Sometimes I wonder if the usefulness of calculus is overstated compared to other areas of math. Linear algebra & discrete math pop up a lot more than integrals in CS.
I loved my real & complex analysis courses but my courses on linear algebra, abstract algebra, & discrete math have been much more useful.
I can understand and essentially agree
with everything you said except your
first sentence, and I'm not sure the
rest of what you said does much to
support your first sentence!
One point is, CS isn't the only area for
applications!
E.g., in the software for my startup,
sure, I have some matrix theory,
right there in the code, but it turns
out the matrix theory is what is left
for the actual code after some
earlier derivations very much in
calculus!
When I was a prof in a B-school and
teaching linear programming, right,
awash in linear algebra, I mentioned
to my students, all of whom had had
the required courses in calculus,
that I regarded it as a "pillar of
Western Civilization". I still do.
Without Newton's second law, Maxwell's
equations, etc., I strongly suspect
that Western Civilization would be a
very different and much less good
place.
E.g., my father in law eventually
slowed down his farming and got a
job in town. He was head of the
REMC -- Rural Electric Membership
Cooperative. So, it was the local
electric utility. They handled
only the last few miles and bought
their electric power from the grid,
really from one private power company.
Some of his customers were factories,
and at one point he asked me why his
engineers put large capacitors outside
some of the factories. Well, I'd been
a ugrad math major but, except for
one course I wanted instead of another
that would have been required, also
a physics major, and had done well in
ordinary differential equations, so
had see the differential equations of
basic passive AC circuit theory, that is,
with resistors, capacitors, and inductors.
So, sure, the factories had a lot of
big electric motors with a lot of
inductance. So, the utility pushed
current to the motors but half
a cycle later the motor pulled more
current. So, net, the utility was
moving a lot more electrons than
necessary to deliver the power it
was getting paid for and, thus, was
getting more power losses in its
lines. So, put a capacitor just
outside the plant, and then the
plant looks like a pure resistor
to the electric company and all the
extra electron moving is just between
the motors and the capacitor
just outside the plant. Ah,
applied calculus!
There are many more such examples;
the examples say that calculus
is really important but don't
really settle your question about
"overstated"; for that question,
I don't know what to say!
I loved my real & complex analysis courses but my courses on linear algebra, abstract algebra, & discrete math have been much more useful.