01:简介
全球最大的软件公司微软
02:常识
微软,开发软件时,收集的资料应算是全面性的,算是够齐全的了
所以以最微软最普及的办公软件WORD应是够客观的
03:材料
微软 OFFICE WORD 软件
04:操作步验如图示
注意事项:提供的截图接口虽为英文(我会加注中文字),但是请参考相同位置及图标即可
看你须要那个符号
自行复制/粘贴
= equals sign equality 5 = 2+3
5 is equal to 2+3
≠ not equal sign inequality 5 ≠ 4
5 is not equal to 4
≈ approximately equal approximation sin(0.01) ≈ 0.01,
x≈ymeansxis approximately equal toy
> strict inequality greater than 5 > 4
5 is greater than 4
< strict inequality less than 4 < 5
4 is less than 5
≥ inequality greater than or equal to 5 ≥ 4,
x≥ymeansxis greater than or equal toy
≤ inequality less than or equal to 4 ≤ 5,
x ≤ ymeansxis less than or equal toy
( ) parentheses calculate expression inside first 2 × (3+5) = 16
[ ] brackets calculate expression inside first [(1+2)×(1+5)] = 18
+ plus sign addition 1 + 1 = 2
− minus sign subtraction 2 − 1 = 1
± plus - minus both plus and minus operations 3 ± 5 = 8 and -2
± minus - plus both minus and plus operations 3 ∓ 5 = -2 and 8
* asterisk multiplication 2 * 3 = 6
× times sign multiplication 2 × 3 = 6
⋅ multiplication dot multiplication 2 ⋅ 3 = 6
÷ division sign / obelus division 6 ÷ 2 = 3
/ division slash division 6 / 2 = 3
— horizontal line division / fraction
mod modulo remainder calculation 7 mod 2 = 1
. period decimal point, decimal separator 2.56 = 2+56/100
ab power exponent 23= 8
a^b caret exponent 2 ^ 3= 8
√a square root
√a⋅√a= a
√9= ±3
3√a cube root 3√a⋅3√a⋅3√a= a 3√8= 2
4√a fourth root 4√a⋅4√a⋅4√a⋅4√a= a 4√16= ±2
n√a n-th root (radical) forn=3,n√8= 2
% percent 1% = 1/100 10% × 30 = 3
‰ per-mille 1‰ = 1/1000 = 0.1% 10‰ × 30 = 0.3
ppm per-million 1ppm = 1/1000000 10ppm × 30 = 0.0003
ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7
ppt per-trillion 1ppt = 10-12 10ppt × 30 = 3×10-10
∠ angle formed by two rays ∠ABC = 30°
measured angle ABC = 30°
spherical angle AOB = 30°
∟ right angle = 90° α = 90°
° degree 1 turn = 360° α = 60°
deg degree 1 turn = 360deg α = 60deg
′ prime arcminute, 1° = 60′ α = 60°59′
″ double prime arcsecond, 1′ = 60″ α = 60°59′59″
line infinite line
AB line segment line from point A to point B
ray line that start from point A
arc arc from point A to point B = 60°
⊥ perpendicular perpendicular lines (90° angle) AC⊥BC
| | parallel parallel lines AB| |CD
≅ congruent to equivalence of geometric shapes and size ∆ABC≅ ∆XYZ
~ similarity same shapes, not same size ∆ABC~ ∆XYZ
Δ triangle triangle shape ΔABC≅ ΔBCD
|x-y| distance distance between points x and y |x-y| = 5
π pi constant π= 3.141592654...
is the ratio between the circumference and diameter of a circle
c=π⋅d= 2⋅π⋅r
rad radians radians angle unit 360° = 2π rad
c radians radians angle unit 360° = 2πc
grad gradians / gons grads angle unit 360° = 400 grad
g gradians / gons grads angle unit 360° = 400g
Algebra symbols
x x variable unknown value to find when 2x= 4, thenx= 2
≡ equivalence identical to
≜ equal by definition equal by definition
:= equal by definition equal by definition
~ approximately equal weak approximation 11 ~ 10
≈ approximately equal approximation sin(0.01) ≈ 0.01
∝ proportional to proportional to
y∝xwheny=kx, kconstant
∞ lemniscate infinity symbol
≪ much less than much less than 1 ≪ 1000000
≫ much greater than much greater than 1000000 ≫ 1
( ) parentheses calculate expression inside first 2 * (3+5) = 16
[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18
{ } braces set
⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋ = 4
⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉ = 5
x! exclamation mark factorial 4! = 1*2*3*4 = 24
|x| single vertical bar absolute value | -5 | = 5
f(x) function of x maps values of x to f(x) f(x) = 3x+5
(f∘g) function composition (f∘g) (x) =f(g(x)) f(x)=3x,g(x)=x-1 ⇒(f∘g)(x)=3(x-1)
(a,b) open interval (a,b) = {x|a<x<b} x∈ (2,6)
[a,b] closed interval [a,b] = {x|a≤x≤b} x∈ [2,6]
∆ delta change / difference ∆t=t1-t0
∆ discriminant Δ =b2- 4ac
∑ sigma summation - sum of all values in range of series ∑xi= x1+x2+...+xn
∑∑ sigma double summation
∏ capital pi product - product of all values in range of series ∏xi=x1∙x2∙...∙xn
e e constant/ Euler's number e= 2.718281828... e= lim (1+1/x)x,x→∞
γ Euler-Mascheroni constant γ = 0.5772156649...
