Ministère de l’Enseignement et Supérieur
et de la Recherche Scientifique
Ecole Normale Supérieur
ةمدقلا ةبقلا
رئازجا –
Vieux Kouba-Alge
2010
2011
1
-1-I
3
-1-1-I 3
-1-1-I 3
-2-1-I 4
-3-1-I 4
-4-1-I 5
-5-1-I 6
-6-1-I 6
-2-I 7
-1-2-I 7
-2-2-I 8
-3-2-I 8
-4-2-I 8
-5-2-I 9
-6-2-I 9
-7-2-I 10
-8-2-I 12
-9-2-I 18
-10-2-I 20
-1-II 21
-2-II
22
-3-II 25
-4-II 25
-5-II 26
-1-5-II 26
-2-5-II 27
-3-5-II 28
-6-II 28
-7-II 28
-8-II 28
-9-II 29
-1-9-II 29
-2-9-II 29
-3-9-II 30
-4-9-II 31
32 -1-III
-2-III 33
-3-III 33
-4-III 36
-5-III 45
46 -6-III
-1-6-III لكشلا نم ام كتلا سح
: f x dx
...
46
-2-6-III لكشلا نم ام كتلا سح
:2
0
cos ,sin
R d
...
48
-3-6-III
لكشلا نم ام كتلا سح
, 0
:ei x f x dx
...
49
-4-6-III ةر شملا ام كتلا ضعب سح
...
52
مت خلا ...
60
عجارملا ...
61
1
ﺔﻤﺩﻘﻤ : ﺞﺌﺎﺘﻨﻝﺍ ﻥﻤ ﺩﺍﺩﻋﻷﺍ ﺕﻨﺎﻜ ﺩﻘﻝ ﻷﺍ ﺔﻴﺘﻴﻀﺎﻴﺭﻝﺍ
