ءﺎﯾﻣﯾﻛﻟا و ءﺎﯾزﯾﻔﻟا ﺢﯾﺣﺻﺗ ﺔﯾدﺎﻌﻟا ةرودﻟا 2016
- ءﺎﯾﻣﯾﻛﻟا :
لوﻷا ءزﺟ :
(1 -1 : 1 ءﺎﻣﻟا ﻊﻣ كﺎﯾﻧوﻣﻷا لﻋﺎﻔﺗ ﺔﻟدﺎﻌﻣ :
( ) + ( ) ⇄ ( ) + ( )
-2 -1 1 :
= = [ ]
= [ ] = .
= ∗ ,
= , = %
-3 -1 : 1 نزاوﺗﻟا ﺔﺗﺑﺎﺛ :
=[ ][ ]
[ ]
=[ ]
⟹ [ ] =
= [ ]
− [ ] = ( )
− ⟹ =
−
-2 (1 (1-2-1
= + [ ]
[ ]
ﺔﻧﻣﯾﮭﻟا لﺎﺟﻣ ططﺧﻣ :
PH < [ ] = [ ] >
[ ] < [ ] = [ ] > [ ]
(% ) لﺛﻣﯾ ( )ﻰﻧﺣﻧﻣﻟا (% ) لﺛﻣﯾ ( ) ﻰﻧﺣﻧﻣﻟا -2 -2 (1 أ -
= ( / ) = ,
-ب
= [ ]
= [ ] = [ ] %([ ]) = % =
%[ ] = % = [ ]
-3 -2 (1
فﻔﺧﻣ لوﻠﺧﻣﻟا نﺎﻛ ﺎﻣﻠﻛ ﻲﺋﺎﮭﻧﻟا مدﻘﺗﻟا ﺔﺑﺳﻧ دادزﺗ ∶ >
(2 -1 : 2
+ ⇄ +
-2 (2
= [ ][ ]
[ ][ ] = =
= , , = ,
-3 (2
= [ ]
[ ] =
− =
− = √
⇒ = − √
+ √ = √
= √
+ √ ⟹ [ ] = [ ] √ + √
[ ] = .
+ = ⟶ [ ] = . √ ′
+ √ ′ ﻊﻣ -4 : (2 نزاوﺗﻟا دﻧﻋ طﯾﻠﺧﻟا ﺔﻣﯾﻗ :
= + [ ]
[ ]
[ ] = √
+ √ و
⎩
⎪⎪
⎨
⎪⎪
⎧ [ ] = −
= − [ ]
[ ] = − . √ ′
+ √ ′
[ ] = − √
+ √ =
+ √
[ ]
[ ] = + √
√ + √
= √
= +
√ = − √
≃ ,
ﻲﻧﺎﺛﻟا ءزﺟﻟا :
(1 دوﻧﻷا دﻧﻋ لﻋﺎﻔﺗﻟا ﺔﻟدﺎﻌﻣ :
ﺔﯾدوﻧأ ةدﺳﻛأ :
تﺎﻧورﺗﻛﻟإ نادﻘﻓ .
( ) + ( ) → ( ) + ( ) + é
( 2
( ) + ( ) → ( )+ ( )+ ( )
رﯾﻓو
= . 0 0
− X +
[ ] = +
= [ ] +
= ([ ] − [ ] ) ⟹ = ( − )
( 3
(é) = = ( − )
.
= ( − )
= .
( − )
= ∗ ,
, , − ⟹ = ,
ءﺎﯾزﯾﻔﻟا :
- ﺔﯾووﻧﻟا تﻻوﺣﺗﻟا :
⟶ + ( ( 2
|∆ | =
( )
−
( )+
( )|∆ | = + , ≃ ,
( 3 - 1 - 3 :
( )
= ( ) = ( )
/ . /( )
= = =
= ( )
د وھ ﺢﯾﺣﺻﻟا حارﺗﻗﻻا :
- 2 - 3 :
= ⟹ =
( ( )
( )
= − ⟹ ( )
( ) = .
