علائم و رمـــوز الرياضـــــــيات

‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج‬
‫اﻟﺮﺣﻤـــﻦﻋﺒﺪاﻟﺮﺣـــﻴﻢ‬
‫ﺑﺴـــﻢ اﷲ‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫‪1‬‬
2
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
α
А
Alpha
‫اﻟﻔﺎ‬
β
В
Beta
‫ﺑﺘﺎ‬
γ
Г
Gamma
δ
Δ
Delta
ε
Е
Epsilon
ζ
Z
Zeta
η
H
Eta
‫إﺗﺎ‬
θ
Θ
Theta
‫ﺗﻴﺘﺎ‬
ι
I
Iota
‫ﻳﻮﺗﺎ‬
κ
K
Kappa
‫آﺎﺑﺎ‬
λ
Λ
Lambda
μ
M
Mu
‫ﻣﻴﻮ‬
ν
N
Nu
‫ﻧﻴﻮ‬
ξ
Ξ
Xi
‫آﺴﺎي‬
ο
O
Omicron
π
Π
Pi
‫ﺑﺎي‬
ρ
Ρ
Rho
‫رو‬
σ
Σ
Sigma
τ
Τ
Tau
υ
Υ
Upsilon
φ
Φ
Phi
‫ﻓﺎي‬
χ
Χ
Chi
‫آﺎي‬
ψ
Ψ
Psi
‫ﺑﺴﺎي‬
ω
Ω
Omega
‫أوﻣﻴﻐﺎ‬
‫ﻏﺎﻣﺎ‬
‫دﻟﺘﺎ‬
‫إﺑﺴﻠﻮن‬
‫زﻳﺘﺎ أو دﻳﻐﺎﻣﺎ‬
‫ﻻﻣﺪا أو ﻻﻣﺒﺪا‬
‫أﻣﻴﻜﺮون‬
‫ﺳﻴﻐﻤﺎ‬
‫ﺗﺎو‬
‫أوﺑﺴﻠﻮن‬
3
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫اﻟﻌﻼﻣﺔ‬
‫إﻧﺠﻠﻴﺰي‬
≤
Less than equal
≥
Greater than
‫ﻋﺮﺑﻲ‬
‫ﻣﺜﺎل‬
‫ أﺻﻐﺮ أو ﻳﺴﺎوي‬x ≤ y
y ‫ أﺻﻐﺮ أو ﺗﺴﺎوي‬x
‫ أآﺒﺮ أو ﻳﺴﺎوي‬a ≥ b
b ‫ أآﺒﺮ أو ﺗﺴﺎوي‬a
equal
<
Less than
>
Greater than
≅
Approximately
Congruent
∝
Proportional
≡
Is congruent to
Modulo
≠
Not equal
±
Plus-minus
=
Equal
×
Times, cross
‫ أﺻﻐﺮ‬3 < 4
‫ أآﺒﺮ‬3 > 2
‫ ﺗﻘﺮﻳﺒًﺎ‬1.99997 ≅ 2
(‫ ﻣﺘﻄﺎﺑﻖ )هﻨﺪﺳﻪ‬ΔABC ≅ ΔA ′B ′C ′
‫ ﻣﺘﻨﺎﺳﺐ‬F ∝ x ⇒ F = kx
‫ﺗﻜﺎﻓﺆ‬
‫ ﻣﺘﻄﺎﺑﻘﺔ‬5 ≡ 1(mod 2)
‫ ﻻ ﻳﺴﺎوي‬3 ≠ 2
‫ زاﺋﺪ ﻧﺎﻗﺺ‬x 2 = 1 ⇒ x = ±1
‫( ﻳﺴﺎوي‬a = b ) & (b = c ) ⇒ a = c
، ‫ ﺿﺮب ﻋﺪدي‬2 × 3 = 6
‫→ ﺟﺪاء‬
‫ﺿﺮب ﻣﺘﺠﻬﻲ‬
A = ax i + ay j + az k
→
B = bx i + b y j + bz k
i
→ →
A × B = ax
bx
+
Plus
-
Minus
‫ ﺟﻤﻊ‬2 + 3 = 5
‫ ﻧﺎﻗﺺ‬، ‫ ﻃﺮح‬2 − 3 = −1
j
k
ay
by
az
bz
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫‪ 6 ÷ 3 = 2‬ﺗﻘﺴﻴﻢ‬
‫‪ 50%‬اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﻳﺔ‬
‫‪00‬‬
‫‪ 50 0‬اﻟﻨﺴﺒﺔ ﻓﻲ اﻷﻟﻒ‬
