Calculus notation question from old theoretical biology paper I'm working through The Moulding of Senescence by Natural Selection from 1966, and it uses an odd notation, $(\delta_x)(q_x)/(\delta x)$. I haven't seen the notation in the numerator. I'm assuming it's not equivalent to dq_x/dx, but it's not explained in the paper and I'm not sure how I'd even Google it to figure out what it means. Can anyone explain? Thank you!

 A: I've looked at the paper and it seems that the notation used is the same as that of actuarial notation for life tables.
In particular,
$${}_{\;\;\;\delta x}q_x = \text{ the probability of death between ages } x \text{ and } x+\delta x \; .$$
So, the $\delta x$ is not indicating a derivative, but is a front index of the mortality variable $q$ and it indicates the time interval over which a death might occur.
A: $\delta q$ in mechanics at least refers to a variation.
A variation is a change that does not occur in time.
For example, suppose you have a system of particles with positions and momenta $q_i, p_i$ subject to a central force.
And you'd like to see the effect a small instantaneous change in one of the particles positions on the system dynamics.
$\delta q_i$ refers to a variation in particle's  $i$ position.
This variation is not dependent on time.
from this you can derive Lagrangian mechanics.
In a continuous system (take a string for example) the discrete index $i$ is replaced with $x\in R$.
so the variation $\delta q_x$ allows you to derive the forces acting on the string and develop the wave equation as a limiting process of discrete variations.
