2 ms·
I had self-studied this and then later studied under a teacher as well. I think the thing that I found hardest in my self-study was (and unfortunately this is
by kenjackson 8y ago
I had self-studied this and then later studied under a teacher as well.
I think the thing that I found hardest in my self-study was (and unfortunately this is about 25 years ago so my recollection might be a bit off) that it seemed like there was a lot written on just two equations (the heat equation and the wave equation). I didn't get why is 50 pages dedicated to one equation. Up until that point it felt like Calculus was about techniques to solve equations, and then it suddenly became mostly about how to solve these two equations (there was a third, but I can't recall what it was now), which never really resonated with me.
- sampo 8y agoHeat equation / diffusion equation (same thing): parabolic. Wave equation: hyperbolic. Laplace's equation: elliptic. Laplace's equation is the steady state (equilibrium) solution of heat equation when the boundary conditions (or anything) don't change in time.
- kenjackson 8y agoThanks. And yes, Laplace was the third one. I think even your simple categorization would have made things much simpler for me. Or maybe I was just an idiot as an undergrad. :-)