ﻭ ﺕﺩﻬﺘﺠﺍﻭ ،ﺔﻴﻨﺎﺴﻨﻹﺍ ﺎﻬﺘﻋﺩﺒﺃ ﻲﺘﻝﺍ ﻰﻝ
ﻡﻝ ﻲﺘﻝﺍ ﺓﺭﻴﺨﻷﺍ ﻩﺫﻫ ،ﺔﻴﻘﻴﻘﺤﻝﺍ ﺩﺍﺩﻋﻷﺍ ﺔﻋﻭﻤﺠﻤ ﻰﻝﺇ ﺕﻠﺼﻭﺘ ﻥﺃ ﻰﻝﺇ ﺎﻫﺭﻴﻭﻁﺘ ﻲﻓ ﻴﺭﻝﺍ ﺝﺎﻴﺘﺤﺍ ﻲﻁﻐﺘ ﺎ
ﻴﻀﺎﻴﺭ لﻜﺎﺸﻤﻝ لﻭﻠﺤ ﻥﻋ ﻪﺜﺤﺒ ﺀﺎﻨﺜﺃ ﻲﻀ ﺎ
ﺔﻴﺘ ﻥﻤ ﺔﺤﻭﺭﻁﻤ
لﺜﻤ ،ﺏﻝﺎﺴ ﺎﻫﺯﻴﻤﻤ ﺔﻴﻨﺎﺜﻝﺍ ﺔﺠﺭﺩﻝﺍ ﻥﻤ ﺕﻻﺩﺎﻌﻤ لﺤ ﺎﻬﻨﻴﺒ :
2 2 0
x + = ﻯﺩﺃ ﺎﻤﻤ
ﻲﻀﺎﻴﺭﻝﺎﺒ ﺔﻋﻭﻤﺠﻤ ﻲﻓ ﺩﻭﺠﻭﻤﻝﺍ ﺹﻘﻨﻝﺍ ﻲﻁﻐﺘ ﺓﺩﻴﺩﺠ لﺌﺎﺴﻭ ﻥﻋ ﺙﺤﺒﻝﺍ ﻰﻝﺇ
ﺩﻌﺒ ﺎﻤ ﻲﻓ ﻲﻤﺴ ﺩﻴﺩﺠ ﺩﺩﻋ ﻰﻝﺇ لﻭﺼﻭﻝﺍ ﻲﻫ ﺙﺤﺒﻝﺍ ﺔﺠﻴﺘﻨ ﺕﻨﺎﻜﻓ ،ﺔﻴﻘﻴﻘﺤﻝﺍ ﺩﺍﺩﻋﻷﺍ ﻜﻓ ﺕﺩﺃ ﺙﻴﺤ ،ﺎﻴﺩﻘﻋ ﺍﺩﺩﻋ ﺔﻴﻘﻴﻘﺤﻝﺍ ﺩﺍﺩﻋﻷﺍ ﺔﻋﻭﻤﺠﻤ ﻊﻴﺴﻭﺘ ﻰﻝﺇ ﺩﺩﻌﻝﺍ ﺍﺫﻫ ﺓﺭ
ﺕﻴﻤﺴ ،ﻩﻼﻋﺃ ﺓﺭﻭﻜﺫﻤﻝﺍ ﺕﻻﺩﺎﻌﻤﻠﻝ لﻭﻠﺤ ﻰﻠﻋ ﺎﻬﻴﻓ لﻭﺼﺤﻝﺍ ﻥﻜﻤﻴ ﺔﻋﻭﻤﺠﻤﻝ ﺔﻴﺩﻘﻌﻝﺍ ﺩﺍﺩﻋﻷﺍ ﺔﻋﻭﻤﺠﻤﺒ )
ﺔﺒﻜﺭﻤﻝﺍ ﻭﺃ (
ﺭﺜﻜﺃ ﺹﺍﻭﺨ ﻙﻠﻤﺘ ﺔﻴﺩﻘﻋ ﻊﺒﺍﻭﺘ ﺕﻓﺭﻋ ﺎﻤﻜ ،
ﺭ ﻲﻓ ﺍﺫﻫ لﻜ ﺝﺭﺩﻨﻴﻝ ،ﺓﺩﻘﻌﻤﻝﺍ ﺕﻼﻤﺎﻜﺘﻝﺍ لﻴﻬﺴﺘﻭ ﺔﻴﻠﻴﻠﺤﺘﻝﺍ ﻊﺒﺍﻭﺘﻝﺎﻜ ﺔﻴﻤﻭﻤﻋ ﻲﻀﺎﻴ
ﺤﻝﺍ ﻥﻤ ﺎﻴﺴﺎﺴﺃ ﺍﺀﺯﺠ ﺢﺒﺼﺃ ﻱﺫﻝﺍ ،ﻱﺩﻘﻌﻝﺍ لﻴﻠﺤﺘﻝﺍ ﻭﻫﻭ ﻻﺃ لﻘﺘﺴﻤ ﺎ
ﻭﻴﻝﺍ ﺔﺠ ﺔﻴﻤ
ﻥﻴﻴﺌﺎﻴﺯﻴﻔﻝﺍﻭ ﻥﻴﺴﺩﻨﻬﻤﻝﺍﻭ ﻥﻴﻴﻀﺎﻴﺭﻠﻝ ...
