[hprotagonist]

my linear algebra professor began his first lecture with a 5 minute rant informally titled “how you could have gotten an A in differential equations last semester without ever having taken calculus”

That certainly got our attention. I’ve always found linear algebra to be kind of ... almost soothing.

[eximius]

That's a rant I'd like to hear.

[hprotagonist]

"look guys, at end of class, exam is always long list of silly second order system of differential equations.

Well, every time, we can make so-called "guess" that solution looks like e*rt. Why? We know that because professors will only give well-behaved systems on final exams because it's hard to grade the other kind.

So we know characteristic polynomials look like so (because of course they do, you can just memorize this) ... so now we lift out the coefficients into nifty thing called _matrix_ and now follow these easy four steps to get roots, plug back in, and incidentally these are "eigenvalues", we'll talk about this later ...

Bam. Done. A-, easy. No sweat."

[eximius]

Minus the matrix bits, that's basically how I slogged through DiffEq. Showing up to class was pointless because the prof would make up an equation to exploratively solve and inevitably it would be poorly behaved and the lecture would end with "... And and and for this kind of problem we have to use numerical methods".