Differential Equations: I hate them.

[trancefishy]

Yep. Taking the course now, and out of all my math courses (calc 1-3, matrix theory&linear algebra , abstract algebra I & II, linear programming, and real analysis) I'd have to say that it's the worst. Not because it's difficult, but because it's so boring.

It seems to me, and this probably has a lot to do with my particular class, that the entire thing is set up as a recipe book. You look at the DE, decide what grouping it falls under, and apply repeated mechanical mindless steps to eventually get to a meaningless (and often rather ugly) answer.

I'll conceed that they are useful, but mathematically speaking, especially at the procedural level I'm exposed to at the moment, they are no fun at all.

 

[mathwonk]

read arno'ld's book, which makes them seem rather beautiful and geometric and natural. also martin braun's book which makes them seem fun and fascinating.

 

[trancefishy]

Might do that.

I do see that there is some beauty underlying all of this, but when you're given a DE and told "solve", it is just an ugly process. clever, but ugly.

 

[jf117]

Could I have the exact reference for this "arno'ld's book", please?

J

 

[mathwonk]

the book i have by arnold is titled ordinary differential equations, mit press, copyright 1973, isbn 0-262-51018-9 paperback, and is much cheaper than the newer slightly expanded edition. the older book by witold hurewicz is also excellent but this is more modern and clearer, less technical.

 

[mathwonk]

also my little post here titled trivial solution process is an attempt to introduce some logic and beauty into one case of solving de's, the easiest one. at least if you know some linear algebra, and how to find an inverse from a minimal polynomial it will speak to you.