‫→ →‬
‫‪A ⋅ B = A B cosθ‬‬
‫ﺿﺮب داﺧﻠﻲ‬
‫‪ 5! = 1 × 2 × 3 × 4 × 5 = 120‬ﻋﺎﻣﻠﻲ أو ﻓﺎآﺘﻮرﻳﻞ‬
‫ﺟﺬر‬
‫ﺟﺬر ﺗﺮﺑﻴﻊ‬
‫‪4=2‬‬
‫ﺟﺬر ﺗﻜﻌﻴﺐ‬
‫‪27 = 3‬‬
‫‪3‬‬
‫ﺟﺬر ﻧﻮﻧﻲ‬
‫‪m‬‬
‫‪n‬‬
‫ﻧﺎﻗﻞ أو ﻳﺒﺎدل ﺻﻔﻮف و أﻋﻤﺪة ﻓﻲ ﻣﺼﻔﻮﻓﺔ‬
‫ﻧﺎﻗﻞ‬
‫‪4‬‬
‫‪ : Division‬أو ‪ /‬أو‬
‫‪Divided by‬‬
‫÷‬
‫‪Percent‬‬
‫‪%‬‬
‫‪Per thousand‬‬
‫‪00‬‬
‫‪Dot‬‬
‫‪.‬‬
‫‪Factorial‬‬
‫!‬
‫‪0‬‬
‫‪Square root‬‬
‫‪Transpose‬‬
‫‪AT‬‬
‫‪B = A T ⇒ b ji = aij‬‬
‫‪ 5.3 ⇒ [ x ] = 5 & y = 5.6 ⇒ [ y ] = 6‬ﺟﺰء ﺻﺤﻴﺢ‬
‫⎤ ‪a12‬‬
‫⎦⎥ ‪a22‬‬
‫‪ ⎡ a11‬ﻣﺼﻔﻮﻓﺔ‬
‫‪⎢a‬‬
‫‪⎣ 21‬‬
‫‪ 3(2 + (4 − 1)) = 15‬هﻼﻻن ‪ ،‬ﻗﻮﺳﺎن‬
‫ﻣﺠﻤﻮﻋﻪ‬
‫ﻣﺘﺘﺎﻟﻴﻪ‬
‫‪Bracket‬‬
‫][‬
‫‪Matrix‬‬
‫‪Parentheses‬‬
‫) (‬
‫‪Set Braces‬‬
‫}{‬
‫‪Sequence‬‬
‫ﺟﺰء آﺴﺮي‬
‫]‪[10, 20‬‬
‫) ‪( −1,0‬‬
‫ﻓﺘﺮة ﻣﻐﻠﻘﺔ‬
‫ﻓﺘﺮة ﻣﻔﺘﻮﺣﺔ‬
‫‪close –interval‬‬
‫‪open-interval‬‬
‫]‪[,‬‬
‫)‪(,‬‬
5
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
[, )
close-open
( ,]
open-close
∗
Convolution
‫ﻓﺘﺮة ﻣﻐﻠﻘﺔ ﻣﻦ‬
( −5, −2]
‫اﻟﻄﺮف اﻷﻳﺴﺮ‬
[ −10,13)
‫ﻓﺘﺮة ﻣﻐﻠﻘﺔ ﻣﻦ‬
‫اﻟﻄﺮف اﻷﻳﻤﻦ‬
‫ﻣﻠﻔﻮف‬
‫ﻓﻲ ﺗﺤﻮﻳﻼت ﻓﻮرﻳﻴﻪ‬
F { g (x ) * f (x )} = F { g (x )} × F {f (x )}
Absolute value
∑
‫اﻟﻘﻴﻤﺔ اﻟﻤﻄﻠﻘﺔ‬
Determinant
‫ﻣﺤﺪدة‬
Summation
‫ﻣﺠﻤﻮع‬
⎧x , x > 0
x =⎨
⎩−x , x < 0
a11
a21 a22
n =10
∑
n =0
∏
Product
‫ﺿﺮب‬
n =10
∩
‫ﺗﻘﺎﻃﻊ‬
= a11 × a22 − a12 × a21
1
1 1
1
= + + ⋅⋅⋅ +
n +2 2 3
11
∏
n =0
Intersection
a12
1
1 1
1
= × × ⋅⋅⋅×
n +1 2 3
11
n =10
∩A
n
= A 0 ∩ A1 ∩ ⋅⋅⋅ ∩ A10
n
= A 0 ∪ A1 ∪ ⋅⋅⋅ ∪ A10
n =0
n =10
∪
Uonion
‫ﺗﺤ ﺎدإ‬
∪A
n =0
6
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
∫
Integral
‫ﺗﻜﺎﻣﻞ‬
2
∫
1
1 2 1
3
xdx = x 2 = (4 − 1) =
2 1 2
2
∫∫
Double integral
‫ﺗﻜﺎﻣﻞ ﺛﻨﺎﺋﻲ‬
∫∫ f (x , y )dxdy
