Drive Your Calculus Teacher Mad

Drive your calculus teacher mad Of course, we could also use Newton’s equation of motion* F = ma: ml d²θ/dt² = −mgθ (5) which amounts to differentiating (2) with respect to t. Sure, you and I know how to solve differential equations like this. The fly by night physicist, however, prefers the “drive your calculus teacher mad” approach. Write d²θ/dt² out as d/dt dθ/dt and cancel the ds: ℓ/t dθ/dt ~ θ/t² (6) Note that in this respect, Leibniz¹¹ had better notation than Newton. Then (5) becomes, after some more canceling, ml θ/t² ~ mgθ, that is, t² ~ ℓ/g, the correct answer. Your calculus teacher screams. But this sort of fly by night maneuver is basically correct,¹² and in essence amounts to dimensional analysis. When we discuss the expanding universe in chapter VII.3, we will use this approach to great advantage.

A textbook page jokingly presents a deliberately reckless-looking shortcut for solving a pendulum-style differential equation. The “fly by night physicist” cancels differentials and reaches the correct dimensional result, driving a calculus teacher mad while secretly illustrating dimensional analysis. EN: A textbook page jokingly presents a deliberately reckless-looking shortcut for solving a pendulum-style differential equation. The “fly by night physicist” cancels differentials and reaches the correct dimensional result, driving a calculus teacher mad while secretly illustrating dimensional analysis.

• @ithueti / 13114 2024-06-07