Calculus is needed to understand, like, basic sophomore and junior year engineering stuff. You can maybe pass the tests without understanding where the models came from if your professors are just really lazy and only give you canned problems, but that isn’t a goal we should strive for.

And engineers should usually be using battle-tested models rather than coming up with their own derivations, so to some extent using the calculus day-to-day shouldn’t be necessary in many cases. But it is necessary in order to understand where the models came from. This is what separates engineers from tech-priests.

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a while backtracking to find where they lost track of the concrete rules, and then we could work our way forward to catch up to their intuition. Practical results are good guideposts but don’t replace full understanding I think.

That’s just my perspective, though, I have a pretty simplistic, algebraic way of looking at math. I could never be a mathematician or see true beauty in math, it is just a bunch of little rules to me.

IMO calculus class is fundamentally just relatively abstract compared to the stuff before it. But once you’ve finished it, your engineering and science classes should be full of practical, reinforcing applications, right?

Isn't the actual calculations of e.g. integrals the least useful part of calculus for non-stem students? Instead the basic concepts are where the easily accessible value lies.

Teaching tricks without teaching the concepts not only fails in the way you describe (it prevents building ideas further). It also fails to teach anything useful at all. Because barely anyone outside of STEM wil ever have to solve any kind of integral or derivative in their life.

The valuable part of calculus to me was understanding the concepts of limits, differentiation, integration, and a tiny bit of differential equations.

Learning how to actually solve integrals or differential equations was useless other than it teaching me more about calculus and how it is useful. For calculations in practice I will turn to wolfram alpha, but it has some value to understand what wolfram alpha is doing under the hood.

I think a calculus course whose tests defocusses calculations might be very valuable for practically minded people. Knowing to think about derivatives is much more useful in practice than actually being able to calculate a derivative.

How you can use R without knowing calculus? Why would you even turn to R if you didn’t have a calculus problem to solve?

You don't use calc much when you use R, unless you're working on a problem that involves calculus, which isn't many problems, usually?

R is usually used to do data stuffs in my experience. Like, "take in this data from this CSV, and do these manipulations" which may involve math but not often calculus.

I am totally for software assisted math. Math isn’t just pencil on paper, and it isn’t only proof, and it’s great to talk about over beers.

using those "data stuffs" are usually based on calculus. Statistics and probability are both defined in terms of calculus.

calculus is the most basic of mathematical machinery, that it is essentially a requirement to do anything else.

You're kind of arguing that you can't walk without studying kinematics.

im not though. I don't think you need to know measure theory and understand how to formalize probability in terms of sigma algebras to do professional stats.

But I would be very skeptical of a professional data scientist that doesn't understand things like derivative, integral, limit on an intuitive level. I don't know how you would understand distributions without that knowledge

R is not exclusive to professional data scientists.

Sure thing, you may be calling a function that does some regression or something, but you aren't "doing calculus" when you are programming that in R.

Are probability and statistics really practically based on calculus? Most math curriculums do not have a calculus requirement to take statistics.

for actual understanding, yes it is. The most basic important results, the law of large numbers, and the central limit theorem both require calculus to understand.

if you make a class without calculus, it is essentially just a bag of tricks and surface level understanding

rho(x) is the probability density function, and it better sum up to 1 for all possible values of x.

One time I asked an engineer if he used calculus and he said no, so it must not be useful.

It depends on what the definition of 'using calculus' is, as well. I use the concepts of integration and differentiation all the time in my work: it's completely integral (hah) to a good chunk of what I do (as well as complex numbers, fourier transforms, and a bunch of other 'advanced' maths). What I don't do is grind through working out the analytic solutions to odd integrals or differentials. Firstly because it's rarely useful, and secondly because I have a machine to do that for me in the cases that it is. I think it's unfortunately common to have the attitude that the latter is the majority of what calculus actually is in practice, because it makes up a lot of calculus education, but it's not the case.

R is a calculus. In fact all programming is reducible to first order predicate calculus. The Leibniz rule is pretty cool.

As an engineer calculus is pretty fundamental to my job. It underpins all sorts of stuff - Heat transfer, fluid flow, stress and strain rates, beam deflection, fracture mechanics etc.

I may not be solving differential equations by hand but I'm using knowledge about calculus everytime I reason about our industrial process.

The excel part is probably referring to solvers - where you plug in boundary conditions and spits out a solution. Edit - and excel or R (or Matlab) is what you use in lieu of needing to solve this stuff by hand.

If that were the case, I’d be extremely wary of their scientific output.

What did they do with Excel and R?

As a chemical engineering student, it's a whole lot of formulas cobbled together to spit out calculations that would otherwise be done on hand (especially empirical methods that compute estimates where a clean answer is not possible like $\int{\frac{\sin{x}}{x}}$).

The formulas usually come from what you study in school (e.g. the Redlich-Kwong equation in Physical Chemistry to estimate the properties of real/non-ideal gases).

What's neat is that before computers were popular in the early 20th century, these calculations (mostly empirical equations' iterations) had to be done by hand by engineers. So yeah... you can imagine how tedious it was (especially when you have tiny errors due to humans compounding) yet they were still able to build complex things (like factories!).

Engineers didn’t do those calculations by hand. They were done by “computers” who were mostly youngish women with slide rules.

all those formulas were derived using calculus...