
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 
(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  Leibniz'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's notation 


time second derivative 
derivative of derivative 

D_{x }y 
derivative 
derivative  Euler's notation 
D_{x }y for the first derivative 
D_{x}^{2}_{}y 
second derivative 
derivative of derivative 
D_{x}^{2}_{}y for the second derivative 

partial 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 contour / line integral 

∯ 
closed surface integral 
closed surface integral 

∰ 
closed volume integral 
closed volume integral 

[a,b] 
closed interval 
closed interval 
[a,b] = {x  a ≤ x ≤ b} 
(a,b) 
open interval 
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 
vector 


unit vector 
unit vector 

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

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

Fourier transform 
Fourier transform 
X(ω) = {f (t)} 
δ 
delta function 
delta function 

∞ 
lemniscate 
infinity symbol 
