Table of Calculus & Analysis Symbols with Examples

 

Math Calculus & Analysis with Examples

Symbol	Symbol Name	Symbol Meaning	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	Dx y for the first derivative
Dx2y	second derivative	derivative of derivative	Dx2y for the second derivative
	partial 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 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*=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	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

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