ﻲﺘﻝﺍ ﺔﻴﻜﻴﺴﻼﻜﻝﺍ ﻕﺭﻁﻝﺍ ﻰﻠﻋ ﺀﺎﻤﻠﻌﻝﺍ ﺩﺎﻤﺘﻋﺎﻓ،
ﺫﻝﺍ ﺩﻴﺤﻭﻝﺍ لﻴﺒﺴﻝﺍ ﺕﻨﺎﻜ ﻱ
،ﺊﻁﺒﺒ ﺭﻴﺴﺘ ﻲﻤﻠﻌﻝﺍ ﺭﻭﻁﺘﻝﺍ ﺓﺭﻴﺘﻭ لﻌﺠ ﻪﻨﻋ ﻰﻨﻏ ﻻ
ﺀﺎﺸﻨﺇﻭ ﺔﺴﺍﺭﺩﻓ ﺔﻘﻴﻗﺩﻝﺍ ﻡﻭﻠﻌﻝﺍ ﺭﻭﻁﺘﻝ ﺔﻴﻤﺘﺤ ﺓﺭﻭﺭﻀﻜ ﺀﺎﺠ ﺔﻴﺩﻘﻌﻝﺍ ﺩﺍﺩﻋﻷﺍ ﺔﻋﻭﻤﺠﻤ
ﺏﻠﻗ ﻱﺩﻘﻌﻝﺍ ﻊﺒﺎﺘﻝﺍ ﺕﺎﻴﺭﻅﻨ ﺩﻌﺘ ﻙﻝﺫﻝ ﺕﺎﻴﻀﺎﻴﺭﻝﺍ
ﻥﺇﻭ ،ﻥﺭﻗ ﺫﻨﻤ ﻊﺴﻭﺘﺘ ﻲﺘﻝﺍ ﺔﺜﻴﺩﺤﻝﺍ
ﻬﻝﺍ ﻕﺌﺍﺭﻁﻝﺍ ﺎ
ﻲﺸﻭﻜ ﻡﻝﺎﻌﻝﺍ ﺫﻨﻤ ﻡﻠﻌﻝﺍ ﺍﺫﻫ ﻲﻓ لﻤﻌﺘﺴﺘ ﻲﺘﻝﺍ ﺔﻠﺌ CA UCHY
ﺩﻗ
ﻝﺍ ﺔﻴﻀﺎﻴﺭﻝﺍ ﺙﺎﺤﺒﻷﺍ ﻥﻤ ﺭﻴﺜﻜﻝ ﺕﻁﻋﺃ ﺔﻁﺎﺴﺒ ﻰﻀﻭﻔﻝﺍﻭ ﺽﻭﻤﻐﻝﺎﺒ ﻡﺘﻬﺘ ﺕﻨﺎﻜ ﻲﺘ
ﻭ ﺔﻴﺌﻭﻀﻝﺍ ﺔﻴﺌﺎﻴﺯﻴﻔﻝﺍ ﺕﺎﻴﺭﻅﻨﻝﺍ ﻲﻓ ﻡﻭﻬﻔﻤﻝﺍ ﺍﺫﻫ لﺎﺨﺩﺇ ﻥﺇ ،ﻥﻴﺭﻴﺒﻜ ﺎﺤﻭﻀﻭ ﺩﻬﻤﻭ ﺔﻁﺎﺴﺒﻝﺍ ﻰﻬﺘﻨﻤ ﻲﻓ ﺭﻴﺘﺎﺴﺩ ﻰﻝﺇ ﻡﻠﻌﻝﺍ ﺍﺫﻫ لﺼﻭﺃ ﺔﺼﺎﺨ ﺓﺭﻭﺼﺒ ﺔﻴﺌﺎﺒﺭﻬﻜﻝﺍﻭ
ﺕﺎﻴﺭﻅﻨ ﻡﺩﻘﺘ ﻰﻠﻋ ﺩﻴﺩﺠﻝﺍ ﻡﻭﻬﻔﻤﻝﺍ ﺍﺫﻫ ﺩﻋﺎﺴ ﺩﻘﻝﻭ ،ﺔﻴﺌﺎﻴﺯﻴﻔﻝﺍ ﺕﺎﻔﺸﺘﻜﻹﺍ ﻥﻤ ﺭﻴﺜﻜﻝ
2
ﺱﻜﺎﻤ لﻴﻭ
W ELL ﺯﺘﺭﻫﻭ MA X
HERTZ ﺴﻴﻁﻭﺭﻬﻜﻝﺍ
ﻲﺘﻝﺍ ﺕﺎﻴﺭﻅﻨﻝﺍ ﻩﺫﻫ ﺔﻴ
ﺔﺜﻴﺩﺤﻝﺍ ﺕﺎﻓﺎﺸﺘﻜﻻﺍ ﻰﻝﺇ ﺕﺩﺎﻗ .
