I think my point is that the history of mathematics is exponentially more interesting than mathematics. We like mathematics, but we like stories far more than we like whatever mathematics is.
Mythology > MathematicsWas not my question. Nearly everyone uses computers. Computers would not be possible without electronics. How many computer users work with Maxwell's Equations or have even heard of Kirchhoff's circuit laws? A very tiny percentage, undoubtedly.
The reason I asked was the Penn State professor's epiphany that no engineer among the many he asked actually used calculus.
I don't have learn sorting algorithms, I just use list.sort or sorted.
In my experience, almost everyone out of college who I've met who claims to know calculus.
As to your question I've touched on a little for manipulation of some of the classic equations in ecology and population biology, growth curves, population growth, etc. Barely needed to crack an introductory textbook to do it though. Had I learned real calculus and maybe differential equations there is some really interesting modelling I'd be able to do in this space, but instead I'm stuck seeing the diffuse shadow of the idea on the wall of Plato's cave. That's not a wistful lament though because to your point, time spent boning up on linear algebra instead of calculus would provide at least an order of magnitude more utility for my work.
That was not my point. No one learns math because of historical fascination. The point was simply the stories about the math are more interesting than the math itself, which isn't any stretch of the imagination.
Imo, history of mathematics is not interesting unless you are interested in mathematics itself too. It is sort of stuff that some people good in math and interested in care about, but is otherwise completely uninteresting for anybody else.
Unless you turn it into history tabloid. Which you can do in pretty much any field, but also it will loose any meaning. At that point, you can do paris Hilton or Kayne West.
When I want to write or tune a Kalman filter or some other control system, I need to work out the differential equations that govern a system, often from first principles if the system isn't a simple textbook example like an inverted pendulum. Sometimes I need to design that system myself or find out what change to its dynamics will fix a noise problem (eg. add a capacitor here, etc), and without an understanding of calculus I would be searching in the dark or stuck trying to look up known solutions in textbooks.
It also comes up a lot when I want to do probability or statistical calculations, because I end up needing to integrate various functions or products of functions to find means / medians / covariances / etc. Sometimes I can get away with leaning on Mathematica to do those integrals for me, but sometimes I can't, like when one of those functions is an arbitrary input like f(x). Even when I can use Mathematica to perform the integral, I need to know calculus for that to be any clearer than a magic spell. Without knowing calculus, how would I ever guess that I can solve my problem by typing "ln(x0-a)/arctan(x + a)" into wolfram alpha and then plotting the result?
Recently I had the need to do work backwards: find the function that satisfies certain properties like - being smooth and monotonic, zero at the origin, having a certain area within certain bounds, having a certain covariance, nowhere going to infinity, etc. This sounds very abstract but was the key to cracking a concrete signal processing problem.
And then there's all the optimization work, where I need to write numerical code that will look for the maxima or minima of some unknown function, to eg. design the best possible motor you can pack into a box of certain size and weight. 3rd-party libraries are certainly helpful but I usually find I need to supplement them with domain logic to keep it from getting stuck in a local optimum or rule out physically impossible search spaces.
A few months ago I needed to write a finite-element solver to handle soft, thin woven fabrics, where the material can support tension but not compression stresses and the material properties are different depending on the axis of the weave. I would have been at a total loss to get that done without calculus.
Even when I am pulling something out of a textbook, most engineering textbooks past the first-year-undergraduate level will presume some familiarity with calculus.
Not to mention properly thinking about current issues like inflation, CO2 emissions, etc, where the discussion bounces back and forth between integral and derivative quantities.
I'm not even a "math guy". I didn't do well in math in school, and I always struggle a lot to learn new math until I have an application in mind that I need it for. It's only because of how often I need it for my projects that I've ended up learning a lot of math, not the other way around.