Calculus symbols

Calculus & analysis math symbols table

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
	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
∬	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
z	complex conjugate	z = a+bi → z = a-bi	z = 3 + 2i
Re(z)	real part of a complex number	z = a+bi → Re(z)=a	Re(3 - 2i) = 3
Im(z)	imaginary part of a complex number	z = a+bi → Im(z)=b	Im(3 - 2i) = -2
| z |	absolute value/magnitude of a complex number	|z| = |a+bi| = √(a2+b2)	|3 - 2i| = √13
arg(z)	argument of a complex number	The angle of the radius in the complex plane	arg(3 + 2i) = 33.7°
∇	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
∞	lemniscate	infinity symbol