ﺓﺭﺍﺯﻏﻭ ﻱﺩﻘﻌﻝﺍ لﻴﻠﺤﺘﻝﺍ ﺏﻌﺸﺘﻭ ﺓﺭﻴﺒﻜﻝﺍ ﺔﻴﻤﻫﻷﺍ ﻩﺫﻬﻝ ﺍﺭﻅﻨﻭ ﻪﺘﺎﻤﻭﻠﻌﻤ
ﺎﻨﻴﺄﺘﺭﺃ ﻥﺃ
ﺕﻼﻤﺎﻜﺘﻝﺍ ﺏﺎﺴﺤ لﺌﺎﺴﻤ ﻭﻫﻭ ﻻﺃ ﻱﺩﻘﻌﻝﺍ لﻴﻠﺤﺘﻝﺍ ﻥﻤ ﺀﺯﺠ ﻰﻠﻋ ﺎﻨﺘﺴﺍﺭﺩ ﻲﻓ ﺭﺼﺘﻘﻨ ﺔﻴﺩﻘﻌﻝﺍ ﻊﺒﺍﻭﺘﻝﺍ ﺕﺍﺫ ﺕﻼﻤﺎﻜﺘﻝﺍ ﺏﺎﺴﺤ ﻰﻝﺇ ﺓﺭﻜﺫﻤﻝﺍ ﻩﺫﻫ ﻲﻓ ﺎﻨﻗﺭﻁﺘ ﺙﻴﺤ ،ﺔﻴﺩﻘﻌﻝﺍ لﺼﻔﻝﺍ ﻲﻔﻓ لﻭﺼﻓ ﺔﺜﻼﺜ ﻰﻝﺇ ﺎﻨﺘﺴﺍﺭﺩ ﺎﻨﻤﺴﻗ ﺩﻗﻭ ﺏﺴﺍﻭﺭﻝﺍ ﺔﻴﺭﻅﻨ ﺔﻁﺴﺍﻭﺒ لﻭﻷﺍ
ﻲﻓﻭ ﺔﻴﺩﻘﻌﻝﺍ ﻊﺒﺍﻭﺘﻝﺍ ﺹﺍﻭﺨ ﻰﻝﺇ ﺎﻨﻗﺭﻁﺘ ﺕﺎﻴﺭﻅﻨ ﺽﻌﺒ ﻰﻝﺇ ﺎﻨﻗﺭﻁﺘ ﻲﻨﺎﺜﻝﺍ لﺼﻔﻝﺍ
ﺏﺴﺍﻭﺭﻝﺍ ﺔﻴﺭﻅﻨﻭ ﻲﺸﻭﻜ ﺔﻴﺭﻅﻨ ﺎﻫﺯﺭﺒﺃ لﻤﺎﻜﺘﻝﺍ ﻩﺎﻨﺼﺼﺨ ﺩﻘﻓ ﺙﻝﺎﺜﻝﺍ لﺼﻔﻝﺍ ﺎﻤﺃ
ﺕﻼﻤﺎﻜﺘﻝﺍ ﻲﻓ ﺏﺴﺍﻭﺭﻝﺍ ﺔﻴﺭﻅﻨ ﻕﻴﺒﻁﺘ ﻰﻝﺇ .
ﻭ ﺃ ﻝﺍ ﺩﻴﻔﻴ ﻪﺠﺌﺎﺘﻨﺒ ﻊﻀﺍﻭﺘﻤﻝﺍ ﺙﺤﺒﻝﺍ ﺍﺫﻫ ﻥﺃ ﻰﻨﻤﺘﻨ ﺍﺭﻴﺨ ﻤ
ﻲﻓ ﻥﻴﺼﺼﺨﺘ
ﻀﻴ ﻥﺃﻭ ﻱﺩﻘﻌﻝﺍ لﻴﻠﺤﺘﻝﺍ ﻉﻭﻀﻭﻤ ﻲﻓ ﺹﺨﻷﺎﺒﻭ ﺕﺎﻴﻀﺎﻴﺭﻝﺍ ﺔﺒﺘﻜﻤﻝﺍ ﻰﻝﺇ ﻑﻴ
ﻉﻭﻀﻭﻤﻝﺍ ﺍﺫﻫ لﻭﺤ ﺍﺩﻴﺩﺠ ﺎﻌﻀﺍﻭﺘﻤ ﺎﻌﺠﺭﻤ ﺔﻴﻌﻤﺎﺠﻝﺍ .