( ( )
( ) = . ⟹ = ,
/ = ∗ , =
- 3 - 3 :
( ) = ( ) ⟹ = + ( )
( ) = ( )+ ( )
( )
= / . ( + ( ) ( )
= / +
= / ⟹ =
ءﺎﺑرﮭﻛﻟا :
(1 - 1 -1 : رﺎﯾﺗﻟ ةدﺷ ﺎﮭﻘﻘﺣﺗ ﻲﺗﻟا ﺔﯾﻠﺿﺎﻔﺗﻟا ﺔﻟدﺎﻌﻣﻟا :
تارﺗوﺗﻟا ﺔﯾﻓﺎﺿإ نوﻧﺎﻗ بﺳﺣ :
+ + =
+ + . + =
+ =
= + + ﻊﻣ
-2 -1 : = = ∶ ﻲﻟﺎﺗﻟﺎﺑ و = ﺎﻧﯾدﻟ = دﻧﻋ
-3 -1 :
= +
مﺋادﻟا مﺎظﻧﻟا ﻲﻓ :
= −
= −
= −
, ⟹ =
ﺎﯾﻧﺎﯾﺑﻣ ﺎﻧﯾدﻟ مﺋادﻟا مﺎظﻧﻟا ﻲﻓ و :
= = .
= = , = ,
مﺋادﻟا مﺎظﻧﻟا ﻲﻓ ىرﺧأ ﺔﮭﺟ نﻣ و :
= .
= =
,
=
ﻰﻧﺣﻧﻣﻟا دﺎﻣﺗﻋﺎﺑ و :
= −
= −
=
-4 (1 ﺎﯾﻧﺎﯾﺑﻣ ﺎﻧﯾدﻟ :
= + + و = .
= ( + + ) = . ( + + )
= ,
(2 -1 -2 : يرود ﮫﺑﺷ مﺎظﻧ )
فﯾﻌﺿ دوﻣﺧ (
-2 -2 : ﺔﯾﻠﺿﺎﻔﺗﻟا ﺔﻟدﺎﻌﻣﻟا :
+ + =
+ + + = =
+ ( + ) + = =
+ +
+ =
-2 (3
( ) = = ∶ دﻧﻋ ﺎﻧﯾدﻟ
= = ( )
( ) = ﺎﯾﻧﺎﯾﺑﻣ
= ( , . )( )
= , .
= ﺎﻧﯾدﻟ = ∶ دﻧﻋ و
( ) = ( ) = ( )
= ∗ , ( − , )
( ) = , .
| | = − = , .
(3 -1 : 3
= ∆ ⟹ = . ∆ = ∗ ,
≃
: نﯾﻧرﻟا دﻧﻋ : (3-2
= .
= ∶ دﻟوﻣﻟا لﺎﻌﻔﻟا رﺗوﺗﻟا ﺔﻣﯾﻗ ( ) رﯾﺑﻌﺗ نﻣ ﺎﻧﯾدﻟ و = =
ﮫﻧﻣو :
+ = ⟹ = − =
, −
= ,
∶ﻲھ ﺔﻣﯾﻗ
= ⟹ =
= ∗ ∗ , ∗ ( ) ⟹ = , .
= ,
= √ ثﯾﺣ = = دﻧﻋ ﺔطﺳوﺗﻣﻟا ﺔﯾﺋﺎﺑرﮭﻛﻟا ةردﻘﻟا (3-3
= . = (
√ ) = .
= ( , )( , )
≃ ,
كﯾﻧﺎﻛﯾﻣﻟا :
لوﻷا ءزﺟﻟا :
( 1 ﺔﻟدﺎﻌﻣﻟا ﻠﺿﺎﻔﺗﻟا
ﺔﻋرﺳﻟا ﺎﮭﻘﻘﺣﺗ ﻲﺗﻟا ﺔﯾ :
قﯾﺑطﺗﺑ )
ق . م . ن : (
⃗ = ⃗ ⟹ ⃗ + ⃗ = ⃗
− + = ⃗ روﺣﻣﻟا ﻰﻠﻋ
− + =
− + =
ﻊﺿﻧ :
= ,
= ,
= − + , .
( 2 ﺔﯾدﺣﻟا ﺔﻋرﺳﻟا رﯾﺑﻌﺗ :
مﺋادﻟا مﺎظﻧﻟا ﻲﻓ :
ﺔﯾﻠﺿﺎﻔﺗﻟا ﺔﻟدﺎﻌﻣﻟا نﻣ ⟸ = و =
= − + ,
. ⟹ = − . .