∫∫∫
∫
Triple integral
‫ﺗﻜﺎﻣﻞ ﺛﻼﺛﻲ‬
Line integral
‫ﺗﻜﺎﻣﻞ ﺧﻄﻲ‬
∫∫∫ g (x , y , z )dxdydz
∫ dl
∫∫
Surface integral
∫∫∫
Volume integral
Contour integral
C
‫ﺗﻜﺎﻣﻞ ﺳﻄﺤﻲ‬
A
‫ﺗﻜﺎﻣﻞ ﺣﺠﻤﻲ‬
Therefore
‫إذن‬
∵
Because
‫ﻷن‬
∃
Exist
∃/
Not exist
∀
For all
⇒
⇐
∫∫∫ dν
V
∴
¬ ‫∼ أو‬
∫∫ d σ
Propositional
if then
‫ﻣﻜﻤﻢ وﺟﻮدي‬
b ‫ ﺗﻮﺟﺪ‬a ‫∀ ﻟﺠﻤﻴﻊ‬a , ∃b
‫ﻣﻜﻤﻢ ﻏﻴﺮ ﺟﻮدي‬
b ‫ ﻻ ﺗﻮﺟﺪ‬a ‫∀ ﻟﺠﻤﻴﻊ‬a , ∃/b
‫ﻣﻜﻤﻢ آﻠﻲ‬
b ‫ ﺗﻮﺟﺪ‬a ‫∀ ﻟﺠﻤﻴﻊ‬a , ∃b
‫ ∼( ∼ ﻧﻘﻴﺾ أو ﻧﻔﻲ‬p ) = p
‫ إﺳﺘﻨﺘﺎج ﻣﻦ اﻟﻄﺮف‬p ⇒ q ⎫
⇒ p⇒r
‫ اﻷﻳﺴﺮ‬q ⇒ r ⎬
⎭
‫إﺳﺘﻨﺘﺎج ﻣﻦ اﻟﻄﺮف‬
‫اﻷﻳﻤﻦ‬
7
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
⇔
if and only if
iff
∈
Membership
Element of
∉
Not member
‫ إﺳﺘﻨﺘﺎج ﻣﻦ اﻟﻄﺮﻓﻴﻦ‬p ⇒ q ⎫
⇒ p ⇔q
‫ إذا و ﻓﻘﻂ إذا‬q ⇒ p ⎬
⎭
‫ ﻳﻨﺘﻤﻲ‬A = {a ,b ,c } , a ∈ A
‫ﻋﻀﻮ ﻣﻦ‬
‫ ﻻ ﻳﻨﺘﻤﻲ أو‬A = {a ,b ,c } , d ∉ A
‫ﻏﻴﺮﻋﻀﻮ‬
∪
Union
‫ إﺗﺤﺎد‬A = {a ,b ,c } , B = {a , d }
A ∪ B = {a ,b ,c , d }
Intersection
‫ ﺗﻘﺎﻃﻊ‬A ∩ B = {a}
⊆ ‫⊂ و‬
(proper) Subset
‫ ﺟﺰﺋﻴﻪ‬C = {a} , C ⊆ A
⊇‫⊃ و‬
superset
‫إﺣﺘﻮاء‬
∩
⊄
Not subset
∅
Empty set
‫⊂ ∅ ﻏﻴﺮ ﺟﺰﺋﻴﻪ‬
/ B
‫{ = ∅ اﻟﻤﺠﻤﻮﻋﻪ اﻟﺨﺎﻟﻴﻪ‬
}
∅′ = M
‫ﻣﺘﻤﻢ اﻟﻤﺠﻤﻮﻋﺔ اﻟﺨﺎﻟﻴﺔ ﻳﺴﺎوي اﻟﻤﺠﻤﻮﻋﺔ‬
‫اﻟﺸﺎﻣﻠﺔ‬
‫ أو‬D X '
Derivation to x
x ‫إﺷﺘﻘﺎق ﺑﺎﻟﻨﺴﺒﺔ ل‬
d
dx
∂
,
df
= 2x
dx
,
∂f
= 2x
∂x
,
df 2
= 6x
dx 2
f ′(x ) = 2x
Paritial
‫ﺗﻔﺎﺿﻞ ﺟﺰﺋﻲ‬
derivation
dn
dx n
f (x ) = x 2
Derivation n
order
nth , nth
n ‫ﺗﻔﺎﺿﻞ رﺗﺒﺔ‬
f (x ) = x 2
f (x ) = x
3
8
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
∂n
∂x n
Partial
derivation n
‫ﺗﻔﺎﺿﻞ ﺟﺰﺋﻲ رﺗﺒﺔ‬
n
f (x ) = x
3
,
∂f 2
= 6x
∂x 2
order nth
∇
Nabla
Laplace
‫ﻧﺎﺑﻼ أو ﻣﻌﻤﻞ‬
‫ﻻﺑﻼس‬
∇=
∂
∂
∂
+
+
∂x ∂y ∂z
operator (Nabla)
∇2
Square Lap. Op.
