Calculus & analysis symbols 
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  Leibniz's notation 
(3x^{3})'
= 9x^{2} 
y '' 
second derivative 
derivative of derivative 
(3x^{3})''
= 18x 
y^{(n)} 
nth derivative 
n times derivation 
(3x^{3})^{(3)} = 18 

derivative 
derivative  Lagrange's notation 
d(3x^{3})/dx
= 9x^{2} 

second derivative 
derivative of derivative 
d^{2}(3x^{3})/dx^{2}
= 18x 

nth derivative 
n times derivation 


time derivative 
derivative by time  Newton notation 


time second derivative 
derivative of derivative 


partial derivative 

∂(x^{2}+y^{2})/∂x
= 2x 
∫ 
integral 
opposite to derivation 

∬ 
double integral 
integration of function of 2 variables 

∭ 
triple integral 
integration of function of 3 variables 

∮ 
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*=abi 
z* = 3 + 2i 
z 
complex conjugate 
z = a+bi →
z =
abi 
z = 3 + 2i 
∇ 
nabla / del 
gradient / divergence operator 
∇f (x,y,z) 

vector 



unit vector 


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


laplace transform 
F(s) =
{f (t)} 


Fourier transform 
X(ω) =
{f (t)} 

δ 
delta function 


∞ 
lemincate 
infinity symbol 
