What’s really memorable about this past week, for me, was a short collaboration between my alter egos the kid and the undergraduate. The undergrad was struggling with easy stuff – and the kid really, really wanted to get it right.
I had been struggling with circuit theory… specifically with RLC circuits. Yes, I solved them long ago in college – although, in fact, I didn’t actually study elementary differential equations until I was a graduate student. (I hadn’t had them before I transferred to Caltech as a sophomore… where they had been covered freshman year.) I had also never seen Laplace transforms until I was a graduate student. I learned both during the 1st course for which I was a TA.
And here I was, all bollixed up, unable to get what I expected.
On the other hand, I had gotten there after deciding that I needed to solve one of the simplest possible LRC circuits, rather than the more complicated ones to which I was trying to apply a slightly more sophisticated method.
Anyway, I woke up one morning dreaming about it, and determined to forget all the complicated stuff… just solve the second-order differential equation for current… and then solve the equation using Laplace transforms. In fact, I solved the voltage balance rather than the second-order ODE using Laplace transforms – and there is one little tricky detail….
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