Laplacian
AB
→
AB
↔
AB
Line segment
Ray
Infinity line
‫ﻣﺮﺑﻊ )ﺗﺮﺑﻴﻊ( ﻣﻌﻤﻞ‬
∂2
∂2
∂2
∇ = 2+ 2+ 2
‫ﻻﺑﻼس‬
∂x
∂y
∂z
2
‫ﻗﻄﻌﺔ ﻣﺴﺘﻘﻴﻢ‬
(‫ﺷﻌﺎع )ﻣﺴﺘﻘﻴﻢ‬
‫ﻣﺴﺘﻘﻴﻢ ﻏﻴﺮ ﻣﻨﺘﻪ‬
‫ ﻣﺜﻠﺚ‬ΔABC , ABC ‫اﻟﻤﺜﻠﺚ‬
Δ
Triangle
∠
Angle
(‫∠ زاوﻳﻪ )ﺣﺎدة‬ABC , ABC ‫اﻟﺰاوﻳﻪ‬
∟
Right angle
(‫زاوﻳﻪ )ﻗﺎﺋﻤﺔ‬
Square
Parallelogram
‫ﻣﺮﺑﻊ‬
‫ﻣﺘﻮازي اﻷﺿﻠﻊ‬
○
Circle
‫داﺋﺮﻩ‬
⊥
Perpendicular
‫ ﻋﻤﻮد‬AB ⊥ AC
Parallel
‫ ﻣﻮازي‬AB
AC
∼
Similar
‫ ﺗﺸﺎﺑﻪ‬ΔABC ∼ ΔA ′B ′C ′
≅
Congruent
‫ ﺗﻄﺎﺑﻖ‬ΔABC ≅ ΔA ′B ′C ′
Arc
‫ﻗﻮس‬
ABC ‫ﻗﻮس‬
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫"‪ 30°15' 25‬ﻋﻼﻣﺔ اﻟﺪرﺟﻪ‬
‫ﻋﻼﻣﺔ اﻟﺪﻗﻴﻘﺔ‬
‫ﻋﻼﻣﺔ اﻟﺜﺎﻧﻴﺔ‬
‫ﻓﻲ اﻟﺼﻔﺤﺔ ) ‪( −1,5.7‬‬
‫إﺣﺪاﺛﻴﺎت آﺎرﺗﻴﺰﻳﺔ‬
‫‪9‬‬
‫‪Degree‬‬
‫‪°‬‬
‫‪Minute‬‬
‫'‬
‫"‬
‫‪Second‬‬
‫‪Cartesian‬‬
‫) ‪(x , y‬‬
‫‪Coordinate‬‬
‫ﻓﻲ اﻟﻔﻀﺎء )‪ (1.4,0, 2‬إﺣﺪاﺛﻴﺎت ﻓﻀﺎﺋﻴﺔ‬
‫إﺣﺪاﺛﻴﺎت ﻗﻄﺒﻴﺔ‬
‫‪°‬‬
‫) ‪(9, 25‬‬
‫→‬
‫‪AB‬‬
‫‪ V ⊕W‬ﻣﺠﻤﻮع ﻣﺒﺎﺷﺮ‬
‫ﻣﺘﺠﻬﻪ‬
‫‪ W‬و‪ V‬ﻓﻀﺎﺋﺎن ﻣﺘﺠﻬﻴﺎن‬
‫‪Space Coo.‬‬
‫) ‪(x , y , z‬‬
‫‪Polar Coo.‬‬
‫) ‪( r ,θ‬‬
‫‪Vector‬‬
‫→‬
‫‪Direct sum‬‬
‫⊕‬
‫‪n‬‬
‫ﺗﺤﻠﻴﻞ اﻟﻔﻀﺎﺋﺎت اﻟﻤﺘﺠﻬﻴﺔ أو اﻟﺰﻣﺮ‬
‫‪X = ⊕X i‬‬
‫‪i =1‬‬
‫اﻟﻰ ﻓﻀﺎﺋﺎت ﻣﺘﺠﻬﻴﺔ ﺟﺰﺋﻴﺔ أو اﻟﻰ زﻣﺮ ﺟﺰﺋﻴﺔ‬
‫‪n‬‬
‫ﺗﺤﻠﻴﻞ اﻟﻔﻀﺎﺋﺎت اﻟﻤﺘﺠﻬﻴﺔ أو اﻟﺰﻣﺮ‬
‫‪X = ⊗X i‬‬
‫‪i =1‬‬
‫ﺟﺪاء ﻣﺒﺎﺷﺮ ‪ ،‬ﺟﺪاء‬
‫‪Direct product‬‬
‫⊗‬
‫ﺳﻠّﻤﻲ‬
‫اﻟﻰ ﻓﻀﺎﺋﺎت ﻣﺘﺠﻬﻴﺔ ﺟﺰﺋﻴﺔ أو اﻟﻰ زﻣﺮ ﺟﺰﺋﻴﺔ‬
‫‪p ∧q‬‬
‫‪q‬‬
‫‪p‬‬
‫ﺛﺎﺑﺖ اﻟﻮﺻﻞ‬
‫‪T‬‬
‫‪T‬‬
‫‪T‬‬
‫)اﻟﻌﻄﻒ( ‪ ،‬و‬
‫‪F‬‬
‫‪F‬‬
‫‪T‬‬
