Mathematical notations in physics

Physics is a science that is essentially based on measurement and modeling. The physicist’s background must therefore contain the tools and methods that allow him to:

1. derive rational information from his measurements.
2. approach the behavior of a model system using mathematical analysis.

Notations

Tab. 1 Mathematical notations

Symbol	Signification
def =	equal by definition
≃	approximately equal to
∼	equal in order of magnitude
A≫B	A very large in front of B
A≪B	A very small in front of B
AB⌢	arc length
[G]	dimension of the quantity G
	statistical mean of a random quantity or time mean of a signal
σs	standard deviation associated with a random quantity
srms	effective value of a signal
(ν) = TF[s(t)]	Fourier transform of the signal s(t)
(νx,νy) = TF2D[s(x,y)]	two-dimensional Fourier transform of the signal s(x,y)
δ(t)	Dirac impulse
z	complex magnitude
z*	conjugate complex
Re(z)	real part of z
Im(z)	imaginary part of z
∣z∣	modulus of z
arg(z)	argument of z
(x, y, z)	Cartesian base
(r, θ, z)	cylindrical base
(r, φ, z)	spherical base
∥∥ or A	norm of vector
	scalar product of two vectors
∧	vector product of two vectors
Az	component along the axis (Oz) = Az =  ⋅ z
= dy/dt	first derivative with respect to time
= d2y/dt2	second derivative with respect to time
∂f(x,y,z,t)/∂x or f′x	partial derivative of f with respect to the variable x
Df(x,y,z,t)/Dt	particular derivative of f with respect to the variable t
∮C(M,t)⋅d	circulation of a vector field along the closed-circuit C
∬S(M,t)⋅dS	Flow of a vector field
f or f	gradient of a scalar field f
div or ⋅	divergence of a vector field
or ∧	rotational of a vector field
Δf = ⋅f = ∇2f	Laplacian of a scalar field f
Δ	Laplacian of a vector field

 

Source: FEMTO, Les cours de physique. License CC BY-NC 4.0. Translated and adapted by Nicolae Sfetcu