>The central method for coming up with force laws and field equations is to
extremize the action integral usually defined in terms of a
Langrangian function. For this you need a form of calculus for solving extremal
problems in functionals. This is the so-called calculus of
variations. You can't do physics without it, or something mathematically
C'mon Bob. English. Unless, that is, you are simply trying to impress.
"QDurham" <[Only registered users see links. ]> wrote in message
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It's easier to think that a calculus of variations is necessary to solve
Newton's a = (vt-vi)/t and g; than it is to solve Galileo's g = 2s/tē =
"Donald G. Shead" <[Only registered users see links. ]> wrote in message
news:5kvTa.11960$[Only registered users see links. ].pro digy.com...
Donald, you might be disappointed to learn that the tools you used to build
bridges were developed from calculus. For example if I apply a bending
moment on an "I" beam, you have an equation that will predict the stress and
strain. That equation was developed with calculus.
"Danny Deger" <[Only registered users see links. ]> wrote in message
news:bfug4c$iu8rl$[Only registered users see links. ].uni-berlin.de...
Danny m'boy: You might get somebody to believe that line; but I know better:
Even back in the days when I used to joke that "6 munts ago I couldn't even
spell "ingineer", and now I are one" I knew better: That the calculus was a
crock; used by professional engineers only to impress other scientists that
their professional status was [almost] on a par with theirs.
For the first few years those of us who hadn't made the grade yet, studied
and carried little shirt pocket manuals that contained all the essentials
needed: They had all the _simple beam_ formulas for designing with concrete
and steel; as well as tables and mathematical formulas: They even had
diagrams of finite elements showing how they led to the calculus.
That was learning engineering from the 'grass roots'; with a little help
from the sliderule: I remember the instructions that came with my first
sliderule predicted that learning the proper use of it would be the most
important thing that I'd ever learn: Which it WAS! Limited of course to
three significant figures which is "close enough for bridge work".
Then of course we soon had access to main-frame computers where virtually
all aspects of design could be carried out by anyone with an optimum
knowledge of design and construction; just by filling in essential data.
I was (among) the first to realize that electronic calculators were a boon
to engineering; especially in that they could take the drudgery and tendency
to err out of it: In particular, programmable calculators could iterate
quickly, and store many program steps; which eliminated such errors; to the
With my TI 59 card programmable calculator I soon had readily available
programs for virtually all of the basic formulas in most of the manuals used
by "Highway Senior Engineers (Bridge Design)"; of my ilk. I could do _some_
things with these, quicker and better than they could.
Since I've retired I've been told that the pound is [legally] a unit of
mass, and of course you know I don't swallow that any better than I do your
claim about formulas being derived with the calculus.
Don't go away mad Dan; I'm not(:-) We'll both survive learning that the
measure of mass is inertia, and the calculus is just a sophisticated way of
plotting the infinitesimal coordinates of infinitesimal ratios; that
represent changing rates; of changes in motion.