‫‪F‬‬
‫‪T‬‬
‫‪F‬‬
‫‪F‬‬
‫‪F‬‬
‫‪F‬‬
‫‪p ∨q‬‬
‫‪q‬‬
‫‪p‬‬
‫‪T‬‬
‫‪T‬‬
‫‪T‬‬
‫‪T‬‬
‫‪F‬‬
‫‪T‬‬
‫‪T‬‬
‫‪T‬‬
‫‪F‬‬
‫‪F‬‬
‫‪F‬‬
‫‪F‬‬
‫‪and‬‬
‫∧‬
‫ﺻﺢ‬
‫‪True‬‬
‫‪T‬‬
‫ﻏﻠﻂ‬
‫‪False‬‬
‫‪F‬‬
‫ﺛﺎﺑﺖ اﻟﻔﺼﻞ ‪ ،‬أو‬
‫‪or‬‬
‫∨‬
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫!‪n‬‬
‫= ‪P n = (n )k‬‬
‫‪k‬‬
‫!) ‪(n − k‬‬
‫ﺗﺒﺪﻳﻞ‬
‫‪10‬‬
‫‪Permutation‬‬
‫‪ (n ) k‬أو‬
‫‪ k‬ﺷﺊ ﻣﻦ ‪ n‬ﺷﺊ‬
‫‪Pkn‬‬
‫ﺗﺒﺪﻳﻞ اﻷﺷﻴﺎء ﻣﺴﻤﻮح و ﺗﻜﺮارهﺎ ﻏﻴﺮ ﻣﺴﻤﻮح‬
‫⎞‪⎛n‬‬
‫!‪n‬‬
‫= ⎟⎟ ⎜⎜ = ‪C n‬‬
‫!) ‪k ⎝ k ⎠ k!(n − k‬‬
‫ﺗﻮﻓﻴﻘﻴﺔ‬
‫‪Combination‬‬
‫‪ k‬ﺷﺊ ﻣﻦ ‪ n‬ﺷﺊ‬
‫) (‬
‫أو ‪C kn‬‬
‫‪n‬‬
‫‪k‬‬
‫اﻟﺘﺒﺪﻳﻞ و اﻟﺘﻜﺮار ﻏﻴﺮ ﻣﺴﻤﻮح‬
‫= ‪ i‬اﻟﻌﺪد اﻟﺨﻴﺎﻟﻲ‬
‫‪−1‬‬
‫‪Imaginary‬‬
‫‪i‬‬
‫‪number‬‬
‫‪ e = 2.7182818284...‬ﻋﺪد ﻧﺎﺑﻴﺮ‬
‫‪Napier’s‬‬
‫ﻋﺪد أوﻳﻠﺮ‬
‫‪constant‬‬
‫‪e‬‬
‫‪Euler’s number‬‬
‫‪π = 3.14159265...‬‬
‫اﻟﻨﺴﺒﺔ اﻟﺜﺎﺑﺘﺔ‬
‫‪ϕ = 1.618033988‬‬
‫اﻟﻨﺴﺒﺔ اﻟﺬهﺒﻴﺔ‬
‫ﻣﺘﻮﺳﻂ أو وﺳﻂ‬
‫‪n‬‬
‫‪∑xn‬‬
‫‪n =1‬‬
‫‪n‬‬
‫‪Pi‬‬
‫‪π‬‬
‫‪ϕ‬‬
‫‪mean‬‬
‫‪x‬‬
‫‪Golden ratio‬‬
‫= ‪x‬‬
‫‪sin x‬‬
‫‪=1‬‬
‫‪x →0‬‬
‫‪x‬‬
‫‪lim‬‬
‫‪1‬‬
‫∞‪= +‬‬
‫‪x −1‬‬
‫‪lim+‬‬
‫ﻧﻬﺎﻳﺔ‬
‫ﻻ ﻧﻬﺎﻳﺔ‬
‫‪Infinity‬‬
‫∞‬
‫‪x →1‬‬
‫}⋅⋅⋅ ‪= {1, 2,3, 4,‬‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫اﻟﻄﺒﻴﻌﻴﻪ‬
‫}⋅⋅⋅ ‪= {0,1, 2,3, 4,‬‬
‫‪limit‬‬
‫‪lim‬‬
‫‪0‬‬
‫اﻷﻋﺪاد اﻟﻄﺒﻴﻌﻴﻪ ﻣﻊ‬
‫‪0‬‬
‫‪Natural‬‬
‫‪numbers‬‬
‫‪Natrural with 0‬‬
‫‪0‬‬
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫}⋅⋅⋅ ‪= {⋅⋅⋅, −2, −1,0,1,2,‬‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫‪11‬‬
