# Calculus Symbols

**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 – Leibniz’s notation

(3

*x*^{3})’ = 9*x*^{2}*y*”

second derivative

derivative of derivative

(3

*x*^{3})” = 18*x**y*

^{(n)}

nth derivative

n times derivation

(3

*x*^{3})^{(3)}= 18derivative

derivative – Lagrange’s notation

*d*(3

*x*

^{3})/

*dx*= 9

*x*

^{2}

second derivative

derivative of derivative

*d*

^{2}(3

*x*

^{3})/

*dx*

^{2}= 18

*x*

nth derivative

n times derivation

time derivative

derivative by time – Newton notation

time second derivative

derivative of derivative

partial derivative

∂(

*x*^{2}+*y*^{2})/∂*x*= 2*x*∫

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 + 2

*i*

*z**

complex conjugate

*z*=

*a*+

*bi*→

*z**=

*a*–

*bi*

*z**= 3 + 2

*i*

*z*

complex conjugate

*z*=

*a*+

*bi*→

*z*=

*a*–

*bi*

*z*= 3 + 2

*i*

∇

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