SYMBOL

NAME

ℝ

real numbers

[a, b]

closed interval {x | a ≤ x ≤ b}

(a, b)

open interval {x | a < x < b}

[a, b)

half-open interval {x | a ≤ x < b}

(a, b]

half-open interval {x | a < x ≤ b}

|a|

absolute value of a

ℚ

rational numbers

ℝⁿ

n-dimensional space

i, j, k

standard basis in ℝ³

‖a‖

norm of a vector a

a · b

inner product of the vectors a and b

a × b

cross product of the vectors a and b

(r, θ, z)

cylindrical coordinates

(ρ, θ, ϕ)

spherical coordinates

D_r(x₀)

disk of radius r about x₀

limit as x approaches x₀

left-hand limit; x → b from below

partial derivative of f with respect to x

D f(x₀)

derivative of f at the point x₀

∇f

grad f, gradient of the function f

C¹

continuously differentiable

c

a path

C²

twice continuously differentiable

Hf(x₀)

Hessian of f at the point x₀

∇

del or nabla

∇ · F

div F, divergence of F

∇ × F

curl F, curl of F

∇²

Laplacian

double integral

triple integral

Jacobian

c_op

opposite path

path integral

line integral

scalar surface integral

vector surface integral