‫‪Integer numbers‬‬
‫اﻟﺼﺤﻴﺤﻪ‬
‫‪⎧m‬‬
‫⎫‬
‫⎬‪= ⎨ : m , n ∈ , n ≠ 0‬‬
‫‪⎩n‬‬
‫⎭‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫‪Rational‬‬
‫اﻟ ُﻤﻨﻄﻘﺔ‬
‫‪numbers‬‬
‫إﺗﺤﺎد ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد اﻟ ُﻤﻨﻄﻘﺔ و اﻟﻐﻴﺮ‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫ُﻣﻨﻄﻘﺔ‪) ،‬اﻟﺴﺎﻟﺒﺔ و اﻟﻤﻮﺟﺒﺔ و اﻟﺼﻔﺮ(‬
‫اﻟﺤﻘﻴﻘﻴﺔ‬
‫‪Real numbers‬‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد اﻟﺤﻘﻴﻘﻴﺔ اﻟﻤﻮﺟﺒﺔ و اﻟﺼﻔﺮ ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫‪Positive Real‬‬
‫‪.‬‬
‫اﻟﺤﻘﻴﻘﻴﺔ اﻟﻤﻮﺟﺒﺔ‬
‫‪mumbers‬‬
‫ﻣﺠﻤﻮﻋﺔ ﻋﺪدﻳﺔ ﺗﻜﻮن ﻓﻴﻬﺎ اﻷﻋﺪاد ﺑﺼﻮرة‬
‫ﻣﺠﻤﻮﻋﺔ اﻷﻋﺪاد‬
‫‪Complex‬‬
‫اﻟﻤﺮآﺒﺔ أو اﻟﻌﻘﺪﻳﺔ‬
‫‪numbers‬‬
‫‪x + iy‬‬
‫و هﻜﺬا ‪ ،‬ﺳﻠﺴﻠﺔ ﻏﻴﺮ‬
‫‪and so on‬‬
‫‪+‬‬
‫⋅⋅⋅‬
‫ﻣﻨﺘﻬﻴﺔ‬
‫) ‪ y := f ( x‬ﺗﻌﺮﻳﻒ اﻟﻄﺮف‬
‫اﻷﻳﺴﺮ ﻣﻦ ﺧﻼل‬
‫اﻟﻄﺮف اﻷﻳﻤﻦ‬
‫‪Left hand side‬‬
‫=‪:‬‬
‫‪is defined by‬‬
‫‪the right hand‬‬
‫‪side‬‬
‫‪max {−1,3,4,2} = 4‬‬
‫ﻧﻬﺎﻳﺔ ﻋﻈﻤﻰ‬
‫‪Maximum‬‬
‫} { ‪max‬‬
‫‪min {−1,3,4, 2} = −1‬‬
‫ﻧﻬﺎﻳﺔ ﺻﻐﺮى‬
‫‪Minimum‬‬
‫} { ‪min‬‬
‫‪1‬‬
‫‪2‬‬
‫= ‪sin 30°‬‬
‫‪1‬‬
‫‪2‬‬
‫= ‪cos 60°‬‬
‫ﺟﻴﺐ‬
‫ﺟﻴﺐ اﻟﺘﻤﺎم‬
‫‪ tan 45° = 1‬ﻇﻞ‬
‫‪Sine‬‬
‫‪sin‬‬
‫‪Cosine‬‬
‫‪cos‬‬
‫‪Tangent‬‬
‫‪tan‬‬
12
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
cot
Cotangent
sec
Secant
csc
Cosecant
‫ﻗﺎﻃﻊ اﻟﺘﻤﺎم‬
Arc sin
Arc sine