φ golden ratio golden ratio constant
π pi constant π= 3.141592654...
is the ratio between the circumference and diameter of a circle
c=π⋅d= 2⋅π⋅r
· dot scalar product a·b
× cross vector product a×b
A⊗B tensor product tensor product of A and B A⊗B
inner product
[ ] brackets matrix of numbers
( ) parentheses matrix of numbers
|A| determinant determinant of matrix A
det(A) determinant determinant of matrix A
||x|| double vertical bars norm
AT transpose matrix transpose (AT)ij= (A)ji
A† Hermitian matrix matrix conjugate transpose (A†)ij= (A)ji
A* Hermitian matrix matrix conjugate transpose (A*)ij= (A)ji
A-1 inverse matrix A A-1=I
rank(A) matrix rank rank of matrix A rank(A) = 3
dim(U) dimension dimension of matrix A rank(U) = 3
Probability and statistics symbols
P(A) probability function probability of event A P(A) = 0.5
P(A∩B) probability of events intersection probability that of events A and B P(A∩B) = 0.5
P(A∪B) probability of events union probability that of events A or B P(A∪B) = 0.5
P(A|B) conditional probability function probability of event A given event B occured P(A | B) = 0.3
f(x) probability density function (pdf) P(a≤x≤b) =∫ f(x)dx
F(x) cumulative distribution function (cdf) F(x) =P(X≤x)
μ population mean mean of population values μ= 10
E(X) expectation value expected value of random variable X E(X) = 10
E(X | Y) conditional expectation expected value of random variable X given Y E(X | Y=2) = 5
var(X) variance variance of random variable X var(X) = 4
σ2 variance variance of population values σ2= 4
std(X) standard deviation standard deviation of random variable X std(X) = 2
σX standard deviation standard deviation value of random variable X σX=2
median middle value of random variable x
cov(X,Y) covariance covariance of random variables X and Y cov(X,Y) = 4
A ⊅ B not superset set A is not a superset of set B {9,14,28} ⊅ {9,66}
2A power set all subsets of A
empty set Ø = { } C = {Ø}
complex numbers set = {z|z=a+bi, -∞<a<∞, -∞<b<∞} 6+2i∈
⋅ and and x⋅y
^ caret / circumflex and x^y
& ampersand and x&y
+ plus or x+y
∨ reversed caret or x∨y
| vertical line or x|y
x' single quote not - negation x'
x bar not - negation x
¬ not not - negation ¬x
! exclamation mark not - negation !x
⊕ circled plus / oplus exclusive or - xor x⊕y
~ tilde negation ~x
⇒ implies
⇔ equivalent if and only if (iff)
↔ equivalent if and only if (iff)
∀ for all
∃ there exists
∄ there does not exists
∴ therefore
∵ because / since
∫ integral opposite to derivation ∫f(x)dx
∫∫ double integral integration of function of 2 variables ∫∫f(x,y)dxdy
∫∫∫ triple integral integration of function of 3 variables ∫∫∫f(x,y,z)dxdydz
∮ closed contour / line integral
∯ closed surface integral
∰ closed volume integral
[a,b] closed interval [a,b] = {x|a≤x≤b}
(a,b) open interval (a,b) = {x|a<x<b}
i imaginary unit i≡ √-1 z= 3 + 2i
z* complex conjugate z=a+bi→z*=a-bi z*= 3 - 2i
z complex conjugate z=a+bi→z=a-bi z= 3 - 2i
∇ nabla / del gradient / divergence operator ∇f(x,y,z)
Α α Alpha a al-fa
Β β Beta b be-ta
Γ γ Gamma g ga-ma
Δ δ Delta d del-ta
Ε ε Epsilon e ep-si-lon
Ζ ζ Zeta z ze-ta
Η η Eta h eh-ta
Θ θ Theta th te-ta
Ι ι Iota i io-ta
Κ κ Kappa k ka-pa
Λ λ Lambda l lam-da
Μ μ Mu m m-yoo
Ν ν Nu n noo
Ξ ξ Xi x x-ee
Ο ο Omicron o o-mee-c-ron
Π π Pi p pa-yee
Ρ ρ Rho r row
Σ σ Sigma s sig-ma
Τ τ Tau t ta-oo
Υ υ Upsilon u oo-psi-lon
Φ φ Phi ph f-ee
Χ χ Chi ch kh-ee
Ψ ψ Psi ps p-see
Ω ω Omega o o-me-ga
