Dear fellow controlniks
There have been some responses to our posting of our proposals for
a revised MCA nomenclature. We purposely waited for a few things
to happen before responding: the time seems ripe now. We'll tackle
things one at a time. First, the question of the systematic
use of partial and total derivatives in our definitions. The
comments that prompted the matter are repeated at the end of this
message.
Although our biochemical colleagues probably regard us (write
us off?) as "mathematicians", we certainly won't fit the bill for
our colleagues from the Maths department. But we believe that this
business can be solved from basic principles. Let's review some
calculus (we are reduced to using ASCII art for our mathematical
notation: in the following we use "d" for a total differential
operator and "c" for a partial differential operator - from "curly
dee").
Consider a function z = f(x,y). The total differential dz is given
by (this is standard calculus)
dz = (cz/cx)dx + (cz/cy)dy ..............(1)
where cz/cx and cz/cy are partial derivatives at constant y and x
respectively.
The total differential describes the situation where both x and y
can vary simultaneously. Geometrically, this means a point moves along
a curve on a surface determined by z = f(x,y) in a direction which
is neither parallel with the xz- nor the yz-coordinate plane.