‫ﻗﻮس اﻟﺠﻴﺐ‬
Arc cos
Arc cosine
‫ ﻇﻞ اﻟﺘﻤﺎم‬cot 45° = 1
‫ﻗﺎﻃﻊ‬
‫ﻗﻮس اﻟﺠﻴﺐ ﺗﻤﺎم‬
secθ =
1
cosθ
cscθ =
1
sin θ
Arc sin
1
= 30°
2
π
45° = ( ) rad
4
Arc cos
Arc tan
Arc tangent
Arc cot
Arc cotangent
Arc sec
Arc secant
Arc csc
Arc cosecant
‫ أو‬sinh
Hyperbolic sine
sh
‫ أو‬cosh
ch
sec h
Hyperbolic
cosine
Hyperbolic
secant
cs c h
Hyperbolic
cosevant
: ‫ رادﻳﺎن‬Radian
2
π
= 45° = ( ) rad
2
4
‫ﻗﻮس اﻟﻈﻞ‬
‫ﻗﻮس اﻟﻈﻞ ﺗﻤﺎم‬
‫ﻗﻮس اﻟﻘﺎﻃﻊ‬
‫ﻗﻮس اﻟﻘﺎﻃﻊ اﻟﺘﻤﺎم‬
e x − e −x
sinh x =
(‫)اﻟﻬﺬﻟﻮﻟﻲ‬
2
‫ﺟﻴﺐ اﻟﺰاﺋﺪي‬
e x + e −x
cosh x =
(‫)اﻟﻬﺬﻟﻮﻟﻲ‬
2
‫ﺟﻴﺐ اﻟﺘﻤﺎم اﻟﺰاﺋﺪي‬
‫ﻗﺎﻃﻊ اﻟﺰاﺋﺪي‬
(‫)اﻟﻬﺬﻟﻮﻟﻲ‬
‫ﻗﺎﻃﻊ اﻟﺘﻤﺎم اﻟﺰاﺋﺪي‬
(‫)اﻟﻬﺬﻟﻮﻟﻲ‬
sec hx =
2
e x + e −x
cs c hx =
2
e − e −x
x
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫ﻇﻞ اﻟﺘﻤﺎم اﻟﺰاﺋﺪي‬
‫‪e 2x − 1‬‬
‫‪tanh x = 2 x‬‬
‫)اﻟﻬﺬﻟﻮﻟﻲ(‬
‫‪e +1‬‬
‫ﻇﻞ اﻟﺘﻤﺎم اﻟﺰاﺋﺪي‬
‫‪e 2x + 1‬‬
‫‪coth x = 2 x‬‬
‫)اﻟﻬﺬﻟﻮﻟﻲ(‬
‫‪e −1‬‬
‫ﻗﻮس اﻟﺠﻴﺐ اﻟﺰاﺋﺪي‬
‫)اﻟﻬﺬﻟﻮﻟﻲ(‬
‫‪⎧1, i = j‬‬
‫‪⎩0, i ≠ j‬‬
‫⎨ = ‪δ ij‬‬
‫)‪n (n + 1‬‬
‫‪2‬‬
‫‪tangent‬‬
‫‪th‬‬
‫‪ cot anh Hyperbolic‬أو‬
‫‪cotangent‬‬
‫‪Arc hyperbolic‬‬
‫‪coth‬‬
‫‪Arc sinh‬‬
‫‪sine‬‬
‫ﻗﻮس اﻟﺠﻴﺐ اﻟﺘﻤﺎم‬
‫اﻟﺰاﺋﺪي )اﻟﻬﺬﻟﻮﻟﻲ(‬
‫‪cosine‬‬
‫دﻟﺘﺎ آﺮوﻧﻜﺮ‬
‫‪ tanh‬أو‬
‫‪Kronecher delta‬‬
‫‪Tensor‬‬
‫‪Arc cosh‬‬
‫‪δ‬‬
‫‪ T ij‬أو ‪T jki‬‬
‫‪T jki‬‬
‫‪ i‬دﻟﻴﻞ ﻋﻠﻮي و ‪ j‬و ‪ k‬دﻻﺋﻞ ﺳﻔﻠﻴﻪ‬
‫= ‪Sn‬‬
‫‪Hyperbolic‬‬
‫‪Arc hyperbolic‬‬
