ‬ ‫أﻧﻨﺎ‬ ‫هﻮ‬
,
‫ﻣﺸﻜﻠﺔ‬ ‫هﻨﺎﻟﻚ‬ ‫ﺗﻜﻮن‬ ‫ﻧﺘﻴﺠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺣﺼﻠﻨﺎ‬ ‫أو‬
,
‫أن‬ ‫هﻮ‬
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫وآﺬﻟﻚ‬ ‫اﻟﻤﺪﺧﻠﺔ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ﺑﺈﻇﻬﺎر‬ ‫ﻳﻘﻮم‬ ‫اﻟﻤﺎﺗﻼب‬
,
‫آﺒﺮ‬ ‫إﻟﻰ‬ ‫ﻳﺆدي‬ ‫ﻣﻤﺎ‬
‫اﻟﺒﺮﻧﺎﻣ‬
‫ﺑﺴﻴﻂ‬ ‫ﺷﺊ‬ ‫ﻳﺆدي‬ ‫أﻧﻪ‬ ‫ﺣﻴﻦ‬ ‫ﻓﻲ‬ ‫اﻟﻤﻜﺘﻮب‬ ‫ﺞ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻈﻬﻮر‬ ‫ﻣﻦ‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫وآﺬﻟﻚ‬ ‫اﻟﻤﺪﺧﻠﺔ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫أﺧﻔﺎء‬ ‫ﻳﺘﻢ‬
)
ً
‫ﻼ‬‫ﻣﺜ‬ ‫واﻟﺠﻤﻊ‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫إدﺧﺎل‬ ‫ﻋﻤﻠﻴﺔ‬ ‫وﻟﻜﻦ‬
‫اﻟﻤﺴﺘﺨﺪم‬ ‫ﻳﺄﻣﺮﻩ‬ ‫ﻣﺎ‬ ‫ﺑﺘﻨﻔﻴﺬ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫وﻳﻘﻮم‬ ‫ﻃﺒﻴﻌﻲ‬ ‫ﺑﺸﻜﻞ‬ ‫ﺗﺘﻢ‬
(
‫ﻋﻼﻣﺔ‬ ‫وﺿﻊ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬
)
;
(
‫ﺑﻌﺪ‬

19. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻃﻠﺐ‬ ‫ﺑﻌﺪ‬ ‫أو‬ ‫ﻣﺪﺧﻠﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫آﻞ‬
‫ﻣﺎ‬ ‫ﻧﺘﻴﺠﺔ‬
)
ً
‫ﻼ‬‫ﻣﺜ‬ ‫اﻟﺠﻤﻊ‬
(
‫إذا‬ ‫اﻟﻤﺪﺧﻠﺔ‬ ‫اﻟﻘﻴﻢ‬ ‫أو‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫إﻇﻬﺎر‬ ‫وﻳﺘﻢ‬
‫ذﻟﻚ‬ ‫اﻟﻤﺴﺘﺨﺪم‬ ‫ﻃﻠﺐ‬
,
‫اﻟﺮﻣﺰ‬ ‫إﺳﺘﺨﺪام‬ ‫دون‬ ‫اﻟﻤﻄﻠﻮﺑﺔ‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫أو‬ ‫اﻟﻤﺪﺧﻼت‬ ‫ﺣﺮف‬ ‫وﺿﻊ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬
‫اﻟﻤﺬآﻮر‬ ‫اﻟﺮﻣﺰ‬
)
;
(
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫اﻧﻈﺮ‬
‫واﻟﻤﻌﺮوﻓﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫ﻣﺴﺒﻘ‬ ‫اﻟﻤﻌﺮﻓﺔ‬ ‫اﻟﻤﺘﻐﻴﺮات‬ ‫ﺑﻌﺾ‬
:

20. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

21. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺮآﺐ‬ ‫اﻟﻌﺪد‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﻮق‬ ‫اﻟﻜﺘﺎﺑﺔ‬
‫آﺘﺒﻨﺎ‬ ‫إذا‬ ‫أﻧﻪ‬ ‫ﺗﻌﻠﻤﻨﺎ‬
)
i
(
‫اﻟﺘﺎﻟﻲ‬ ‫ﻳﻈﻬﺮ‬ ‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬
‫اﻟﻘﻴﻤﺔ‬ ‫هﺬﻩ‬ ‫ﻓﻮق‬ ‫اﻟﻜﺘﺎﺑﺔ‬ ‫ﻳﻤﻜﻨﻨﺎ‬ ‫آﻤﺎ‬
,
‫ﻗﻴﻤﺘﻪ‬ ‫ﺗﻐﻴﻴﺮ‬ ‫أي‬
,
‫اﻟﺮﻣﺰ‬ ‫ﻟﻬﺬا‬ ‫ﻗﻴﻤﺔ‬ ‫ﺑﻮﺿﻊ‬ ‫ﺳﻨﻘﻮم‬ ‫ﺣﻴﺚ‬
,
‫أﻧﻈﺮ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬
‫واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻤﺪﺧﻠﺔ‬ ‫اﻟﻘﻴﻢ‬ ‫إﻟﻐﺎء‬
‫ﻳﻤﻜ‬
‫واﻟﻨﺘﺎﺋﺞ‬ ‫اﻟﻤﺪﺧﻠﺔ‬ ‫اﻟﻘﻴﻢ‬ ‫ﻣﺴﺢ‬ ‫ﻟﻠﻤﺎﺗﻼب‬ ‫ﻦ‬
)
‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﺗﺴﺠﻴﻞ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬ ‫ﺗﺴﺠﻞ‬ ‫واﻟﺘﻲ‬
(
,
‫دون‬
‫ﺑﻜﺘﺎﺑﺘﻪ‬ ‫ﻗﻤﺖ‬ ‫ﻣﺎ‬ ‫ﻣﺴﺢ‬
,
‫أﻣﺮ‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫وذﻟﻚ‬
Clear
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

22. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫أﻣﺮ‬ ‫ﺗﻨﻔﻴﺬ‬ ‫ﺑﻌﺪ‬ ‫وﻟﻜﻦ‬
Clear
‫ﻟﻠﻤﺎﺗﻼب‬ ً
‫ﺎ‬‫ﻣﺴﺒﻘ‬ ‫ﺑﺘﻌﺮﻳﻔﻬﺎ‬ ‫ﻗﻤﺖ‬ ‫اﻟﺘﻲ‬ ‫اﻟﺤﺮوف‬ ‫ﻣﻦ‬ ‫ﺣﺮف‬ ‫أي‬ ‫ﺑﻮﺿﻊ‬ ‫ﻗﻢ‬ ‫وﻟﻠﺘﺄآﺪ‬
,
‫ان‬ ‫ﺳﺘﻼﺣﻆ‬
‫ا‬
‫اﻵن‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻳﺘﻌﺮف‬ ‫ﻻ‬ ‫ﻟﻤﺎﺗﻼب‬
,
‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫ﻟﻠﻤﺘﻐﻴﺮات‬ ‫اﻟﺠﺰي‬ ‫اﻟﻤﺴﺢ‬ ‫ﻋﻤﻠﻴﺔ‬
:
‫اﻟﺒﺮﻧﺎﻣﺞ‬ ‫ﻟﻜﻞ‬ ‫آﻠﻲ‬ ‫ﻣﺴﺢ‬ ‫ﺑﻌﻤﻠﻴﺔ‬ ‫ﻧﻘﻮم‬ ‫أن‬ ً
‫ﺎ‬‫ﺷﺮﻃ‬ ‫ﻟﻴﺲ‬
,
‫واﺣﺪ‬ ‫ﻟﻤﺘﻐﻴﺮ‬ ‫ﻣﺴﺢ‬ ‫ﻋﻤﻞ‬ ‫اﻟﻤﻤﻜﻦ‬ ‫ﻣﻦ‬ ‫ﺑﻞ‬
‫ﻓﻘﻂ‬
,
‫أﻣﺮ‬ ‫آﺘﺎﺑﺔ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬
Clear
‫اﻟﻤﺘﻐﻴﺮ‬ ‫إﺳﻢ‬ ‫ﺛﻢ‬
,
‫ﻣﻦ‬ ً
‫ﻼ‬‫ﻟﻜ‬ ‫ﻗﻴﻢ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻔﻲ‬
(a) &
(b)
‫اﻟﺼﻮ‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫رة‬

23. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻗﻴﻤﺔ‬ ‫ﺑﻤﺴﺢ‬ ‫ﺳﻨﻘﻮم‬ ‫ﺛﻢ‬
(a)
‫ﻓﻘﻂ‬
,
‫ﺗﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

24. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻷواﻣﺮ‬
‫اﻟﻜﺮام‬ ‫إﺧﻮاﻧﻲ‬
,
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺒﺮﻧﺎﻣﺞ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻷواﻣﺮ‬ ‫ﺑﻌﺾ‬ ‫ﻧﺴﺘﻜﻤﻞ‬
,
‫اﷲ‬ ‫ﺑﺈذن‬ ‫وﺳﻨﺘﻨﺎول‬
‫اﻟﻤﺜﻠﺜﻴﺔ‬ ‫اﻟﺪوال‬
Trigonometric functions
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﻤﺜﻠﺜﻴﺔ‬ ‫اﻟﺪوال‬
Inverse Trigonometric functions
‫اﻟﺰاﺋﺪﻳﺔ‬ ‫اﻟﺪوال‬
Hyperbolic Functions
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﺰاﺋﺪﻳﺔ‬ ‫اﻟﺪوال‬
Inverse Hyperbolic functions
ً
‫ﻻ‬‫أو‬
:
‫اﻟﻤﺜﻠﺜﻴﺔ‬ ‫اﻟﺪوال‬
Trigonometric Functions
Trigonometric Function
Built In Function
Sine
sin
Cosine
cos
Tangent
tan
Secant
sec
Cosecant
csc
Cotangent
cot
‫ﻣﻼﺣﻈﺔ‬
:
‫اﻟﺪاﺋﺮي‬ ‫ﺑﺎﻟﺘﻘﺪﻳﺮ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﺑﻘﻴﺎس‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬
Radian
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻻﺣﻆ‬

25. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺨﺎص‬ ‫اﻟﺠﺰء‬ ‫ﻓﻲ‬ ‫أآﺜﺮ‬ ‫ﺑﺎﻟﺘﻔﺼﻴﻞ‬ ‫اﻟﺠﺰء‬ ‫هﺬا‬ ‫ﺷﺮح‬ ‫وﺳﻴﺘﻢ‬
Plotting 2D
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﻤﺜﻠﺜﻴﺔ‬ ‫اﻟﺪوال‬
:
Built In function Inverse Trigonometric Function
asin Inverse Sine
acos Inverse Cosine
atan Inverse tangent
asec Inverse Secant
acsc Inverse Cosecant
acot Inverse Cotangent
‫ﺗﺎﻣﺔ‬ ‫ﺑﺴﻬﻮﻟﺔ‬ ‫اﻷﺟﺰاء‬ ‫ﺗﻠﻚ‬ ‫ﺣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻗﺎﺑﻠﻴﺔ‬ ‫ﻣﺪى‬ ‫ﻟﺘﺮى‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﻤﺜﻠﺜﻴﺔ‬ ‫اﻟﺪوال‬ ‫ﻟﻜﻞ‬ ‫اﻟﻄﺮﻳﻘﺔ‬ ‫ﺑﻨﻔﺲ‬

26. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺰاﺋ‬ ‫اﻟﺪوال‬
‫ﺪﻳﺔ‬
Hyperbolic functions
Built in functions Inverse Hyperbolic functions
sinh Hyperbolic Sine
Cosh Hyperbolic Cosine
Tanh Hyperbolic Tangent
Sech Hyperbolic Secant
Csch Hyperbolic Cosecant
Coth Hyperbolic Cotangent
‫ﻟﻠﺪو‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﺑﻌﺾ‬
‫اﻟﺰاﺋﺪﻳﺔ‬ ‫ال‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻘﻖ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

27. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫اﻟﻨﺘﻴﺠﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻘﻖ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

28. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http

29. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http

30. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﺰاﺋﺪﻳﺔ‬ ‫اﻟﺪوال‬
Built in function Inverse Hyperbolic Functions
Asinh Inverse hyperbolic Sine
Acosh Inverse hyperbolic Cosine
Atanh Inverse hyperbolic tangent
Asec Inverse hyperbolic secant
Acsc Inverse hyperbolic cosecant
Acot Inverse hyperbolic cotangent
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﺰاﺋﺪﻳﺔ‬ ‫ﻟﻠﺪوال‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻟﻘﻮاﻧﻴﻦ‬ ‫ﺑﻌﺾ‬

31. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬
‫ﺑﺎﻟﻤﺘﻐﻴﺮ‬
(z)
‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫اﻟﻤﻌﺎدﻻت‬ ‫ﻓﻲ‬
‫اﻟﻌﻜﺴﻴﺔ‬ ‫اﻟﺰاﺋﺪﻳﺔ‬ ‫اﻟﺪوال‬
.

32. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﻴﻮم‬ ‫اﷲ‬ ‫ﺑﺈذن‬ ‫ﺳﻨﺘﻨﺎول‬ ‫اﻟﻜﺮام‬ ‫أﺧﻮاﻧﻲ‬
‫اﻷﺳﻴﺔ‬ ‫اﻟﺪوال‬
Exponential Function
‫وﻋﻤﻠﻴﺎﺗﻬﺎ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬
Complex numbers and their Processes
‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫اﻟﻠﻐﺮﺗﻤﺎت‬
Natural Logarithm
‫اﻟﻘﻴﻤ‬
‫اﻟﻤﻄﻠﻘﺔ‬ ‫ﺔ‬
Absolute Value
‫اﻟﺘﻘﺮﻳﺒﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
Approximation Processes
‫اﻷﺳﻴﺔ‬ ‫اﻟﺪاﻟﺔ‬
Exponential Function
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫اﻟﺼﻴﻐﺔ‬ ‫ﺗﺄﺧﺬ‬ ‫اﻷﺳﻴﺔ‬ ‫اﻟﺪاﻟﺔ‬
y
x e
=
‫ﻓﻲ‬ ‫ﻓﺘﺨﺘﺼﺮ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫أﻣﺎ‬
exp
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬
ers
Complex Numb
‫اﻟﺤﻘﻴﻘﻲ‬ ‫ﻟﻸﻋﺪد‬ ‫ﺟﺰء‬ ‫ﺗﻮاﺟﺪ‬ ‫وهﻲ‬ ‫واﺣﺪة‬ ‫ﺻﻴﻐﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺗﺄﺧﺬ‬
Real number
‫اﻟﻌﺪد‬ ‫وﺟﺰء‬
‫اﻟﺘﺨﻴﻠﻲ‬
Imaginary Numbers
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻴﻐﺔ‬ ‫ﻓﻲ‬ ‫وﺗﻜﻮن‬
*
z z y i
= +
‫ﻣﺜﻞ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻓﻲ‬ ‫ﺗﺘﻢ‬ ‫واﻟﺘﻲ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻌﺪﻳﺪ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ‫وﻳﺘﻢ‬
‫اﻟﻌﺪد‬ ‫إﺧﺘﻴﺎر‬
‫ﻓﻘﻂ‬ ‫اﻟﺤﻘﻴﻘﻲ‬
‫ﻓﻘﻂ‬ ‫اﻟﺘﺨﻴﻠﻲ‬ ‫اﻟﻌﺪد‬ ‫إﺧﺘﻴﺎر‬
‫اﻟﺰاوﻳﺔ‬ ‫إﻳﺠﺎد‬
Phase Angle
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫اﻟﺤﺼﻮل‬ ‫وﻳﺘﻢ‬
1 Imaginary number
tan ( )
Real number
angel −
=
‫اﻟﻤﻄﻠﻘﺔ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫إﻳﺠﺎد‬
:
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫اﻟﺤﺼﻮل‬ ‫وﻳﺘﻢ‬
2 2
Absolute Value= X Y
+
‫ﻣﺮآﺒﻴﻦ‬ ‫ﻋﺪدﻳﻦ‬ ‫ﺟﻤﻊ‬
:
‫ﻋﻦ‬ ‫ذﻟﻚ‬ ‫وﻳﺘﻢ‬
‫ﺑﻌﻀﻬﺎ‬ ‫ﻣﻊ‬ ‫اﻟﺤﻘﻴﻘﻴﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺟﻤﻊ‬ ‫ﻃﺮﻳﻖ‬
,
‫اﻷﻋﺪاد‬ ‫وﺟﻤﻊ‬
‫ﺑﻌﻀﻬﺎ‬ ‫ﻣﻊ‬ ‫اﻟﻤﺮآﺒﺔ‬
‫اﻟﻌﻤﻠﻴﺎ‬ ‫ﺗﻠﻚ‬ ‫ﻣﺸﺎهﺪة‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫ت‬

33. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻣﻼﺣﻈﺔ‬
:
‫اﻟﺤﺴﺎﺑﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﺟﻤﻴﻊ‬ ‫ﺗﺘﻢ‬
)
‫وﻏﻴﺮهﺎ‬ ‫واﻟﻄﺮح‬ ‫اﻟﺠﻤﻊ‬
(
ً
‫ﺎ‬‫أﻳﻀ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻋﻠﻰ‬
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻲ‬ ‫رأﻳﻨﺎ‬ ‫آﻤﺎ‬
angle
‫اﻟﻄ‬ ‫زاوﻳﺔ‬ ‫ﻹﻳﺠﺎد‬
‫آﺘﺎﺑﺔ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫ﻮر‬
angle(z)
‫اﻟﻤﺮآﺐ‬ ‫اﻟﻌﺪد‬ ‫رﻣﺰ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﺣﻴﺚ‬
z
‫اﻷﻣﺮ‬ ‫هﺬا‬ ‫ﻓﻲ‬
,
‫وهﻮ‬ ‫ﺁﺧﺮ‬ ‫أﻣﺮ‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫ذﻟﻚ‬ ‫ﺗﻨﻔﻴﺬ‬ ً
‫ﺎ‬‫أﻳﻀ‬ ‫ﻳﻤﻜﻨﻨﺎ‬
atan2

34. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫اﻟﻠﻮﻏﺎرﻳﺘﻤﺎت‬
Natural Logarithm
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫ﻟﻠﻮﻏﺎرﻳﺘﻤﺎت‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﺮﻣﺰ‬
log(x)
‫ﻷﻋ‬ ‫اﻟﺘﻘﺮﻳﺒﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
‫رﻗﻤﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫واﻗﻌﺔ‬ ‫ﺪاد‬
‫ﺻﺤﻴﺤﻴﻦ‬ ‫رﻗﻤﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫واﻗﻊ‬ ‫ﺑﺄﻧﻪ‬ ‫ﻳﻤﺘﺎز‬ ‫ﻋﺸﺮي‬ ‫رﻗﻢ‬ ‫أي‬
,
‫هﺬﻳﻦ‬ ‫أﺣﺪ‬ ‫إﺧﺘﻴﺎر‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺪرة‬ ‫ﻟﻪ‬ ‫ﻓﺎﻟﻤﺎﺗﻼب‬
‫اﻷﻣﺮﻳﻦ‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫اﻟﺮﻗﻤﻴﻦ‬
Ceil
‫اﻷآﺒﺮ‬ ‫اﻟﺮﻗﻢ‬ ‫ﻹﺧﺘﻴﺎر‬
,
‫واﻷﻣﺮ‬
Floor
‫اﻷﺻﻐﺮ‬ ‫اﻟﺮﻗﻢ‬ ‫ﻹﺧﺘﻴﺎر‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

35. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﺑﺈذ‬ ‫وﺳﻨﺘﻨﺎول‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ً
‫ﺎ‬‫ﻣﻌ‬ ‫ﻧﺴﺘﻜﻤﻞ‬
‫اﻟﺘﺎﻟﻲ‬ ‫اﷲ‬ ‫ن‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬
Matrices
‫آﺎﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﻮاﺿﻴﻊ‬ ‫وﻧﺘﻨﺎول‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻣﺎهﻲ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫آﺘﺎﺑﺔ‬ ‫آﻴﻔﻴﺔ‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻓﻲ‬ ‫اﻟﺤﺴﺎﺑﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
‫ﺧﺎﺻﺔ‬ ‫ﻣﺼﻔﻮﻓﺎت‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺤﺪد‬ ‫ﻋﻨﺼﺮ‬ ‫إﺳﺘﺨﺮاج‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ‫ﻣﺎ‬ ‫ﻋﻨﺼﺮ‬ ‫ﺗﻐﻴﻴﺮ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻣﺎهﻲ‬
:
‫واﻟ‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫هﻲ‬
‫وأﻋﻤﺪة‬ ‫ﺻﻔﻮف‬ ‫ﺻﻮرة‬ ‫ﻓﻲ‬ ‫وﺿﻌﻬﺎ‬ ‫ﻳﺘﻢ‬ ‫ﺘﻲ‬
,
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺸﻜﻞ‬ ‫وﺗﺄﺧﺬ‬
‫اﻟﺤﺪود‬ ‫آﺜﻴﺮات‬ ‫ﺣﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫وﺗﺴﺘﺨﺪم‬
Polynomials,
‫اﻟﻤﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺣﻞ‬ ‫وﻓﻲ‬
,
‫ه‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫ﻻﺣﻘ‬ ‫ﺷﺮﺣﻪ‬ ‫ﺳﻴﺘﻢ‬ ‫آﻤﺎ‬
‫اﷲ‬ ‫ﺑﺈذن‬ ‫اﻹﺳﺒﻮع‬ ‫ﺬا‬
.
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫آﺘﺎﺑﺔ‬ ‫آﻴﻔﻴﺔ‬
:
‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫إدﺧﺎل‬ ‫ﻳﺘﻢ‬
,
‫وهﻜﺬا‬ ‫اﻟﺜﺎﻧﻲ‬ ‫ﺛﻢ‬
.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﻣﺜﻞ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫آﺘﺎﺑﺔ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
‫اﻟﻘﻴﻢ‬ ‫إدﺧﺎل‬ ‫ﻗﺒﻞ‬ ‫وﻟﻜﻦ‬
‫اﻟﺘﺎﻟﻴﺔ‬
,
‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫آﺘﺎﺑﺔ‬ ‫ﻳﺘﻢ‬ ‫ﺑﺄﻧﻪ‬ ‫ﻳﻌﻠﻢ‬ ‫أن‬ ‫اﻟﺠﻤﻴﻊ‬ ‫ﻋﻠﻰ‬
,
‫وﻳﺘﻢ‬
‫اﻟﻔﺼﻞ‬
‫ﺑﻔﺎﺻﻠﺔ‬ ‫إﻣﺎ‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫أرﻗﺎم‬ ‫ﺑﻴﻦ‬
Comma (,)
‫ﻣﺴﺎﻓﺔ‬ ‫ﺑﻌﻤﻞ‬ ‫أو‬
Space
‫ﺑﻴﻦ‬
‫اﻷرﻗﺎم‬
,
‫ﺑﻌﺪ‬
‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﻦ‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻓﺼﻞ‬ ‫ﻳﺘﻢ‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻗﻴﻢ‬ ‫إدﺧﺎل‬
‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﺼﻒ‬
)
‫إدﺧ‬ ‫ﺳﻴﺘﻢ‬ ‫اﻟﺬي‬
‫ﺎل‬
‫ﻗﻴﻤﻪ‬
(
‫ﻣﻔﺘﺎح‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻀﻐﻂ‬ ‫إﻣﺎ‬
Enter
‫أو‬
‫اﻟﻤﻨﻘﻮﻃﺔ‬ ‫اﻟﻔﺎﺻﻠﺔ‬ ‫ﺑﺈﺳﺘﺨﺪام‬
Semicolon ( ; ),
‫أﻧﻈﺮ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬

36. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫واﺣﺪ‬ ‫واﻟﺸﻜﻞ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻗﻴﻢ‬ ‫ﻹدﺧﺎل‬ ‫ﻣﺘﻌﺪدة‬ ‫أﺳﺎﻟﻴﺐ‬ ‫ﻧﺮى‬ ‫ﻓﻜﻤﺎ‬
‫اﻟﻄﺮق‬ ‫ﺟﻤﻴﻊ‬ ‫ﻓﻲ‬
.
‫اﻟﻤﺼﻔﻮﻓﺎت؟‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﻢ‬ ‫اﻟﺘﻲ‬ ‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫هﻲ‬ ‫ﻓﻤﺎ‬
1-
‫اﻟﺠﻤﻊ‬
2-
‫اﻟﻄﺮح‬
3-
‫اﻟﻀﺮب‬
4-
‫اﻟﻘﺴﻢ‬
5-
‫اﻷﺳﻴﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬
‫اﻟﺠﻤﻊ‬
:
‫ﻣﺼﻔﻮﻓﺘﻴﻦ‬ ‫ﺟﻤﻊ‬ ‫ﺷﺮط‬ ‫ﻧﺬآﺮ‬ ‫أن‬ ً
‫ﻻ‬‫أو‬ ‫ﻳﺠﺐ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫إﺳﺘﺨﺪام‬ ‫ﺑﺒﺪء‬ ‫اﻟﺸﺮوع‬ ‫ﻓﻲ‬ ‫اﻟﺒﺪء‬ ‫ﻗﺒﻞ‬
.
‫ﻣﺼﻔﻮﻓﺘﻴﻦ‬ ‫ﺟﻤﻊ‬ ‫ﺷﺮط‬
:
‫ﻣﺼﻔﻮﻓﺘﻴﻦ‬ ‫ﻟﺪﻳﻨﺎ‬ ‫أن‬ ‫ﻟﻨﻔﺘﺮض‬
A & B,
‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫ﻧﻔﺲ‬ ‫ﻟﻪ‬ ‫آﻼهﻤﺎ‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫ﺟﻤﻌﻬﻤﺎ‬ ‫ﻓﺸﺮط‬
m,
‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻧﻔﺲ‬ ‫وآﺬﻟﻚ‬
n.
‫واﻷﻋﻤﺪة‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫ﻧﻔﺲ‬ ‫ﻳﺤﻤﻼن‬ ‫ﻷﻧﻬﺎ‬ ‫ﺟﻤﻌﻬﻤﺎ‬ ‫ﻳﻤﻜﻦ‬ ‫اﻟﺘﺎﻟﻴﺘﺎن‬ ‫اﻟﻤﺼﻔﻮﻓﺘﺎن‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬

37. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﺗ‬ ‫آﻴﻒ‬
‫ﻣﺼﻔﻮﻓﺘﻴﻦ‬ ‫ﺟﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺘﻢ‬
:
‫اﻟﻌﻨﺼﺮ‬ ‫ﺑﺠﻤﻊ‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺗﺘﻢ‬
‫ﻓﻲ‬ ‫ﻳﻨﺎﻇﺮﻩ‬ ‫وﻣﺎ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ً
‫ﻼ‬‫ﻣﺜ‬ ‫اﻷول‬ ‫ﻟﻠﺼﻒ‬ ‫اﻷول‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬
‫اﻟﺜﺎﻧﻴﺔ‬
,
‫اﻷول‬ ‫ﻟﻠﺼﻒ‬ ‫اﻷول‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺟﻤﻌﻨﺎ‬ ‫ﻗﺪ‬ ‫ﻧﻜﻮن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
.
‫ﺟﻤﻌﻨﺎ‬ ‫ﻗﺪ‬ ‫ﻧﻜﻮن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
1+7=8
‫ﺟﻤﻊ‬
‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬
:
‫ﻟﻠﺼﻒ‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻧﺠﻤﻊ‬
‫اﻟﻤﺼﻔﻮﻓﻮ‬ ‫ﻓﻲ‬ ‫اﻷول‬
‫وﻣﺎ‬ ‫اﻷوﻟﻰ‬
‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ‫ﻳﻨﺎﻇﺮﻩ‬
,
‫ﺟﻤﻌﻨﺎ‬ ‫ﻗﺪ‬ ‫ﻧﻜﻮن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
2+8=10
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫آﺎﻣﻞ‬ ‫إﺗﻤﺎم‬ ‫ﺣﺘﻰ‬ ‫هﻜﺬا‬ ‫وﻧﺴﺘﻤﺮ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫ﺗﻠﺨﻴﺺ‬ ‫وﻳﻤﻜﻦ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫اﻟﺠﻤﻊ‬
‫اﻟﻤﺼﻔﻮﻓﺘﻴﻦ‬ ‫آﺘﺎﺑﺔ‬ ً
‫ﻻ‬‫أو‬ ‫ﻳﺠﺐ‬
A&B,
ً
‫ﺎ‬‫ﺳﺎﺑﻘ‬ ‫ﺗﻌﻠﻤﻨﺎ‬ ‫آﻤﺎ‬
‫اﻟﺠﻤﻊ‬ ‫رﻣﺰ‬ ‫إﺳﺘﺨﺪام‬ ‫ﺛﻢ‬
(+)
‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﻟﻠﺘﺘﻢ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

38. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻃﺮح‬
‫ﻓﻤﺎ‬
‫اﻟﻤﺼﻔﻮﻓﺎت؟‬ ‫ﻃﺮح‬ ‫ﺷﺮط‬ ‫هﻮ‬
‫اﻟﺠﻤﻊ‬ ‫ﺷﺮط‬ ‫ﻧﻔﺲ‬ ‫هﻲ‬ ‫ﺣﻘﻴﻘﺔ‬
,
‫ﻟﻬﺎ‬ ‫ﻃﺮﺣﻬﺎ‬ ‫أو‬ ‫ﺟﻤﻌﻬﺎ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﺗﻜﻮن‬ ‫أن‬ ‫ﻳﺸﺘﺮط‬ ‫ﺣﻴﺚ‬
‫اﻟﻘﻮة‬ ‫ﻧﻔﺲ‬
‫ﺣﻴﺚ‬
m
‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫هﻲ‬
‫وﺣﻴﺚ‬
n
‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﺧﻲ‬
‫أﻧﻈ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺮ‬

39. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺎﺗﻼب‬ ‫ﺑﺮﻧﺎﻣﺞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻧﻔﺲ‬ ‫ﺑﻌﻤﻞ‬ ‫اﻵن‬ ‫ﻟﻨﻘﻢ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﺿﺮب‬
‫اﻟﻤﺼﻔﻮﻓﺎت؟‬ ‫ﺿﺮب‬ ‫ﺷﺮط‬ ‫هﻮ‬ ‫ﻣﺎ‬
‫اﻷوﻟﻰ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫أﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫هﻮ‬ ‫ﻣﺼﻔﻮﻓﺘﻴﻦ‬ ‫أي‬ ‫ﺿﺮب‬ ‫ﺷﺮط‬
n1
‫اﻟﺼﻔﻮف‬ ‫ﻟﻌﺪد‬ ً
‫ﺎ‬‫ﻣﺴﺎوﻳ‬
‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬
m2

40. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻧﻔﺲ‬ ‫ﺑﺈدﺧﺎل‬ ‫اﻵن‬ ‫ﻟﻨﻘﻮم‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

41. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻗﺴﻤﺔ‬
‫ﻟﻠﻤﺼﻔﻮﻓﺎ‬ ‫اﻟﻘﺴﻤﺔ‬ ‫آﻠﻤﺔ‬ ‫وﺟﻮد‬ ‫ﻣﻦ‬ ‫اﻟﺒﻌﺾ‬ ‫ﻳﺴﺘﻐﺮب‬ ‫ﻗﺪ‬
‫ت‬
,
‫ﻣﻮﺟﻮدة‬ ‫أﻧﻬﺎ‬ ‫اﻟﺤﻘﻴﻘﺔ‬ ‫وﻟﻜﻦ‬
‫وﻣﺴﺘﺨﺪﻣﺔ‬
‫ﻟﻮﺟﻮدهﺎ‬ ‫ﻧﻨﺘﺒﻪ‬ ‫ﻻ‬ ‫وﻟﻜﻨﻨﺎ‬ ‫ﺑﻜﺜﻴﺮة‬
,
‫ﺑﺤﻞ‬ ‫ﻧﻘﻮم‬ ‫اﻟﻘﺴﻤﺔ‬ ‫ﻓﺒﻬﺬﻩ‬
ً
‫ﺎ‬‫ﻻﺣﻘ‬ ‫ﺷﺮﺣﻬﺎ‬ ‫ﺳﻴﺘﻢ‬ ‫واﻟﺘﻲ‬ ‫اﻟﻤﻌﺎدﻻت‬
‫اﷲ‬ ‫ﺑﺈذن‬
‫اﻟﻘﺴﻤﺔ‬ ‫ﻋﻤﻞ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻟﻜﻢ‬ ‫أﺷﺮح‬ ‫أن‬ ‫وﻗﺒﻞ‬
,
‫اﻟﺤﺪود‬ ‫آﺜﻴﺮة‬ ‫اﻟﻤﻌﺎدﻻت‬ ‫ﺣﻞ‬ ‫آﻴﻔﻴﺔ‬ ‫ﺷﺮح‬ ‫ﻣﻦ‬ ‫ﻻﺑﺪ‬
‫آﺎﻵﺗﻲ‬ ‫ﻣﻌﺎدﻟﺘﺎن‬ ‫ﻟﺪﻳﻨﺎ‬ ‫أن‬ ‫ﻟﻨﻔﺘﺮض‬
‫اﻟﻨﺎﺗﺞ‬ ‫ﻟﻴﻜﻮن‬ ‫ﺣﻠﻬﻤﺎ‬ ‫ﻳﻤﻜﻦ‬ ‫اﻟﻤﻌﺎدﻟﺘﺎن‬ ‫وآﻠﺘﺎ‬
X=-2
Y=3
‫ذﻟﻚ؟‬ ‫ﻳﺘﻢ‬ ‫ﻓﻜﻴﻒ‬
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫ﺻﻮرة‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﺎدﻟﺘﺎن‬ ‫وﺿﻊ‬ ‫ﻳﻤﻜﻦ‬
‫اﻟﻤﻌﺎدﻟﺘﺎن‬ ‫ﻟﺤﻞ‬ ‫ﻃﺮﻳﻘﺘﺎن‬ ‫هﻨﺎﻟﻚ‬ ‫أن‬ ‫ﻧﺬآﺮ‬ ‫وهﻨﺎ‬
1-
‫اﻟﺤﺬف‬ ‫ﻃﺮﻳﻘﺔ‬
2-
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻗﺴﻤﺔ‬
‫اﻟﺤﺬف‬ ‫ﻃﺮﻳﻘﺔ‬ ً
‫ﺎ‬‫ﺳﺮﻳﻌ‬ ‫وﺳﺄذآﺮ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻗﺴﻤﺔ‬ ‫هﻲ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﻄﺮﻳﻘﺔ‬ ‫أﻣﺎ‬
‫أﺧﺮى‬ ‫ﻣﺮة‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫إﻟﻰ‬ ‫ﻟﻨﻌﻮد‬

42. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻴﻐﺔ‬ ‫ﻓﻲ‬ ‫ﻧﻀﻌﻬﺎ‬ ‫أن‬ ‫ﻳﻤﻜﻨﻨﺎ‬ ‫أﻧﻪ‬ ‫ﻧﺠﺪ‬
‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫أﺟﻞ‬ ‫ﻣﻦ‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
X
‫ﻗﺴﻤﺔ‬ ‫ﻳﺠﺐ‬
A
‫ﻋﻠﻰ‬
B,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
‫ﺗﻌﻨﻲ‬ ‫ﻣﺎذا‬ ‫وﻟﻜﻦ‬
‫اﻷﻋﺪاد؟‬ ‫وﻟﻴﺴﺖ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻧﺎﺣﻴﺔ‬ ‫ﻣﻦ‬
‫اﻟﻤﺼﻔﻮﻓ‬ ‫ﻗﺴﻤﺔ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬ ‫وهﺬا‬
‫ﺎت‬
‫إﻳﺠﺎد‬ ‫ﻋﻨﺪ‬ ‫ﻳﺸﺘﺮط‬ ‫وﻟﻜﻦ‬
inv
‫ﻣﺮﺑﻌﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﺗﻜﻮن‬ ‫أن‬
)
‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻳﺴﺎوي‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫أي‬
)
‫ﻗﻴﻤﺔ‬ ‫إﻳﺠﺎد‬ ‫ﻳﻤﻜﻦ‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
X & Y
‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬ ‫وﺿﻊ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬
‫اﻟﺘﺎﻟﻴﺔ‬
,
‫ﻓﻲ‬ ‫اﻷﺧﺬ‬ ‫ﻣﻊ‬
‫اﻟﻤﺼﻔﻮﻓﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻀﺮب‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺷﺮط‬ ‫ﺗﺘﻮﻓﺮ‬ ‫أن‬ ‫اﻹﻋﺘﺒﺎر‬

43. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫ﻗﻤﻨﺎ‬ ‫ﻓﺈذا‬

44. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫واﻟﻤﺘﺠﻬﺎت‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
‫واﻟﻤﺼﻔﻮﻓﺎت؟‬ ‫اﻟﻤﺘﺠﻬﺎت‬ ‫ﺑﻴﻦ‬ ‫اﻟﻔﺮق‬ ‫ﻣﺎ‬
‫واﺣﺪ‬ ‫ﺑﻌﻤﻮد‬ ‫إﻣﺎ‬ ‫وﻟﻜﻦ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫هﻲ‬ ‫اﻟﻤﺘﺠﻬﺎت‬
Column Vector
‫واﺣﺪ‬ ‫ﺻﻒ‬ ‫أو‬
Row Vector
‫ﺻﻔﻲ‬ ‫ﻟﻤﺘﺠﻪ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
‫ﻟﻤﺘﺠﻪ‬ ‫ﺻﻮرة‬ ‫وهﺬﻩ‬
‫ﻋﻤﻮدي‬
‫واﺣﺪ‬ ‫ﻋﻤﻮد‬ ‫أو‬ ‫واﺣﺪ‬ ‫ﺻﻒ‬ ‫ﻋﻦ‬ ‫وأﻋﻤﺪﺗﻬﺎ‬ ‫ﺻﻔﻮﻓﻬﺎ‬ ‫ﻋﺪد‬ ‫ﻳﺰﻳﺪ‬ ‫اﻟﺘﻲ‬ ‫ﻓﻬﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫أﻣﺎ‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﺛﻢ‬ ً
‫ﻻ‬‫أو‬ ‫اﻟﻤﺘﺠﻬﺎت‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﻢ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫وﺳﻨﺘﻨﺎول‬
‫اﻟﺸﺎﺋ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻣﺎهﻲ‬
‫اﻟﻤﺘﺠﻬﺎت؟‬ ‫ﻋﻠﻰ‬ ‫ﻌﺔ‬
1-
‫اﻟﻤﺘﺠﻪ‬ ‫ﻃﻮل‬
2-
‫ﻋﻨﺼﺮ‬ ‫إﺿﺎﻓﺔ‬
3-
‫ﻋﻨﺼﺮ‬ ‫إﺳﺘﺒﺪال‬
4-
‫ﻋﻨﺼﺮ‬ ‫ﺣﺬف‬ ‫ﻋﻤﻠﻴﺔ‬
5-
‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬
6-
‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬ ‫ﻧﺪاء‬
7-
‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
8-
‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
9-
‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫إﻳﺠﺎد‬
‫اﷲ‬ ‫ﺑﺈذن‬ ‫ﺑﺎﻟﺘﻔﺼﻴﻞ‬ ‫ﻣﻨﻬﺎ‬ ‫آﻞ‬ ‫وﺳﻨﺘﻨﺎول‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫اﻟﺸﺎﺋﻌﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫هﻲ‬ ‫هﺬﻩ‬

45. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ا‬
‫اﻟﻤﺘﺠﻬﺎت‬ ‫ﻋﻠﻰ‬ ‫ﻟﻌﻤﻠﻴﺎت‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺪى‬ ‫ﺻﻔﻲ‬ ‫ﻣﺘﺠﻪ‬ ‫ﺑﺘﻌﺮﻳﻒ‬ ‫ﻟﻨﻘﻮم‬
‫وهﻲ‬ ‫اﻷوﻟﻰ‬ ‫ﺑﺎﻟﻌﻤﻠﻴﺔ‬ ‫ﻧﻘﻮم‬ ‫واﻵن‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻃﻮل‬
‫ﻋﻨﺼﺮ‬ ‫إﺿﺎﻓﺔ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻋﻤﻮدي‬ ‫ﻣﺘﺠﻪ‬ ‫ﺑﻮﺿﻊ‬ ‫ﻟﻨﻘﻮم‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
‫واﺿﺢ‬ ‫هﻮ‬ ‫آﻤﺎ‬
,
‫ا‬ ‫ﻋﺪد‬ ‫أن‬
‫هﻮ‬ ‫اﻟﻤﺘﺠﻪ‬ ‫هﺬا‬ ‫ﻓﻲ‬ ‫اﻟﻤﻮﺟﻮدة‬ ‫ﻟﻌﻨﺎﺻﺮ‬
10
,
‫ﻗﻢ‬ ‫وﻟﻠﺘﺄآﺪ‬
‫اﻷﻣﺮ‬ ‫ﺑﻌﻤﻞ‬
length
‫ﻟﻠﻤﺎﺗﻼب‬ ‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻓﻲ‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

46. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺮﻗﻢ‬ ‫إﺿﺎﻓﺔ‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻘﻞ‬
120
‫اﻟﺤ‬ ‫اﻟﺨﺎﻧﺔ‬ ‫ﻓﻲ‬
‫ﻋﺸﺮة‬ ‫ﺎدﻳﺔ‬
,
‫اﻟﻌﺎﺷﺮة‬ ‫ﻟﻠﺨﺎﻧﺔ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺨﺎﻧﺔ‬ ‫أي‬
,
‫أﻧﻈﺮ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬
‫ﻣﻼﺣﻈﺔ‬
:
‫اﻟﺮﻗﻢ‬ ‫إﺿﺎﻓﺔ‬ ‫ﺗﻤﺖ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻲ‬
120
‫اﻟﺨﺎﻧﺔ‬ ‫إﻟﻰ‬
11
,
‫إذا‬ ‫ﻓﻤﺎذا‬
‫رﻗﻢ‬ ‫ﺑﺈﺿﺎﻓﺔ‬ ‫ﻗﻤﻨﺎ‬
‫و‬ ‫ﺟﺪﻳﺪ‬
‫رﻗﻢ‬ ‫اﻟﺨﺎﻧﺔ‬ ‫ﻓﻲ‬ ‫ﻟﻜﻦ‬
13
,
‫اﻟﺨﺎﻧﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺳﺘﻜﻮن‬ ‫ﻓﻤﺎذا‬
12
‫ﻟﻬﺎ‬ ‫ﻋﻨﺼﺮ‬ ‫أي‬ ‫إﺿﺎﻓﺔ‬ ‫ﻳﺘﻢ‬ ‫ﻟﻢ‬ ‫اﻟﺘﻲ‬
,

47. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫ﻣﺘﺘﺎﻟﻲ‬ ‫ﻋﻨﺼﺮ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫إﺿﺎﻓﺔ‬
‫ﻣﺠﻤﻮﻋﺔ‬ ‫إﺿﺎﻓﺔ‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻔﺘﺮض‬
‫اﻟﺨﺎﻧﺎت‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﻣﻦ‬
11
‫و‬
12
‫و‬
13
‫ﻣﻦ‬ ً
‫ﻻ‬‫ﺑﺪ‬ ‫وﻳﻤﻜﻦ‬
‫ﺣﺪى‬ ‫ﻋﻠﻰ‬ ‫رﻗﻢ‬ ‫آﻞ‬ ‫إدﺧﺎل‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬

48. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻟﻠﻮﻗﺖ‬ ً
‫ا‬‫ﻣﺴﺘﻨﻔﺬ‬ ‫ذﻟﻚ‬ ‫ﻳﺒﺪوا‬ ‫ﻗﺪ‬ ‫وﻟﻜﻦ‬
,
‫إدﺧﺎل‬ ‫ﺗﻢ‬ ‫إذا‬
100
‫رﻗﻢ‬
‫أو‬ ‫ﻣﺘﺘﺎﻟﻲ‬
1000
‫رﻗﻢ‬
,
‫اﻟﻌﻤﻞ؟‬ ‫ﻓﻤﺎ‬
‫اﻟﻤﺘﺘﺎﻟﻴﺔ‬ ‫اﻷرﻗﺎم‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺗﻀﻴﻒ‬ ‫أن‬ ‫أردت‬ ‫إذا‬ ‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫هﻨﺎﻟﻚ‬
‫ﻣﻦ‬ ‫اﻟﻤﺘﺘﺎﻟﻴﺔ‬ ‫اﻷرﻗﺎم‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻧﺬآﺮ‬ ‫أن‬ ‫ﻧﺮﻳﺪ‬ ‫ﻋﻨﺪﻣﺎ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
1
‫إﻟﻰ‬
10
‫اﻟﺘﺎﻟﻲ‬ ‫ﻧﻜﺘﺐ‬
1:10
‫ﻣﻦ‬ ‫اﻟﻤﺘﺘﺎﻟﻴﺔ‬ ‫اﻷرﻗﺎم‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫آﺘﺎﺑﺔ‬ ‫ﻧﺮﻳﺪ‬ ‫وﻋﻨﺪﻣﺎ‬
10
‫إﻟﻰ‬
1200
‫ﻧﻜﺘﺐ‬
10:1200
‫ﻣﻦ‬ ‫اﻟﻤﺘﺘﺎﻟﻴﺔ‬ ‫اﻷرﻗﺎم‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫آﺘﺎﺑﺔ‬ ‫أردﻧﺎ‬ ‫إذا‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
11
‫إﻟﻰ‬
13
‫ﻧﻜﺘﺐ‬ ‫ﻣﺜﺎﻟﻨﺎ‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
11:13
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫اﻟﻜﺘﺎﺑﺔ‬ ‫ﺗﻜﻮن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬

49. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻋﻨﺼﺮ‬ ‫إﺳﺘﺒﺪال‬
‫ﺷﺮوط‬ ‫ﻋﺪة‬ ‫ﺗﺘﻄﻠﺐ‬ ‫ﻋﻨﺼﺮ‬ ‫إﺳﺘﺒﺪال‬ ‫ﻋﻤﻠﻴﺔ‬
1-
‫ﺑﺎﻟﻔﻌﻞ‬ ً
‫ا‬‫ﻣﻮﺟﻮد‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻳﻜﻮن‬ ‫أن‬
2-
‫اﻟﻌﻨﺼﺮ‬ ‫هﺬا‬ ‫ﻣﻜﺎن‬ ‫ﺗﺤﺪد‬ ‫أن‬
‫اﻟﺮﻗﻢ‬ ‫ﻣﻦ‬ ً
‫ﻻ‬‫ﺑﺪ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺗﺴﺘﺒﺪل‬ ‫أن‬ ‫أردﻧﺎ‬ ‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻔﻲ‬
3
‫اﻟﺮﻗﻢ‬ ‫إﻟﻰ‬
15
‫اﻟﺘﺎﻟﻲ‬ ‫آﺘﺎﺑﺔ‬ ‫هﻮ‬ ‫ﻓﻌﻠﻪ‬ ‫ﻋﻠﻴﻨﺎ‬ ‫ﻣﺎ‬ ‫آﻞ‬
A(3)=15
‫ﺣﻴﺚ‬
A
‫اﻟ‬ ‫ﻳﺤﺘﻮى‬ ‫اﻟﺬي‬ ‫اﻟﻤﺘﺠﻪ‬ ‫هﻲ‬
‫ﺗﻐﻴﻴﺮﻩ‬ ‫ﺗﺮﻳﺪ‬ ‫اﻟﺬي‬ ‫ﻌﻨﺼﺮ‬

50. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إﺳﺘﺒﺪال‬
‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إﺿﺎﻓﺔ‬ ‫آﻴﻔﻴﺔ‬ ‫ﺷﺮﺣﻨﺎ‬ ‫آﻤﺎ‬
,
‫آﻤﺎ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺑﺈﺳﺘﺒﺪال‬ ‫ﺳﻨﻘﻮم‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﻲ‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻣﻦ‬ ‫ﻋﻨﺼﺮ‬ ‫ﺣﺬف‬
‫اﻟﺘﺎﻟﻴﺎن‬ ‫اﻟﺸﺮﻃﺎن‬ ‫ﻳﺘﻮﻓﺮ‬ ‫أن‬ ‫ﻳﺠﺐ‬ ‫اﻟﻤﺘﺠﻪ‬ ‫ﻣﻦ‬ ‫ﻋﻨﺼﺮ‬ ‫ﺑﺤﺬف‬ ‫ﻟﺘﻘﻮم‬
1-
‫ﺣﺬﻓﻪ‬ ‫ﺗﺮﻳﺪ‬ ‫اﻟﺬي‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺗﺤﺪﻳﺪ‬
2-
‫ﻣﺮﺑﻌﺔ‬ ‫أﻗﻮاص‬ ‫وﺿﻊ‬
Square Brackets
‫رﻗﻢ‬ ‫أي‬ ‫ﻣﻦ‬ ‫ﺧﺎﻟﻴﺔ‬

51. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻌﺎﺷﺮة‬ ‫اﻟﺨﺎﻧﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺣﺬف‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻲ‬ ‫ﻓﺎﻟﻤﺜﺎل‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬
‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺣﺬف‬
‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻟﺤﺬف‬
,
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫أﻧﻈﺮ‬

52. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻣﻦ‬ ‫ﻣﻜﺎن‬ ‫أي‬ ‫ﻓﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫هﻮ‬ ‫ﺑﻪ‬ ‫اﻟﻤﻘﺼﻮد‬ ‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬
‫اﻟﺘﺎﻟﻲ‬ ‫آﺘﺎﺑﺔ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ذﻟﻚ‬ ‫وﻳﻤﻜﻦ‬
‫ﻋﻨﺼﺮ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫ﻧﺪاء‬
‫ﻣﺘﺠﻪ‬ ‫ﻣﻦ‬ ‫ﻣﺤﺪدة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻗﻴﻢ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬
,
‫اﻷواﻣﺮ‬ ‫ﻧﺎﻓﺬة‬ ‫ﻋﻠﻰ‬ ‫اﻵﺗﻲ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻗﻢ‬
Command Window

53. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺘﺠﻪ‬ ‫ﻓﻲ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
‫ﻣﺘﺠﻪ‬ ‫ﻓﻲ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻹﻳﺠﺎد‬
,
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫ﻳﺘﻢ‬
max,
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫إﻳﺘﺨﺪاﻣﻪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﺣﻴﺚ‬
‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬
‫ﻓﻲ‬ ‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
‫اﻟﻤﺘﺠﻪ‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻓﻲ‬ ‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻹﻳﺠﺎد‬
,
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫ﻳﺠﺐ‬
min
‫وهﻲ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻟﺪى‬ ‫إﺧﺘﺼﺎر‬ ‫وهﻲ‬
‫ﻟﻜﻠﻤﺔ‬ ‫إﺧﺘﺼﺎر‬
minimum
‫اﻷﻗﻞ‬ ‫أي‬
‫اﻵﺗﻲ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻗﻢ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺠﻪ‬ ‫داﺧﻞ‬ ‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﺪد‬ ‫وﻹﻳﺠﺎد‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮع‬ ‫إﻳﺠﺎد‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺟﻤﻴﻊ‬ ‫ﺟﻤﻊ‬ ‫ﻳﻤﻜﻦ‬
,
‫اﻷﻣﺮ‬ ‫ﺑﺈﺳﺘﺨﺪام‬
sum
‫ﻃﺮﻳﻘﺔ‬ ‫ﻳﺄﺧﺬ‬ ‫أن‬ ‫ﻻﺑﺪ‬ ‫اﻷﻣﺮ‬ ‫هﺬا‬ ‫أن‬ ‫ﺣﻴﺚ‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﺑﺎﻟﺼﻮرة‬ ‫ﻳﻨﻔﺬ‬ ‫أن‬ ‫ﻓﻴﺠﺐ‬ ‫ﺗﻨﻔﻴﺬﻩ‬ ‫ﻓﻲ‬
‫اﻵن‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻣﺜﺎل‬ ‫ﺑﻌﻤﻞ‬ ‫وﻓﺎﻟﻨﻘﻮم‬

54. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺘﺠﻪ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫إﻳﺠﺎد‬
‫اﻟﻤﺘﺠﻪ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﺧﺎﺻﻴﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻮﻓﺮ‬
,
‫اﻷﻣﺮ‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫وذﻟﻚ‬
prod
‫إﺧﺘﺼﺎر‬ ‫وهﻮ‬
product
‫آﺘﺎﺑﺘﻪ‬ ‫ﻓﻲ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻮرة‬ ‫اﻷﻣﺮ‬ ‫هﺬا‬ ‫ﻳﺄﺧﺬ‬ ‫أن‬ ‫وﻳﺠﺐ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫ﺗﻄﺒﻴﻘﻴ‬ ً
‫ﻻ‬‫ﻣﺜﺎ‬ ‫ﻟﻨﺄﺧﺬ‬ ‫واﻵن‬

55. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫أﻧﻮاع‬ ‫ﺗﻌﺮﻳﻒ‬ ‫ﻳﺠﺐ‬ ً
‫ﻻ‬‫أو‬
,
‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻣﻦ‬ ‫ﻧﻮﻋﺎن‬ ‫ﻓﻬﻨﺎﻟﻚ‬
1-
‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﻴﺮ‬ ‫ﻣﺼﻔﻮﻓﺔ‬
2-
‫ﻣﺮﺑﻌﺔ‬ ‫أو‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻣﺼﻔﻮﻓﺔ‬
‫ﻓﻬﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺎت‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﻢ‬ ‫ﺳﻮف‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫أﻣﺎ‬
1-
‫اﻟﻤﺘﺠﻪ‬ ‫ﻃﻮل‬
2-
‫ﻋﻨﺼﺮ‬ ‫إﺿﺎﻓﺔ‬
3-
‫ﻋﻨ‬ ‫إﺳﺘﺒﺪال‬
‫ﺼﺮ‬
4-
‫ﺑﺄآﻤﻠﻪ‬ ‫ﻋﻤﻮد‬ ‫أو‬ ‫ﺻﻒ‬ ‫ﺣﺬف‬ ‫ﻋﻤﻠﻴﺔ‬
5-
‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬
6-
‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬ ‫ﻧﺪاء‬
7-
‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
8-
‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
9-
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮع‬ ‫إﻳﺠﺎد‬
10-
‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫إﻳﺠﺎد‬
11-
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻗﻄﺮ‬ ‫إﻳﺠﺎد‬
Diagonal
12-
‫اﻟﺴﺤﺮﻳﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬

56. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﺣﺠﻢ‬ ‫إﻳﺠﺎد‬
‫اﻟﻤﺼ‬ ‫ﺣﺠﻢ‬ ‫ﻹﻳﺠﺎد‬
‫ﻟﻤﺼﻔﻮﻓﺔ‬ ‫واﻷﻋﻤﺪة‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫ﻹﻳﺠﺎد‬ ‫ﻧﻘﻮل‬ ‫دﻋﻮﻧﺎ‬ ‫أو‬ ‫ﻔﻮﻓﺔ‬
,
‫إﺳﺘﺨﺪام‬ ‫ﻳﺠﺐ‬
‫اﻷﻣﺮ‬
size,
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫ﻳﺼﻠﺢ‬ ‫ﻻ‬ ‫ﺣﻴﺚ‬
length,
‫ﻓﺄﻣﺮ‬
length
‫ﻓﻲ‬ ‫وﻟﻴﺲ‬ ‫اﻟﻤﺘﺠﻬﺎت‬ ‫ﻓﻲ‬ ‫ﻳﺴﺘﺨﺪم‬
‫اﻟﻤﺼﻔﻮﻓﺎت‬
,
‫ﺑﻌﻤﻞ‬ ‫ﻧﻘﻮم‬ ‫دﻋﻮﻧﺎ‬ ‫اﻷﻣﺮ‬ ‫وﻟﺘﻮﺿﻴﺢ‬
‫اﻷﻣﺮ‬ ‫هﺬا‬ ‫ﻟﺸﺮح‬ ‫ﻣﺒﺴﻂ‬ ‫ﻣﺜﺎل‬
,
‫ﺑﻌﻤﻞ‬ ‫ﻟﻨﻘﻮم‬ ً
‫ﻻ‬‫أو‬
‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﻴﺮ‬ ‫ﻣﺼﻔﻮﻓﺔ‬
)
‫أن‬ ‫أي‬
‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻳﺴﺎوي‬ ‫ﻻ‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬
(
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
‫اﻷﻣﺮ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫ﻟﻨﻘﻮم‬ ‫واﻵ‬
size
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﺣﺠﻢ‬ ‫ﻟﻤﻌﺮﻓﺔ‬
‫ﻓﻘﻂ‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫ﻧﻌﺮف‬ ‫أن‬ ‫أردﻧﺎ‬ ‫إذا‬ ‫أﻣﺎ‬
‫اﻵﺗﻲ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻧﻘﻮم‬
‫ﻓﻘﻂ‬ ‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻧﻌﺮف‬ ‫أن‬ ‫أردﻧﺎ‬ ‫إذا‬ ‫أﻣﺎ‬
‫اﻟﺘﺎ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫ﻧﻘﻮم‬
‫ﻟﻲ‬

57. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫إﻟﻰ‬ ‫ﻋﻨﺼﺮ‬ ‫إﺿﺎﻓﺔ‬
‫اﻟﻤﺎﺗﻼب‬ ‫داﺧﻞ‬ ً
‫ا‬‫ﺟﺪ‬ ‫اﻟﻬﺎﻣﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻣﻦ‬ ‫هﻲ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪة‬ ‫أو‬ ‫ﻋﻨﺼﺮ‬ ‫إﺿﺎﻓﺔ‬ ‫ﻋﻤﻠﻴﺔ‬
,
‫ﻧﻘﻮم‬ ً
‫ﺎ‬‫وداﺋﻤ‬
‫آﻤﺎ‬ ‫اﻟﻤﺘﻘﺪﻣﺔ‬ ‫اﻟﺒﺮاﻣﺞ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜﻴﺮ‬ ‫ﻓﻲ‬ ‫ﺑﺈﺳﺘﺨﺪاﻣﻬﺎ‬
‫ﻓﻴﻤﺎ‬ ‫ﺳﻴﺘﻀﺢ‬
‫ﺑﻌﺪ‬
,
‫أن‬ ‫ﻳﺠﺐ‬ ‫اﻷﻣﺮ‬ ‫ذﻟﻚ‬ ‫وﻟﺘﻮﺿﻴﺢ‬
‫اﻟﻔﻬﻢ‬ ‫ﻣﺮﺣﻠﺔ‬ ‫ﺗﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫ﻣﺜﺎل‬ ‫ﺑﺈﻋﻄﺎء‬ ‫ﻧﻘﻮم‬
‫ﻟﻬﺎ‬ ‫اﻟﺘﺎم‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫ﺑﺘﻌﺮﻳﻒ‬ ً
‫ﻻ‬‫أو‬ ‫ﻟﻨﻘﻮم‬
‫ﺑﻮﺿﻊ‬ ‫ﻧﻘﻮم‬ ‫أن‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻔﺘﺮض‬
‫رﻗﻢ‬
42
‫اﻟﺨﺎﻣﺲ‬ ‫واﻟﻌﻤﻮد‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﺼﻒ‬ ‫ﻓﻲ‬
,
‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫ﻧﻘﻮم‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬
‫اﻟﺨﺎﻣﺲ‬ ‫ﻟﻠﻌﻤﻮد‬ ‫اﻟﺜﺎﻟﺚ‬ ‫واﻟﺼﻒ‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻓﺈن‬ ‫ﺗﻼﺣﻆ‬ ‫آﻤﺎ‬
,
‫ﺑﻬﻤﺎ‬ ‫ﻗﻴﻢ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﻟﻢ‬
,
‫ﻗﺎم‬ ‫ﻟﺬﻟﻚ‬
‫اﻟﻤﺎﺗ‬
ً
‫ا‬‫ﺻﻔﺮ‬ ‫ﺑﺈﻓﺘﺮاﺿﻬﻤﺎ‬ ‫ﻼب‬
.
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﺜﺎل‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫ذﻟﻚ‬ ‫إﻳﻀﺎح‬ ‫ﻳﻤﻜﻦ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ؟‬ ‫ﻓﻲ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪة‬ ‫إﺿﺎﻓﺔ‬ ‫أردﻧﺎ‬ ‫إذا‬ ‫ﻓﻤﺎذا‬
‫اﻷﻋﺪاد‬ ‫إﺿﺎﻓﺔ‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻘﻮم‬
31
‫و‬
54
‫و‬
13
‫و‬
11
‫واﻟﻌﻤﻮد‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺼﻒ‬ ‫ﻓﻲ‬
‫و‬ ‫واﻟﺜﺎﻟﺚ‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻷول‬
‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺮاﺑﻊ‬
,
‫اﻟﻤﺎﺗﻼب‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ذﻟﻚ‬ ‫ﻳﻤﻜﻦ‬
‫اﻟﺘﺎﻟ‬ ‫ﺑﺎﻟﺸﻜﻞ‬
‫ﻲ‬

58. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﻋﻨﺼﺮ‬ ‫إﺳﺘﺒﺪال‬
‫إﺳﺘﺨﺪاﻣﻬﺎ‬ ‫ﻳﺘﻢ‬ ‫ﻣﺎ‬ ً
‫ا‬‫ﻧﺎدر‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫هﺬﻩ‬ ‫ﺗﻜﻮن‬ ‫ﻗﺪ‬
,
ً
‫ا‬‫ﺟﺪ‬ ‫هﺎﻣﺔ‬ ‫وﻟﻜﻨﻬﺎ‬
,
‫ﺗﻮﻓﺮ‬ ‫ﺣﻴﺚ‬
‫إﺳﺘﺒﺪال‬ ‫إﻣﻜﺎﻧﻴﺔ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫داﺧﻞ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪة‬ ‫أو‬ ‫ﻋﻨﺼﺮ‬
,
‫اﻟﺨﺎﺻﻴﺔ‬ ‫هﺬﻩ‬ ‫وﻟﺘﻮﺿﻴﺢ‬
,
‫ذآﺮﻧﺎ‬ ‫آﻤﺎ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫ﺑﺘﻌﺮﻳﻒ‬ ‫ﺳﻨﻘﻮم‬
ً
‫ﺎ‬‫ﻣﺴﺒﻘ‬
‫ﺻﻔﺮ‬ ‫اﻟﺮﻗﻢ‬ ‫إﻟﻰ‬ ‫اﻷول‬ ‫واﻟﻌﻤﻮد‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺼﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺑﺈﺳﺘﺒﺪال‬ ‫وﻟﻨﻘﻮم‬
‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪة‬ ‫إﺳﺘﺒﺪال‬ ‫أردﻧﺎ‬ ‫وإذا‬
,
‫ﺑﺴﻴﻂ‬ ‫ﻣﺜﺎل‬ ‫ﺑﻌﻤﻞ‬ ‫ذﻟﻚ‬ ‫ﻳﻤﻜﻦ‬
,
‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫ﻟﻨﻘﻞ‬
‫اﻟﺼﻒ‬ ‫ﻧﺴﺘﺒﺪل‬ ‫أن‬
‫ﺻﻔﺮ‬ ‫ﺑﻘﻴﻤﺔ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫إﻟﻰ‬ ‫اﻷول‬ ‫ﻣﻦ‬ ‫واﻟﻌﻤﻮدﻳﻦ‬ ‫واﻟﺜﺎﻧﻲ‬ ‫اﻷول‬
‫ﻋﻨﺼﺮ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫ﺣﺬف‬
‫ﻣﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ‫ﻓﻘﻂ‬ ‫واﺣﺪ‬ ‫ﻟﻌﻨﺼﺮ‬ ‫ﺣﺬف‬ ‫ﺑﻌﻤﻠﻴﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻻﻳﻘﻮم‬
,
‫ﻏﻴﺮ‬ ‫ﻣﻦ‬ ‫أﻧﻪ‬ ‫ﺣﻴﺚ‬
‫ﺣﺬف‬ ‫اﻟﻤﻌﻘﻮل‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫داﺧﻞ‬ ‫ﻣﻦ‬ ‫ﻋﻨﺼﺮ‬
,
‫ﻗﻴﻢ‬ ‫ﺑﻬﻢ‬ ‫واﻟﻌﻤﻮد‬ ‫اﻟﺼﻒ‬ ‫وﺑﻘﻴﺔ‬
,
‫إذا‬ ‫وﻟﻜﻦ‬
‫ﺻﻒ‬ ‫ﺑﺤﺬف‬ ‫ﺗﻘﻮم‬ ‫أن‬ ‫أردت‬
‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﻌﻤﻞ‬ ‫ذﻟﻚ‬ ‫ﻓﻴﻤﻜﻦ‬ ‫آﺎﻣﻞ‬ ‫ﻋﻤﻮد‬ ‫أو‬ ‫آﺎﻣﻞ‬
ً
‫ﻻ‬‫أو‬ ‫ﻧﻘﻮم‬
‫ﻋﻠﻴﻬﺎ‬ ‫ﻟﻠﻌﻤﻞ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫ﺑﻌﻤﻞ‬

59. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫آﻠﻪ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺼﻒ‬ ‫ﺣﺬف‬ ‫ﻧﺮﻳﺪ‬ ‫اﻧﻨﺎ‬ ‫ﻟﻨﻘﻞ‬
‫آﻠﻪ‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﻌﻤﻮد‬ ‫وﻟﺤﺬف‬
,
‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻗﻢ‬
‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬
‫اﻟﻤﺎﺗﻼب‬ ‫داﺧﻞ‬ ً
‫ا‬‫ﺟﺪ‬ ‫هﺎﻣﺔ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫أآﺜﺮ‬ ‫ﻣﻦ‬ ‫ﻋﻨﺼﺮ‬ ‫ﻧﺪاء‬ ‫ﻋﻤﻠﻴﺔ‬
,
‫أﻧﻪ‬ ‫أي‬
‫ﻋﻨﺼﺮ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫ﻧﻮد‬
‫اﻟﻤﺼﻔ‬ ‫ﻣﻦ‬ ‫وﺣﻴﺪ‬
‫ﻮﻓﺔ‬
,
‫اﻟﻌﻤﻮد‬ ‫ورﻗﻢ‬ ‫اﻟﺼﻒ‬ ‫رﻗﻢ‬ ‫ﺑﺬآﺮ‬ ‫وذﻟﻚ‬
‫اﻟﻌﻨﺼﺮ‬ ‫هﺬا‬ ‫ﺑﻪ‬ ‫اﻟﺬي‬
,
‫اﻷﻣﺮ‬ ‫هﺬا‬ ‫وﻟﺘﻮﺿﻴﺢ‬
,
‫ﺑﺴﻴﻂ‬ ‫ﻣﺜﺎل‬ ‫ﺑﻌﻤﻞ‬ ‫ﻧﻘﻮم‬
,
‫ﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺪﻳﻦ‬
‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻲ‬ ‫ذآﺮهﺎ‬ ‫ﺗﻢ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻧﻔﺲ‬
‫ﻟﻨﻘ‬
‫اﻟﺜﺎﻟﺚ‬ ‫واﻟﻌﻤﻮد‬ ‫اﻷول‬ ‫اﻟﺼﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻧﺮﻳﺪ‬ ‫اﻧﻨﺎ‬ ‫ﻞ‬
‫ﻋﻨﺼﺮ‬ ‫ﻣﻦ‬ ‫أآﺜﺮ‬ ‫وﻟﻨﺪاء‬
,
‫اﻟﺮاﺑﻊ‬ ‫إﻟﻰ‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻌﻤﻮد‬ ‫وﻣﻦ‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﺼﻒ‬ ‫ﺑﻨﺪاء‬ ً
‫ﻼ‬‫ﻣﺜ‬ ‫ﻧﻘﻮم‬

60. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﺣﺠﻢ‬ ‫ﻧﻌﺮف‬ ‫أﻧﻨﺎ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫هﺬا‬
,
‫ﺣﺠﻤﻬﺎ‬ ‫ﻧﻌﺮف‬ ‫ﻧﻜﻦ‬ ‫ﻟﻢ‬ ‫إذا‬ ‫ﻣﺎذا‬ ‫وﻟﻜﻦ‬
,
‫ﻧﺤﺼﻞ‬ ‫أن‬ ‫وﻧﺮﻳﺪ‬
‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﺼﻒ‬ ‫ﻣﻦ‬ ً
‫ﻼ‬‫ﻣﺜ‬ ‫اﻷﺧﻴﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻋﻠﻰ‬
‫ﻓﻲ‬ ‫وﻣﻬﺎرﺗﻚ‬ ‫ﺳﺮﻋﺘﻚ‬ ‫ﻣﻦ‬ ‫ﺗﺰﻳﺪ‬ ‫اﻟﺘﻲ‬ ‫اﻷﻣﺜﻠﺔ‬ ‫ﻣﻦ‬ ‫واﻟﻌﺪﻳﺪ‬ ‫ﺑﺎﻟﻌﺪﻳﺪ‬ ً
‫ﺎ‬‫ﺗﻤﺎﻣ‬ ‫اﻟﺸﺮح‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺑﻌﺪ‬ ‫وﺳﻨﻘﻮم‬
‫اﻟﻤﺎﺗﻼب‬
‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
‫ﺑﺸﻜﻞ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻞ‬ ‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺑﺈﻳﺠﺎد‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬
‫ﻣﺨﺘﻠﻒ‬
,
‫ﻳﺒﺤﺚ‬ ‫ﻓﻜﻴﻒ‬
‫اﻷآﺒ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﻋﻦ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ‫ﺮ‬
,
‫ﻋﻦ‬ ‫ﺑﺎﻟﺒﺤﺚ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬
‫ﻓﻲ‬ ‫ﻋﻤﻮد‬ ‫آﻞ‬ ‫ﻓﻲ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬
,
‫ذﻟﻚ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻳﻘﻮم‬ ‫وﺑﻌﺪﻣﺎ‬
,
‫ﺑﻌﻤﻞ‬ ‫ﻳﻘﻮم‬
‫ﻋﻤﻮد‬ ‫آﻞ‬ ‫ﻣﻦ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﺮﻗﻢ‬ ‫ﺑﻪ‬ ‫ﻣﺘﺠﻪ‬
,
‫اﻟﻤﺜﺎل‬ ‫أﻧﻈﺮ‬
‫ﻟﻠﺘﻮﺿﻴﺢ‬ ‫اﻟﺘﺎﻟﻲ‬
‫اﻟﻤﺎﺗﻼب‬ ‫ﻋﻠﻰ‬ ‫إﻧﺸﺎﺋﻬﺎ‬ ‫ﺗﻢ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫اﻵن‬ ‫ﻟﺪﻳﻨﺎ‬
‫اﻷﻣﺮ‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫وﻟﻨﻘﻢ‬
max
ً
‫ﺎ‬‫ﻣﺴﺒﻘ‬ ‫ذآﺮﻧﺎ‬ ‫آﻤﺎ‬
‫ﻋﻤﻮ‬ ‫آﻞ‬ ‫ﻣﻦ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫ﺑﺈﺧﺘﻴﺎر‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻗﺎم‬ ‫ﻓﻠﻘﺪ‬ ‫ﺗﻼﺣﻆ‬ ‫آﻤﺎ‬
‫د‬
,
‫وﻹﺧﺘﻴﺎر‬
‫ﻳﺠﺐ‬ ‫ﺑﻴﻨﻬﻢ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﺮﻗﻢ‬
‫اﻟﺨﺎرج‬ ‫ﻟﻠﻨﺎﺗﺞ‬ ‫اﻷﻣﺮ‬ ‫ﻧﻔﺲ‬ ‫آﺘﺎﺑﺔ‬
,
‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬
‫آﻜﻞ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻓﻲ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﺮﻗﻢ‬

61. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻷﺻﻐﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬
‫آﺜﻴﺮة‬ ً
‫ﺎ‬‫أﻳﻀ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫هﺬﻩ‬
‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﺘﻄﺒﻴﻘﺎت‬ ‫ﻓﻲ‬ ‫اﻹﺳﺘﺨﺪام‬
,
‫ﻧﻔﺲ‬ ‫وهﻲ‬
‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﺨﻄﻮات‬
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫ﻳﺘﻢ‬ ‫وﻟﻜﻦ‬ ‫اﻷآﺒﺮ‬ ‫اﻟﻌﻨﺼﺮ‬ ‫إﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫ذآﺮهﺎ‬
min
‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﺜﺎل‬ ‫وإﻟﻴﻜﻢ‬
‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﻣﺠﻤﻮع‬ ‫إﻳﺠﺎد‬
‫ﻹ‬
‫اﻷﻣﺮ‬ ‫ﺑﺈﺳﺘﺨﺪام‬ ‫ﻧﻘﻮم‬ ‫ﺗﻌﻠﻤﻨﺎ‬ ‫آﻤﺎ‬ ‫اﻟﻤﺠﻤﻮع‬ ‫ﻳﺠﺎد‬
sum
‫ﻳﻘﻮم‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫وﻟﻜﻦ‬
‫ﺑﺈﻳﺠﺎد‬ ‫اﻟﻤﺎﺗﻼب‬
‫ﻣﺘﺠﻪ‬ ‫ﺻﻮرة‬ ‫ﻓﻲ‬ ‫وﺗﻮﺿﻊ‬ ‫ﺣﺪى‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮد‬ ‫آﻞ‬ ‫ﺟﻤﻊ‬
,
‫اﻟﻤﺜﺎل‬ ‫ﻓﻲ‬ ‫آﻤﺎ‬
‫اﻟﺘﺎﻟﻲ‬

62. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫ﺣﺎﺻ‬ ‫إﻳﺠﺎد‬
‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﻞ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺿﺮب‬ ‫ﻳﻤﻜﻦ‬
,
‫ﻋﻠﻰ‬ ‫ﻋﻤﻮد‬ ‫ﻟﻜﻞ‬ ‫ﺗﻜﻮن‬ ‫اﻟﻀﺮب‬ ‫ﻋﻤﻠﻴﺔ‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻓﻲ‬ ‫وﻟﻜﻦ‬
‫وﻳﺘﻢ‬ ‫ﺣﺪى‬
‫ﻣﺘﺠﻪ‬ ‫ﻓﻲ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫وﺿﻊ‬
,
‫ﺿﺮب‬ ‫ﻳﺘﻢ‬ ‫أﺧﺮى‬ ‫ﻣﺮة‬ ‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬ ‫ﺗﻢ‬ ‫وإذا‬
‫ﺟﻤﻴﻌﻬﺎ‬ ‫اﻟﻤﺘﺠﻪ‬ ‫ﻋﻨﺎﺻﺮ‬
,
‫ﻟﻴﻨﺘﺞ‬
‫ﺟﻤﻴﻌﻬﺎ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫اﻟﻀﺮب‬ ‫ﺣﺎﺻﻞ‬
,
‫اﻟﻤﺜﺎل‬ ‫أﻧﻈﺮ‬
‫اﻟﺘﺎﻟﻲ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻗﻄﺮ‬ ‫إﻳﺠﺎد‬
‫أآﺎدﻳﻤﻲ‬ ‫إﺳﺘﺨﺪام‬ ‫ذات‬ ‫ﺗﻜﻮن‬ ‫ﻗﺪ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫هﺬﻩ‬
,
ً
‫ا‬‫ﺟﺪ‬ ‫هﺎﻣﺔ‬ ‫وﻟﻜﻨﻬﺎ‬
,
‫أن‬ ً
‫ﺎ‬‫وﺧﺼﻮﺻ‬
‫ﺗﺨﺪم‬ ‫اﻟﺨﺎﺻﻴﺔ‬ ‫ﺗﻠﻚ‬
‫اﻟﻤﺮﺑﻌﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬
)
‫اﻷﻋﻤﺪة‬ ‫ﻋﺪد‬ ‫ﻳﺴﺎوي‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬
(
,
‫وﻳﺘﻢ‬
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬
diag,
‫وهﺬ‬
‫ﻣﺜﺎل‬ ‫ا‬
‫ﻟﺬﻟﻚ‬

63. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻗﻄﺮ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻠﻴﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻌﺪﻳﺪ‬ ‫ﻋﻤﻞ‬ ‫اﻵن‬ ‫ﻳﻤﻜﻨﻨﺎ‬
,
‫ﻋﻤﻠﻴﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫ﻧﺮﻳﺪ‬ ً
‫ﻼ‬‫ﻓﻤﺜ‬
‫اﻟﻤﺼﻔﻮﻓﺔ‬ ‫ﻟﻌﻨﺎﺻﺮ‬ ‫اﻟﺠﻤﻊ‬
‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﺗﻠﻚ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺤﺼﻮل‬ ‫ﻧﺮﻳﺪ‬ ‫أﻧﻨﺎ‬ ‫أو‬
‫اﻟﺴﺤﺮﻳﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬
‫اﻟﺒﻌﺾ‬ ‫ﻳﺴﺘﻐﺮﺑﻬﺎ‬ ‫ﻗﺪ‬ ‫آﻠﻤﺔ‬ ً
‫ﺎ‬‫ﺣﻘ‬
,
‫وﻟ‬
‫ﺳﺤﺮﻳﺔ‬ ‫إﻧﻬﺎ‬ ً
‫ﺎ‬‫ﻓﺤﻘ‬ ‫ﺣﻘﻴﻘﺔ‬ ‫ﻜﻨﻬﺎ‬
,
‫أن‬ ‫ﺣﻴﺚ‬
‫اﻟﻘﺪرة‬ ‫ﻟﺪﻳﻪ‬ ‫اﻟﻤﺎﺗﻼب‬
‫ﺑﺈﺧﺘﻴﺎر‬ ‫اﻟﻤﺎﺗﻼب‬ ‫ﻳﻘﻮم‬ ‫ﻣﺮﺑﻌﺔ‬ ‫ﻣﺼﻔﻮﻓﺔ‬ ‫إﻧﺘﺎج‬ ‫ﻋﻠﻰ‬
‫ﻋﺸﻮاﺋﻲ‬ ‫ﺑﺸﻜﻞ‬ ‫أرﻗﺎﻣﻬﺎ‬
,
‫إﻻ‬ ‫ﻋﻠﻴﻚ‬ ‫ﻣﺎ‬ ‫آﻞ‬
‫اﻷﻣﺮ‬ ‫إﺳﺘﺨﺪام‬
magic
‫وﺗﺤﺪﻳﺪ‬
N
‫ﺣﻴﺚ‬
‫اﻷﻋﻤﺪة‬ ‫ﻟﻌﺪد‬ ‫اﻟﻤﺴﺎوي‬ ‫اﻟﺼﻔﻮف‬ ‫ﻋﺪد‬ ‫ﺗﻤﺜﻞ‬ ‫اﻧﻬﺎ‬
,
‫هﺬﻩ‬
ً
‫ا‬‫ﺟﺪ‬ ‫ﻣﻬﻤﺔ‬ ‫اﻟﻤﺼﻔﻮﻓﺔ‬
‫إ‬ ‫ﻋﻤﻠﻴﺎت‬ ‫ﻓﻲ‬ ً
‫ﺎ‬‫وﺧﺼﻮﺻ‬
‫اﻷﻧﻈﻤﺔ‬ ‫ﺧﺘﺒﺎر‬
,
‫ﻓﻲ‬ ‫اﷲ‬ ‫ﺑﺈذن‬ ً
‫ﺎ‬‫ﻻﺣﻘ‬ ‫ﺳﻨﺘﺤﺪث‬ ‫آﻤﺎ‬
‫اﻟﻌﺼﺒﻴﺔ‬ ‫اﻟﺸﺒﻜﺎت‬
.
ً
‫ﺎ‬‫ﻣﺒﺴﻄ‬ ً
‫ﻻ‬‫ﻣﺜﺎ‬ ‫وﻟﻨﺄﺧﺬ‬

64. ‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﻟﺒﻮﺻﻠﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻜﺘﺎب‬ ‫هﺬا‬ ‫ﺗﺤﻤﻴﻞ‬ ‫ﺗﻢ‬
.
‫اﻟﻜﺘﺐ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺰﻳﺪ‬
com
.
boosla
.
www
://
http