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.