At home we had an old O-level mathematics (old British system, compulsory at age 16) book lying around. Two things stuck out: A massive amount of material: lots of calculus, matrices, complex numbers, group theory, ... And almost all of it explained extremely badly
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I don't think we did any serious dimensional analysis Most of the course was stamp collecting, learning facts but not quantifying them.... and still somehow being structured so that we didn't have memorise lots of stuff
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I think I first heard the idea in chemistry class (converting between moles and grams and whatnot) but then found it very helpful in checking memorized formulas in high school physics. I've always been impressed by the way that expert fluid mechanicians make use of it...
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solving for steady states on graphs. E.g. computing forces in simple statics problems consisting of rigid free-bodies treated as points or computing currents / voltages in resistor networks. (Of course, these are certainly enriched with knowledge of calculus).
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