Calculus symbols list (ε, y', d/dx , ∫)

Calculus Symbols

Calculus and analysis math symbols and definitions.

Calculus & analysis math symbols table

Symbol Symbol Name Meaning / definition Example

$\lim_{x\to x0}f(x)$ 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 (3x³)' = 9x²

y '' second derivative derivative of derivative (3x³)'' = 18x

y⁽ⁿ⁾ nth derivative n times derivation (3x³)⁽³⁾ = 18

$\frac{dy}{dx}$ derivative derivative - Lagrange's notation d(3x³)/dx = 9x²

$\frac{d^2y}{dx^2}$ second derivative derivative of derivative d²(3x³)/dx² = 18x

$\frac{d^ny}{dx^n}$ nth derivative n times derivation

$\dot{y}$ time derivative derivative by time - Newton notation

time second derivative derivative of derivative

$\frac{\partial f(x,y)}{\partial x}$ 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

z complex conjugate z = a+bi → z = a-bi 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

∞ lemniscate infinity symbol

See also

Math symbols

Algebra symbols

Calculus & analysis

Symbol	Symbol Name	Meaning / definition	Example
$\lim_{x\to x0}f(x)$	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	(3x³)' = 9x²
y ''	second derivative	derivative of derivative	(3x³)'' = 18x
y⁽ⁿ⁾	nth derivative	n times derivation	(3x³)⁽³⁾ = 18
$\frac{dy}{dx}$	derivative	derivative - Lagrange's notation	d(3x³)/dx = 9x²
$\frac{d^2y}{dx^2}$	second derivative	derivative of derivative	d²(3x³)/dx² = 18x
$\frac{d^ny}{dx^n}$	nth derivative	n times derivation
$\dot{y}$	time derivative	derivative by time - Newton notation
	time second derivative	derivative of derivative
$\frac{\partial f(x,y)}{\partial x}$	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
z	complex conjugate	z = a+bi → z = a-bi	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
∞	lemniscate	infinity symbol

Calculus Symbols

Calculus & analysis math symbols table

See also

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