Calculus & Analysis Symbols

Symbol	Symbol Name	Meaning / definition	Example
Lim f(x) x->x0	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 anotation	(3x3)' = 9x2
y ''	second derivative	derivative of derivative	(3x3)'' = 18x
y(n)	nth derivative	n times derivation	(3x3)(3) = 18
dy/dx	Derivative	derivative - Leibniz's notation	d(3x3)/dx = 9x2
d2y/dx2	second derivative	derivative of derivative	d2(3x3)/dx2 = 18x
dny/dxn	nth derivative	n times derivation
ẏ	time derivative	derivative by time - Newton's notation
Ÿ	time second derivative	derivative of derivative
Dx y	Derivative	derivative - Euler's notation
Dx2y	second derivative	derivative of derivative
∂f(x,y)/ ∂x	partial derivative		∂(x2+y2)/∂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*=a-bi	z* = 3 + 2i
Z̅	complex conjugate	z = a+bi → z̅ = a-bi	Z̅ = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
--> x	Vector
x̂	unit vector
x * y	Convolution	y(t) = x(t) * h(t)
ℒ	Laplace transform	F(s) = ℒ {f (t)}
F	Fourier transform	X(ω) =  {f (t)}
Δ	delta function
∞	Lemniscate	infinity symbol