, ; = −
: 3 - 1 - ( 3
= − , ∗ . ∗
, ∗ , ≃ −
( ) ﻰﻧﺣﻧﻣﻟا ﻲﻓ ( ) ﺔﯾرﻛﻠﻟ = − ﺎﯾﻧﺎﯾﺑﻣ ﺎﻧﯾدﻟ و
( )
= ( ) ∶ ﺔﻟاد قﻓاوﯾ ( ) ﻰﻧﺣﻧﻣﻟا نأ ﺞﺗﻧﺗﺳﻧ - 2 - 3 :
( > ) رﺑﻛأ ﺔﯾﻣﻛ ﺔﻠﺗﻛ ﻰﻠﻋ رﻓوﺗﺗ ( ) ﺔﯾرﻛﻟا نوﻛﻟ كﻟذ ﻊﺟرﯾ و ( ) > ( ) ∶ﺎﻧﯾدﻟ ﺔظﺣﻟ لﻛ دﻧﻋ
( 4 ﺔﯾرﻛﻟا ﺔﻛرﺣ ﺔﻌﯾﺑط :
∶ ثﯾﺣﺑ ( ) = − ∶ ﻲھ ﺔﻋرﺳﻟا ﺔﻟدﺎﻌﻣ ( ) ﻰﻧﺣﻧﻣ دﺎﻣﺗﻋﺎﺑ
= ∆
∆ = − −
, − = − ≃ − =
: ﺑ ةرﯾﻐﺗﻣ ﺔﯾﻣﯾﻘﺗﺳﻣ
ﺔﯾﻧﻣزﻟا ﺎﮭﺗﻟدﺎﻌﻣ مﺎظﺗﻧﺎ (a) ﺔﯾرﻛﻟا روﺻﻗ زﻛرﻣ ﺔﻛرﺣ نذإ مﯾﻘﺗﺳﻣ رﺎﺳﻣﻟا و ﺔﺑﺎﺗ عرﺎﺳﺗﻟا -
( )
= − + +
( )
= − +
≃ , دﻧﻋ( ) لﻛﺷﻟا نﻣ ( ) ﺔﯾرﻛﻟا بوﺳﻧأ ﺎﯾﻧﺎﯾﺑﻣ دﺟﻧ ( = ) ضرﻷا ﺢطﺳ ﻰﻠﻋ ( ) ﺔﯾرﻛﻟا طﻘﺳﺗ ﺎﻣدﻧﻋ (
=
= ∆ = − = ∶ ﻲﻟﺎﺗﻟﺎﺑ و ( 6
= − + = ثﯾﺣ
= − +
= ( ) − ⟹ = , (− ,
− ) −
= − , ( )
رﯾﻟوأ ﺔﻘﯾرط بﺳﺣ و :
= ( ) −
∆
∶ ﺎﻧﯾدﻟ ∆ بﺎﺳﺣﻟا ةوطﺧ لﻼﺧ
( ) = + ∆
( ) = − , − ( , ∗ , )
( ) = − ,
ﻲﻧﺎﺛﻟا ءزﺟﻟا :
( 1 ساوﻧﻟا ﺔﻛرﺣﻟ ﺔﯾﻠﺿﺎﻔﺗﻟا ﺔﻟدﺎﻌﻣﻟا :
∆
⃗ =
∆̈
= − =
∆̈ ⟹ ̈ +
∆
=
( 2 - 1 - 2 ﺔﯾوازﻟا ﺔﻋرﺳﻟا ﺔﻟدﺎﻌﻣﻟ يددﻌﻟا رﯾﺑﻌﺗﻟا :
( )
= + ⟶ ̇ ( ) = − +
̇ = ∶ ﺣ ﯾ ث : ﻲھ ̇ و = , ∶ ﺎﯾﻧﺎﯾﺑﻣ
̇ =
̇ =
, ∗ =
∶ = ﺦﯾراوﺗﻟا لﺻأ دﻧﻋ دﯾدﺣﺗ
̇
( )= − ̇
= − ̇ < ⟹ = ⟹ | | = +
= ﮫﻧﻣ و ̇ = − < ∶ ﺎﻧﯾد ﻟ - 2 - 2 ﻲﻠﻟا ﺔﺗﺑﺎﺛ :
⎩ ⎪
⎪ ⎨
⎪ ⎪
⎧ = +
= − ̇ +
̇ +
∆
=
̈ = −( ) + ⟹ ̈ + ( )
( )=
نﻣ 1 ) ( و 2 ) ( دﺟﻧ :
=
∆( ) =
∆
= ∗ ∗ .
( , ) = , . . .
( 3 ﺔﻟﺎﺣ تﺎﻛﺎﻛﺗﺣا ﺔﻠﻣﮭﻣ
:
= =
∆̇ ﺔظﺣﻟ لﻛ دﻧﻋ = ﺔﺗﺑﺎ ﺛ
= . . ( ) = , .
ﻲھ
: t=0 دﻧﻋ ﻲﻠﻟا ﻊﺿوﻟا ﺔﻗﺎط ﺔﻣﯾﻗ
= + ⟹ = −
= −
∆( − ̇
) = −
∆̇
= , .
