i mean even basic differentiation is useful for optimization problems.

datsci_est_2015 a day ago | parent | next [-]

Not to mention physics, which is useful for understanding why things are the way they are. Which, is an important skill lest you fall into anti intellectual traps like flat earthism.

Calculus is a shared language in the grand universal ocean of intellectual cultural. Rejecting calculus is rejecting part of that culture…

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1-more a day ago | parent | next [-]

Yeah, for me the real click was in AP Physics where we derived an equation for some motion property rather than just being handed the formula as I had been in, say, 8th grade science. The meta lesson is that you can use math to get more information out of a model than you think you have, which, yeah, keeps you from becoming a 5G get the facts style individual.

	▲	wombatpm a day ago \| parent [-]
		I loved learning about jerk, snap, crackle, and pop as higher-order derivatives of position wrt time in physics.

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NetMageSCW a day ago | parent | prev [-]

I’m not sure there’s enough overlap between physics and calculus to justify calculus. That might mean you can’t derive physical equations yourself, but no one needs that who isn’t becoming a physicist.

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ndriscoll a day ago | parent | next [-]

F=ma is slightly important for physics, no? And deriving the equations is kind of the point; it's the understanding of "why" something is true.

e.g. I can tell you things act like a spring near (stable) equilibrium, and you can believe me, but why on Earth would that be true? Well, Taylor expand the potential at equilibrium. Define V(0)=0, and equilibrium means V'(0)=0, so V(x) ~ V''(0)/2 x^2, so F = -dV/dx = -V''(0)x, which is a spring with spring constant k=V''(0).

That's all a very conceptual explanation; the point is near an equilibrium, zoom in and you have a parabolic potential! What is the potential for a spring? A parabola! This is basic Calc BC stuff, but it also justifies why we might care about about simple harmonic motion. Calculus is the whole business of "zooming in."

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Animats a day ago | parent | prev | next [-]

> I’m not sure there’s enough overlap between physics and calculus to justify calculus.

You need calculus to design a windmill or an auto engine or an electric motor beyond the "just sort of works" level. Most of analog electrical engineering is defined by calculus. Althogh, yes, you can get LTSPICE to do most of that for you.

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InitialLastName 13 hours ago | parent | next [-]

You can get LTSPICE to do the simulation for you, but it will be much harder to understand why an interesting circuit works (such that you can adjust it or implement it with real components) without understanding some of the calculus behind the simulation.

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Novosell 16 hours ago | parent | prev [-]

Windmills are older than calculus, so that's just not true.

	▲	Animats 8 hours ago \| parent [-]
		Inefficient windmills are older than calculus. Efficient windmills need aerodynamic theory to calculate a good blade design. It's quite difficult to do that. It took several decades to scale up windmills. (A small wind turbine is like a propeller in reverse. A large wind turbine is not, because wind speed varies across the blade circle enough that those stresses dominate the design. It took decades to debug this, and make large wind turbines stable under high winds.)

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tarpitt a day ago | parent | prev [-]

I mean one example is like a dampened spring system or RLC circuits or something. You can simplify a lot of systems down to those types of simple physics systems you learn about in class.

A lot of it I think is just training people to adopt a "physics-like" or "math-like" way of thinking and giving them a general overview of how things work.

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1-more a day ago | parent | prev [-]

I think their answer would be "why would I care how long it takes this ladder to slide down the wall?" Which STINKS don't get me wrong. This is not a group I take seriously.

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tarpitt a day ago | parent [-]

Here is an example of a practical optimization problem:

A factory needs to produce 12,000 components per year. Each production run costs $300 to set up, and storing one component costs $4 per year. What production quantity Q minimizes the annual setup and storage costs?

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BoxwoodSeed 12 hours ago | parent | next [-]

Just like all school problems of this nature I have ever seen, the question lacks precision.

How long does a production run take and how many units can you do in a single sun? Since this isn't mentioned, the answer is to produce everything at the last second of the year. But we are also missing information on why the factory needs to produce 12,000 components in a year and for whom and about the logistics involved in getting those components to the buyer.

I always hated these type of questions for their lack of precision. You haven't even mentioned how many units in a single production run will be faulty and need to be scrapped instead of delivered, how am I supposed to optimize anything?!

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normie3000 a day ago | parent | prev [-]

Can you do a single run on the last day of the year?

	▲	gshubert17 3 hours ago \| parent [-]
		Sure, but to be able to fulfill all the year's orders (expected to total 12,000) a single run would have to be on the first day of the year. Setup cost = 300. Now we have 12,000 components to store. If the orders come in steadily, the last component will be sold on the last day of the year. Average quantity stored over the whole year will be 6,000 components. So storage will cost 24,000. Total cost 24,300. Doing one run each month (quantity = 1,000 a month) would entail setup costs of 3,600. And storage costs of 4 * average storage of 500 components = 2,000. For a total cost of 5,600. All according to the given model, of course, but I think this is the general idea.