2 ms·

I found that statement interesting too, specifically because our math courses had us re-derive a PILE of stuff, and I felt much more enlightened after having do

I found that statement interesting too, specifically because our math courses had us re-derive a PILE of stuff, and I felt much more enlightened after having done that. Summation, for instance, was derived early on. Same with integration (Fundamental Theorem of Calculus). One of my most memorable re-derivations was in my 4th calculus class (Sequences, Series, and Differential Equations, if I recall). We ended up taking the Taylor series approximation of sin(x), cos(x), and e^x. As the patterns started to emerge, the professor encouraged us to look at them carefully and start considering what happened when you substituted ix into the approximation for e^x. This ends up, of course, turning into Euler's formula, e^ix = cos(x) + isin(x). Seeing it with the Taylor series approximations, though, snapped all the pieces together. Up until then, it all seemed like magic (sure, you can talk about vectors and imaginary numbers, but you're just accepting it as true). That derivation fundamentally changed how I look at this stuff.

tonyarkles 15y ago
More on this topic :) Another really fascinating thing for me was first year "Intro to Electricity". That course was relatively formula based; for example, the voltage across a capacitor is given by Vcap = V0 * (1 - e^(-t/tau)). I had a hell of a time remembering that formula, and suffered for it. In second year, we started getting more in depth and had a few more tools at our disposal (e.g. the Laplace transform, Integration, light Differential Equations, etc). At that point, the formulas i = C dv/dt and v = L di/dt became fully engrained in my head. We took those, and derived the equations we'd been using in first year. From that point on, I solved every passive circuit using precisely these first principles, and would consistently get the correct answer faster than many of my classmates who were trying to remember big specific formulas. If I needed it for some reason, I could quickly do the integral for a specific circuit to get the closed-form voltages.

tonyarkles 15y ago

More on this topic :) Another really fascinating thing for me was first year "Intro to Electricity". That course was relatively formula based; for example, the voltage across a capacitor is given by Vcap = V0 * (1 - e^(-t/tau)). I had a hell of a time remembering that formula, and suffered for it. In second year, we started getting more in depth and had a few more tools at our disposal (e.g. the Laplace transform, Integration, light Differential Equations, etc). At that point, the formulas i = C dv/dt and v = L di/dt became fully engrained in my head. We took those, and derived the equations we'd been using in first year. From that point on, I solved every passive circuit using precisely these first principles, and would consistently get the correct answer faster than many of my classmates who were trying to remember big specific formulas. If I needed it for some reason, I could quickly do the integral for a specific circuit to get the closed-form voltages.