‫‪ i = 1, 2‬و ‪ T ij = T 1 j + T 2 j‬ﺗﻴﻨﺴﻮر أو ﻣﻮﺗﺮ‬
‫‪،‬‬
‫‪13‬‬
‫‪1 + 2 + 3 + ⋅⋅⋅ + n‬‬
‫ﻣﺠﻤﻮع ﻣﺘﺘﺎﻟﻴﺔ‬
‫‪ Log 10100 = Log 100 = 2‬ﻟﻮﻏﺎرﻳﺜﻢ‬
‫‪ Log e x = ln x‬اﻟﻠﻮﻏﺎرﻳﺜﻢ اﻟﻄﺒﻴﻌﻲ‬
‫‪Sequence‬‬
‫‪Sn‬‬
‫‪Logarithm‬‬
‫‪Log ab‬‬
‫‪Natural‬‬
‫‪ln‬‬
‫‪logarithm‬‬
‫‪102 = 100‬‬
‫‪ a‬أس ‪n‬‬
‫) ‪ P ( A B‬إﺣﺘﻤﺎل وﻗﻮع ‪ A‬إذا ﺣﺪﺛﺖ ‪ B‬إﺣﺘﻤﺎل‬
‫‪a power n‬‬
‫‪an‬‬
‫‪Probability‬‬
‫|‬
‫ﻓﻲ ﻧﻈﺮﻳﺔ اﻟﺪوال ﻟﺘﻌﺮﻳﻒ ﻗﻴﻤﺔ اﻟﺪاﻟﺔ أو‬
‫اﻹﺷﺘﻘﺎق أو اﻟﺘﻜﺎﻣﻞ ﻓﻲ ﻧﻘﻄﺔ أو ﻧﻘﺎط ﻣﻌﻴﻨﺔ‬
‫‪x =0+‬‬
‫‪∂f‬‬
‫‪∂x‬‬
‫داﻟﺔ أو ﺗﺎﺑﻊ‬
‫‪Function‬‬
‫ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫)) ‪g (x ) → f ( g (x‬‬
‫○‬
‫‪ f‬ﺗﺮآﻴﺐ‬
‫ﺗﺎﺑﻊ اﻟﻌﻼﻣﺔ أو‬
‫‪⎧1, x > 0‬‬
‫⎪ = ‪ sgn x‬اﻹﺷﺎرة‬
‫‪⎨0, x = 0‬‬
‫‪⎪−1, x < 0‬‬
‫⎩‬
‫∞‬
‫ﻧﺤﻮ اﻷﺳﻔﻞ‬
‫‪Rounded down‬‬
‫ﻧﺤﻮ اﻷﻋﻠﻰ‬
‫‪Rounded up‬‬
‫‪∂F ∂F ∂F‬‬
‫‪+ +‬‬
‫‪∂x ∂y ∂z‬‬
‫= ‪divF = ∇⋅ F‬‬
‫‪k‬‬
‫∂‬
‫‪∂z‬‬
‫‪Fz‬‬
‫∂‬
‫‪∂y‬‬
‫‪Fy‬‬
‫∂‬
‫‪∂x‬‬
‫‪Fx‬‬
‫‪sign function‬‬
‫‪sgn x‬‬
‫‪ x‬ﻳﺴﻌﻰ ﻧﺤﻮ‬
‫‪∂F ∂F ∂F‬‬
‫‪i+‬‬
‫‪j+ k‬‬
‫‪∂x ∂y‬‬
‫‪∂z‬‬
‫‪j‬‬
‫‪Composition‬‬
‫‪O‬‬
‫‪Tend to‬‬
‫= ‪gradF =∇× F‬‬
‫‪i‬‬
‫‪14‬‬
‫↓‬
‫ﺗﺪرج‬
‫‪Gradient‬‬
‫↑‬
‫‪grad‬‬
‫ﺗﺒﺎﻋﺪ‬
‫‪Divergence‬‬
‫‪div‬‬
‫‪Rotation‬‬
‫‪curl‬‬
‫دوران‬
‫= ‪curlF = ∇× F‬‬
‫ﻳﻀﻢ هﺬا اﻟﺒﺤﺚ ﻣﻌﻈﻢ ﻋﻼﺋﻢ و رﻣﻮز اﻟﺮﻳﺎﺿﻴﺎت و ﻟﻴﺲ ﺟﻤﻴﻌﻬﺎ ‪ .‬آﺬﻟﻚ ﺑﻌﺾ اﻟﺮﻣﻮز ﻟﻬﺎ إﺳﺘﻌﻤﺎﻻت‬
‫أﺧﺮى أآﺘﻔﻴﺖ ﺑﺄﺷﻬﺮهﺎ ‪.‬‬
‫ﺟﻼل اﻟﺤﺎج ﻋﺒﺪ‬
‫ﺷﺘﺎء ‪2008‬‬
‫ ل ا
ج‬
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