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Calculus & analysis symbols

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Symbol

Symbol Name

Meaning / definition

Example

limit

limit value of a function

 

ε

epsilon

represents a very small number, near zero

ε 0

e

e constant / Euler's number

e = 2.718281828...

e = lim (1+1/x)x , x→∞

y '

derivative

derivative - Lagrange's notation

(3x3)' = 9x2

y ''

second derivative

derivative of derivative

(3x3)'' = 18x

y(n)

nth derivative

n times derivation

(3x3)(3) = 18

derivative

derivative - Leibniz's notation

d(3x3)/dx = 9x2

second derivative

derivative of derivative

d2(3x3)/dx2 = 18x

nth derivative

n times derivation

 

time derivative

derivative by time - Newton's notation

 

http://www.rapidtables.com/math/symbols/math_symbols/time_drivative_II.GIF

time second derivative

derivative of derivative

 

Dx y

derivative

derivative - Euler's notation

 

Dx2y

second derivative

derivative of derivative

 

partial derivative

 

∂(x2+y2)/∂x = 2x

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+biz*=a-bi

z* = 3 - 2i

z

complex conjugate

z = a+biz = a-bi

z = 3 - 2i

nabla / del

gradient / divergence operator

f (x,y,z)

http://www.rapidtables.com/math/symbols/math_symbols/vector.GIF

vector

 

 

http://www.rapidtables.com/math/symbols/math_symbols/unit%20vector.GIF

unit vector

 

 

x * y

convolution

y(t) = x(t) * h(t)

 

http://www.rapidtables.com/math/symbols/calculus_symbols/L.gif

Laplace transform

F(s) = http://www.rapidtables.com/math/symbols/calculus_symbols/L.gif{f (t)}

 

http://www.rapidtables.com/math/symbols/calculus_symbols/F.gif

Fourier transform

X(ω) = http://www.rapidtables.com/math/symbols/calculus_symbols/F.gif{f (t)}

 

δ

delta function

 

 

lemniscate

infinity symbol

 

 

 

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