Calculus

I dreamt that I was taking an exam involving differential equations. I don't know why I dreamt about differential equations. As far as I know, I've never dreamt about them before, not even when I took calculus, lo these many years ago. I did pretty well at calculus in high school, but it's been—let's practice some subtraction now—17 years since I've had to solve a differential equation, or do any higher math than that required to fill out a 1040A.

What I learned from the dream is this:

I don't know how to solve differential equations. I used to know. I don't know now. I don't even know how to begin.

Also, I wish I did know.

Comments

[Doug]

That's the situation, isn't it?

You know the phenomena you observe are derived, you know that getting to what they are derived from involves integration, and you have the feeling that you once knew how to do it -- or didn't have to do it.

Like loneliness and harmony, I know just where I long to be.

[hilllady]

Doug,
Damn, you're good. Do you moonlight as a dream interpreter?

[Doug]

Well, I've listened to some doozies from my wife while [I'm] in a semi-conscious state, dipping into both worlds.

But this one sounded more like one I would have -- a "here's the situation" dream. So I just cheated and pretended that it means to you what it would mean to me. Convinced myself, anyway.

[Weeble]

At the highest level, you have the strategy down pat already. It's all about guess and check. Differential equations classes often just help you guess intelligently and show you how to identify and verify the specific solution. They use fancy names for the methods like the method of undetermined coefficients. But it's really just guess and check. Guessing and checking gets you only so far. You've got to have the right class of differential equation. Otherwise you need fancier tools or more often a computer.