Data Science - Math Fundamentals

Calculus Symbols

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